Let's say you're on the final table bubble with KJ on the cutoff. It folds to you and you have 10 big blinds. In most situations, it should obviously be a shove. But you have a feeling you'll get called with nearly 20% of hands. A range of 77+,A2s+,KTs+,QTs+,JTs,A7o+,K9o+,QJo vs KJo is going to be behind with 42.665% to win. Foretunately, you have fold equity still. If 3 opponents fold 80% of the time each, that's about a .80^3=~51% chance they all fold.
However, on the bubble there are bubble factors you're supposed to adjust for. The chips you lose are supposed to be worth about 1.6 times more than the chips you win because losing chips threatens you being unable to fold up the money and make considerably more.
So when you lose, you aren't losing 10, you're losing 16.
If you get folds 51% of the time and pick up 2.25 (EV of 2.25*.51=1.1475), and you get called and win 12.25 .49*.42665 or expected value of 12.25*.49*.42665=~2.56 and called and lose 16 for EV of -16*.49*.57335=~-4.5, the total sum is 1.15+2.56-4.5=-.79. So the individual result of shoving with KJo is actually losing money. While technically acceptable to shove with some losing hands to force opponent to widen call off range and collectively make more shoving WITH KJo than without it, I think it's a fair assumption that opponents are highly unlikely to adjust very much to you.
Also, opponents probably SHOULD be calling you much tighter than this due to bubble factors themselves, but if you think they probably won't, then shoving becomes incorrect, because their decision to call with hands like A7 and QJ ends up hurting BOTH of you.
A standard "push/fold" chart that doesn't account bubble factors will say to push with
22+ A2s+ A2o+ K6s+ KTo+ Q8s+ QTo+ J8s+ JTo T7s+ 97s+ 87s 76s
But I believe pushing this wide on the bubble is almost certainly a mistake.
Nevertheless, there is a very strange concept with regard to tournaments. If everyone is pushing with wider and calling with wieder, the probability of you being able to continue without having to withstand multiple all ins is low. If you preserve a raise/fold range you can either play very tightly and call off appropriately according to the bubble factors and rarely have an opportunity to steal. This is because the assumption is that "all skill is equal" and thus, all players will play the same way. This isn't the case, so what are the implications? The implications are now that either you have to wait for the best spot you can afford to wait for, or you have to try to play much looser before you have 10BBs.
If tight play forces you to go into this ultra tight blind yourself to death strategy or close to it, it would seem that it's of a huge advantage to eliminate the skill factor of short stacks and put them at the mercy of their cards by raising more widely, particularly in early position than any "chart" might suggest.
There's a reason Phil Helmuth has so many bracelets, so you have to at least entertain some of the ways he plays. When he has 8 big blinds, he will still minraise/fold. That is on much slower structures, mind you, but nevertheless, I think the idea of raise/folding down to 9 big blinds isn't all that bad if
1)You are much more likely to have a monster
2)Opponents are unlikely to really adjust their call range all that much between a minraise and a shove
3)You are close to the final table and thus survival is important, but the difference in chips is not nearly as important as the difference between living to see another hand... A double up will make you so much more likely to final table, and a steal will buy you a lot more hands that will make a difference in how other short stacks are now forced to make a move (and they probably are more likely to move in and bust than you). Consider buying 9 more hands when you win, and pretty much having roughly the sam amount of fold equity if you fold and have 6 big blinds or under 4 if you pay big and small blind and
4)You can raise without having the pot odds adjusted for the bubble factor to call. This is tricky. I tend to have a very polarized range. Either I am getting desperate and will raise with any two from UTG or UTG+1 but will do so infrequently enough that there's a real good chance I have a very strong hand, or I have the very strong hand that I've been waiting for. For example, in 3 rotationsI might try this once with air. If there's 7 opponents that's 21 hands. In 20 hands you have about a 50% chance to get a hand in the TT+, AQs+ range (not including AKo). In 30 hands, JJ+, Aks. Since you're also going to be raising with some hands like 88,99 and widening that range in later position when it folds to you, there's a more likely chance you have a premium hand or strong enough hand to call than a poor hand.
Let's look at the math.There are many different ways to dissect this problem depending on how you view bubble factors and whether or not you want to include your equity from raising preflop. I want to just isolate making the raise from the decision once you are raised.
So your risk is worth 1.6 times more than you gain. You are not risking 6 to win 8+2.25+ your 2 back or risking 6 to win 12.25. Instead you are risking 9.6 to win 12.25. With 1.276 to 1 odds adjusted for bubble factors, you are going to have to be 44% to win. With a hand as bad as 23o, you most certainly are not, so there is an argument to folding. You have to then argue why raise at all? Well, if you only raise about twice every 21 hands with a polarized range of either "any two" or TT+,AKo,AQs+ your opponent is pretty much going to have to all in or fold. So he either risks 8 and is against a very tight range where he is behind, or he picks up 4.25. He is risking 8 (and then some because others could wake up with a hand) to win 4.25. If you adjust his decision for bubble factors, he is risking 12.8 to pick up 4.25. But of course when he shoves and gets called he can still win. So if your opponent gets called 60% of the time that he shoves, being 35% to win when he gets called isn't enough. He needs to be 35.7% vs your range of TT+,AQs+,AKo. If we want to get really accurate, we can say there's a 58.2347% chance that you get dealt TT+,AQs+,AKo+ in 21 hands. If you don't raise in 21 hands you will have to raise with whatever you can come up with. So if you factor that in, he only needs to be 34.25%. I actually think his chances are much worse since you probably will widen range when folded to in later position, so the probability of you not raising within 21 hands is probably much lower.
In theory, he should require the exact same range as you to be able to move in on your raising range, and probably tighter because he has to concern himself with other opponents.
So if there are 6 opponents left to act and they need TT+,AQs+,AKo, what's the chances that you get reraised? In reality it SHOULD be only 22% . Slightly more because opponents that have you covered can call off lighter than you as bubble factors are smaller to them than they are to you if they have you covered in chips.
Raising "any two" vs these opponents should be profitable since 77.9% of the time you pick up 2.25 and 22% you lose 2*1.6 or 3.2. That means you can pick up 1.046 big blinds every 21 hands. Hopefully you get a walk, or find another spot, or also at some point find a spot to get your money in good by opponent that makes a mistake, but losing chips at less than 2 big blinds per rotation on average when you are on the final table bubble is not all that bad. You are losing about .26444 per rotation which means if blinds stay the same, you can survive in this manor an average of 45.37 hands if you have 12 big blinds. Obviously blinds go up and as you become shorter, decisions become more desperate. But even so, everyone else will grow more desperate, and you are still giving yourself a good chance of making the final table and make a lot of money from moving up the money.
You can look at this "hands left" and adjust for the blinds going up by calculating your "burn rate" based upon your strategy at the given level and adjust as you become more desperate. I would say when you move to all in or fold mode to just calculate being on autofold from there.
With 45 hands left or even 35 hands left you can afford to wait for JJ,QQ, KK or AA...
If you can find an equivalent spot where your overall expected value is as good as getting your money in with jacks you should go for it. If it's less, you may have to reconsider even if you have JJ+ if the supernit shoves.
But since there's added value in raising, or having fold equity PLUS being ahead when called, you can widen the range, and adjust for spots. However, what you cannot do is try to justify waiting for any better than this.
Monday, August 17, 2015
Tuesday, August 11, 2015
3Betting Vs a Static Opponent Given Certain Bubble Factors
In poker, aggression is important, but it's also important not to take things too far since you can never get 100% of the prize pool and you are simply helping your opponents make money if you are always too aggressive. Tournaments have bubble factors that should adjust your decisions as we've shown. We've even shown a strategy for unexploitable opening ranges with 20 and 30 big blinds at different bubble factors and vs different 3bet ranges.
But what about your aggression? What about when someone raises 2.2 BBs and you are trying to decide whether or not to jam? How should bubble factors affect your jam range given certain assumptions about your opponents?
Let's say opponent has a "static" or unchanging strategy. He does not adjust at all to bubble factors, and he is predictable in always open raising when it folds to him with 10% of hands regardless of position. He will call 3bet shoves with 99+,AK,AQs (calls with 42.2% of his range). If these assumptions are correct, how often can we Jam vs this player from the button if both the blinds are on autofold?
First we determine how often opponent calls a shove. This is 4.2232/10 since he calls with 4.22% of hands out of 10% or 42.23%. We then run the math assuming we gain 4.5BBs when he folds, and when called we win 22.25BBs when we're called AND win, and lose 20 when we lose. We then multiply that total expected loss by the bubble factor since chips we stand to lose are not equal to the chips we gain. We can adjust until we find the break even point. Based upon these percentages we can find which hands a shove is break even with or better. The real optimal solution may have some flat calls in there, and thus might shove with more premium hands and a small percentage of bluffs and just call with the remainder, but it's not a huge mistake to ignore these and jam or fold.
Jam with:
Bubble Factor of 0.8 jam such that you are 25.74% to win when called:
22+,A2o+,KTo+,QTo+,JTo,A2s+,K2s+,Q2s+,J3s+,T6s+,97s+,86s+,75s+,64s+,53s+
Bubble Factor of 1.0 jam such that you are 32.77% to win when called
TT+,AQo+,AJs+,KJs+,QJs
Bubble Factor 1.2 Jam such that you are 38.58% to win when called
TT+,AKo,AKs
Bubble Factor 1.4 Jam such that you are 43.47% to win when called
JJ+,AKs
Bubble Factor 1.6 Jam such that you are 47.64% to win when called
JJ+
Charted neatly below to eliminate the wording
bubble factor|% to win| hand range:
0.8 25.74% 22+,A2o+,KTo+,QTo+,JTo,A2s+,K2s+,Q2s+,J3s+,T6s+,97s+,86s+,75s+,64s+,53s+
1.0 32.77% TT+,AQo+,AJs+,KJs+,QJs
1.2 38.58% TT+,AKo,AKs
1.4 43.47% JJ+,AKs
1.6 47.64% JJ+
As our opponent folds more than 57.8% of his hands we can push with a lower percentage to win vs whatever calling range he calls off with.
With a larger number of big blinds like 30, you need to Jam with a tighter range of hands since you are giving your opponent a better payout when he calls, and gaining less proportionally to what you lose when you are called and behind.
Obviously a tight player isn't the ideal target to 3bet, but if you have a decent hand you can certainly go for it.
What about other player types? Although I haven't gone through to do the work to define the exact hands, I have came up with the percentages of a few scenarios.
20BB 3 betting over
% to win needed when called if opponent opens with
35% of hands and only calls with 99+,AQ+,AJs,KQs (calls 13% of the time he opens)
bubble factors
0.8 0% any two
1.0 0% any two
1.2 6.55% any two
1.4 13.99% any two
1.6 20.34% any two
30% of hands and only calls with 88+,AJ+,KQ (calls 20.61% of the time he opens)
bubble factors
0.8 0% any two
1.0 6.32% any two
1.2 14.42% any two
1.4 21.23% any two
1.6 27.04%
opens 25% hands and calls with 88+,AJ+,KQ (calls 24.7% of the time he opens)
bubble factors
0.8 any two
1.0 any two
1.2 22.29% any two
1.4 28.47%
1.6 33.75%
Opens 15% of hands and calls with 55+,AT+,KQ (calls 70% of the time he opens)
0.8 36.88%
1.0 42.86%
1.2 47.80%
1.4 51.95%
1.6 55.50%
Opens 20% and calls with 55+,AJ,KQs (calls with 42.2% of the time he opens)
0.8 25.74%
1.0 32.77%
1.2 38.58%
1.4 43.47%
1.6 47.64%
Opens 10% and calls with 99+,AK,AQs (calls with 42.2% of the time he opens)
Jam with
0.8 25.74% 22+,A2o+,KTo+,QTo+,JTo,A2s+,K2s+,Q2s+,J3s+,T6s+,97s+,86s+,75s+,64s+,53s+
1.0 32.77% TT+,AQo+,AJs+,KJs+,QJs
1.2 38.58% TT+,AKo,AKs
1.4 43.47% JJ+,AKs
1.6 47.64% JJ+
It's important to notice that opponents SHOULD call off much tighter as bubble factors increase, but if they don't, you'll have to shove much tighter yourself.
Against an opponent who calls off with the SAME range of hands and raises with the SAME range of hands, you are going to have to tighten up dramatically as bubble factor increases both in your opening range, your call off range and your 3bet range.
However, what tends to happen is opponents might try to exploit by opening just as wide near the bubble, but fold more tightly because they are aware of bubble factors or give too much respect to the 3bet believing that an opponent wouldn't 3bet shove without a huge hand. Or they raise without anticipating the possible reraise and then once it comes they start worrying about the money so they tighten up. So I believe there are certain types of opponents where your range won't change that much, and other types in which it will actually WIDEN because of how they play, but for now until I run the math to prove it, that remains speculation.
What I'm very interested in seeing is if an opponent opens up with say 20% of hands and always assumes a certain 3bet range and actually adjusts his calling off range for the bubble, but not his opening range. Since his calling off range will tigthen up as the bubble factor increases, it becomes correct to raise more, if not for the fact that our bubble factor also increases. There is definitely a point in which WIDENING your 3bet range as you get closer to the bubble is correct to certain opponents, but I will be interested to see how great of an adjustments to call off range opponents have to make for that to be the case.
In the future I hope to work some of those numbers.
But what about your aggression? What about when someone raises 2.2 BBs and you are trying to decide whether or not to jam? How should bubble factors affect your jam range given certain assumptions about your opponents?
Let's say opponent has a "static" or unchanging strategy. He does not adjust at all to bubble factors, and he is predictable in always open raising when it folds to him with 10% of hands regardless of position. He will call 3bet shoves with 99+,AK,AQs (calls with 42.2% of his range). If these assumptions are correct, how often can we Jam vs this player from the button if both the blinds are on autofold?
First we determine how often opponent calls a shove. This is 4.2232/10 since he calls with 4.22% of hands out of 10% or 42.23%. We then run the math assuming we gain 4.5BBs when he folds, and when called we win 22.25BBs when we're called AND win, and lose 20 when we lose. We then multiply that total expected loss by the bubble factor since chips we stand to lose are not equal to the chips we gain. We can adjust until we find the break even point. Based upon these percentages we can find which hands a shove is break even with or better. The real optimal solution may have some flat calls in there, and thus might shove with more premium hands and a small percentage of bluffs and just call with the remainder, but it's not a huge mistake to ignore these and jam or fold.
Jam with:
Bubble Factor of 0.8 jam such that you are 25.74% to win when called:
22+,A2o+,KTo+,QTo+,JTo,A2s+,K2s+,Q2s+,J3s+,T6s+,97s+,86s+,75s+,64s+,53s+
Bubble Factor of 1.0 jam such that you are 32.77% to win when called
TT+,AQo+,AJs+,KJs+,QJs
Bubble Factor 1.2 Jam such that you are 38.58% to win when called
TT+,AKo,AKs
Bubble Factor 1.4 Jam such that you are 43.47% to win when called
JJ+,AKs
Bubble Factor 1.6 Jam such that you are 47.64% to win when called
JJ+
Charted neatly below to eliminate the wording
bubble factor|% to win| hand range:
0.8 25.74% 22+,A2o+,KTo+,QTo+,JTo,A2s+,K2s+,Q2s+,J3s+,T6s+,97s+,86s+,75s+,64s+,53s+
1.0 32.77% TT+,AQo+,AJs+,KJs+,QJs
1.2 38.58% TT+,AKo,AKs
1.4 43.47% JJ+,AKs
1.6 47.64% JJ+
As our opponent folds more than 57.8% of his hands we can push with a lower percentage to win vs whatever calling range he calls off with.
With a larger number of big blinds like 30, you need to Jam with a tighter range of hands since you are giving your opponent a better payout when he calls, and gaining less proportionally to what you lose when you are called and behind.
Obviously a tight player isn't the ideal target to 3bet, but if you have a decent hand you can certainly go for it.
What about other player types? Although I haven't gone through to do the work to define the exact hands, I have came up with the percentages of a few scenarios.
20BB 3 betting over
% to win needed when called if opponent opens with
35% of hands and only calls with 99+,AQ+,AJs,KQs (calls 13% of the time he opens)
bubble factors
0.8 0% any two
1.0 0% any two
1.2 6.55% any two
1.4 13.99% any two
1.6 20.34% any two
30% of hands and only calls with 88+,AJ+,KQ (calls 20.61% of the time he opens)
bubble factors
0.8 0% any two
1.0 6.32% any two
1.2 14.42% any two
1.4 21.23% any two
1.6 27.04%
opens 25% hands and calls with 88+,AJ+,KQ (calls 24.7% of the time he opens)
bubble factors
0.8 any two
1.0 any two
1.2 22.29% any two
1.4 28.47%
1.6 33.75%
Opens 15% of hands and calls with 55+,AT+,KQ (calls 70% of the time he opens)
0.8 36.88%
1.0 42.86%
1.2 47.80%
1.4 51.95%
1.6 55.50%
Opens 20% and calls with 55+,AJ,KQs (calls with 42.2% of the time he opens)
0.8 25.74%
1.0 32.77%
1.2 38.58%
1.4 43.47%
1.6 47.64%
Opens 10% and calls with 99+,AK,AQs (calls with 42.2% of the time he opens)
Jam with
0.8 25.74% 22+,A2o+,KTo+,QTo+,JTo,A2s+,K2s+,Q2s+,J3s+,T6s+,97s+,86s+,75s+,64s+,53s+
1.0 32.77% TT+,AQo+,AJs+,KJs+,QJs
1.2 38.58% TT+,AKo,AKs
1.4 43.47% JJ+,AKs
1.6 47.64% JJ+
It's important to notice that opponents SHOULD call off much tighter as bubble factors increase, but if they don't, you'll have to shove much tighter yourself.
Against an opponent who calls off with the SAME range of hands and raises with the SAME range of hands, you are going to have to tighten up dramatically as bubble factor increases both in your opening range, your call off range and your 3bet range.
However, what tends to happen is opponents might try to exploit by opening just as wide near the bubble, but fold more tightly because they are aware of bubble factors or give too much respect to the 3bet believing that an opponent wouldn't 3bet shove without a huge hand. Or they raise without anticipating the possible reraise and then once it comes they start worrying about the money so they tighten up. So I believe there are certain types of opponents where your range won't change that much, and other types in which it will actually WIDEN because of how they play, but for now until I run the math to prove it, that remains speculation.
What I'm very interested in seeing is if an opponent opens up with say 20% of hands and always assumes a certain 3bet range and actually adjusts his calling off range for the bubble, but not his opening range. Since his calling off range will tigthen up as the bubble factor increases, it becomes correct to raise more, if not for the fact that our bubble factor also increases. There is definitely a point in which WIDENING your 3bet range as you get closer to the bubble is correct to certain opponents, but I will be interested to see how great of an adjustments to call off range opponents have to make for that to be the case.
In the future I hope to work some of those numbers.
Monday, August 10, 2015
How To Avoid All Ins To Crush the Early and Middle Stages Of a Tournament
Summary:
Given our assumptions on blind structure and hands per hour, with 40% chips coming from preflop raises plus postflop action, 40% of chips coming from 3bets plus postflop action, and remaining 20% of chips coming from: blind defends, dead money grabs, squeeze plays, blind defends, walks, flat calls, etc. we can theoretically sustain our chipstack for an entire tournament without ever being all in with a preflop raise on 16.16% of hands dealt and a 3bet on 6.5% of hands. Variance and the assumptions not always being consistent with reality will force us to call off most tournaments in reality, but it's a good starting point to understand the value of applying consistent pressure.
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The interesting aspect of tournaments, is that if you have a high enough win rate at low enough variance, you can in theory avoid ever being all in. At a minimum, if you maintain a pretty high winrate at relatively low variance, you can at least prolong the all in for a considerable amount of time... This can result in an enormous boost to your chances of doing well in a tournament. It's not uncommon for me to triple up my starting stack before I'm all in, and at slower structures I could probably go much longer, but I have a tendency to make a very infrequent mistakes that are very, very large in magnitude, as it can be difficult for me to focus for more than 5 hours.
In a few tournaments I have analyzed, you can avoid an all in if you can steal 3 blinds AND antes successfully per rotation. You can get very close with 2 steals and in slower structures, 2 steals may be enough if the speed of play is fast enough (around 80-120 hands per hour rather than 60-80).
If good hands are such a liability, why not just fold if the pot gets too big? Because as much as you'd love to get through an entire tournament without ever being all in, eventually you will. Plus if you don't occasionally show them a big hand your raises may not get as much respect after awhile.
Certainly an average gain equal to 2 steals per rotation plus a few good hands and the very occasional spot where you have a premium hand AND an opportunity to double up is usually enough to have a great ROI. You can still dramatically reduce your chances of elimination, which will translate into a huge win percentage.
Requiring 2 steals per rotation does not mean you should raise 2 times per rotation because your attempts aren't 100% successful. So how many blind steals should you attempt? That really depends on the probability of success.
If you successfully get everyone to fold 80% of the time, expected value of 4.5 big blinds requires that you steal 2.8846 times per rotation or raising about 32% of the time total.
If you get through 70% of the time you need to come up with a steal attempt 46% of the time, and if it works 60% of the time, you need to come up with a steal attempt a whopping 80.65% of the time.
But hold on, This is assuming that your failed steal atempts always lose. If you are called, you will be forced to muck and never flop a good enough hand to stay, and if you are raised, you will never have a good enough hand to stay.
However, I would say that if you KNEW for a fact that you could steal the blinds his frequently, you probably SHOULD never play a big pot, because you can win without conflict. Why take a 30% chance of elimination if you literally never need to. But you never will have that knowledge with certainty, so even if you are 80% confident, you still must have some threshold since there is a chance you are overconfident, and there is still the 20% of the time that you factored in that things won't go your way.
Obviously if opponents recognized this strategy, they'd reraise more actively, your success would decline and it wouldn't be worth folding, and most importantly, you never KNOW that the conditions will remain. In fact, they probably won't... As such, the idea that you can play that perfect tournament 100% of the time and never be all in is probably nothing more than a deluded fantasy. Nevertheless, it's one in which we still should determine correct play IF it were true, so we can adjust from there.
Often times you may get knocked out after getting short and forced to take a less premium hand and regret not calling off with the premium hand earlier. That doesn't mean you shouldn't be aware of the strategy and try to adjust strategically based upon how close or far away from reality you think this is.
It certainly is a worthy calculation to determine how frequently you need to come up with chips to avoid all ins. Since you are all ins, accepting a lower win rate is perfectly acceptable, but not too much lower.
So you certainly should plan on having some threshold where you will fight back if you flop good enough, you certainly will see some rivers, and you certainly will pick up aces and it will be worth playing to a reraise...
One side of the argument is that you will be 3bet, you will be called and faced with calls more often, and opponents will raise ahead of you enough that you couldn't possibly steal that many blinds if you raised when folded to 100% of the time. The other side is that when called or raised, you have more equity than is calculated. You can still maintain relatively low varience chip accumulation with high percentage Cbets, occasional 4bets when facing 3bets, occasionally calling 3bets, occasionally 3betting yourself (plus a Cbet), and occasionally you will see showdowns and have a chance to win, plus implications of the turn and river.
So let's imagine instead you are called 80% of the time instead of 20%, but your Cbet succeeds 50% of the time. Let's imagine there is no raising by your opponent, and that when your Cbet fails you still have 25% equity in the hand. Let's also assume that if your Cbet is called that the turn and river are always checked.
In this scenario, you need to come up with a steal ATTEMPT plus a Cbet attempt about 40.4% of all hands dealt to be able to sustain your umber of big blinds in the ante stages.
But what if only 40% of your chips came from steal+Cbets and another 40% came from 3bets and 20% came from a mixture of walks, flat calling in position and big and small blind defenses and maybe a few turn and river takedowns and showdown wins? That certainly would require us to steal less often.
So let's first try to factor in your 3bets. In a 3bet you are going to be risking 2.5 times the standard raise of we'll say 2.25xBBs for a total of 5.625BBs to win 4.5xBBs when opponent folds. The intention is not to always get a fold, but set up a profitable Cbet in an inflated pot and taking a pot where you have position throughout the hand.
So we will assume your 3bet works more effectively and that you do this with fewer hands, and as such your Cbet is more effective. We will say that you win the hand 25% of the time when your Cbet fials still. If you were to only 3bet/Cbet because table never folds to you, you only need to succeed 16.22% of the time. But there's a HUGE caveat in that you are personally putting over 12 big blinds into the play when you Cbet and in reality probably more. The strategy can no longer REALLY be said to be all that low varience, so there is a definate tradeoff that occurs. Nevertheless, a preflop raise plus a Cbet risks as much as 5.6 big blinds. So if you have 30 big blinds that's still 18.67% of your stack.
The equivalent of risking potentially 18.67% of your stack means that if you 3bet/Cbet at 66 big blinds, it is about the same as a raise+Cbet is at 30 big blinds. At 20 big blinds a PFR+Cbet is about the same as a 3bet/Cbet is at 44 big blinds. Since the 3bet can be done less frequently with a stronger hand and is thus more successful and has with it a slightly bigger edge, in terms of risk/reward you can actually say that it's more preferable to make. As such, it may be about the same risk/reward profile at 30-50 big blinds as a PFR/Cbet is at 20-30BBs.
Since the result of not accumulating chips early on in the ante stages will inevitably result in fewer chips which will force you to raise more liberally anyways, it may make sense to 3bet in the 30-50BBs range before you are forced into a position to take on that amount of risk, and potentially more. You never know if your opponents will fold to you often enough to keep up with big blinds.
So if we get 40% of the 4.5 per rotation we need from PFR+Cbets, 40% from 3bets and 20% from "other", how frequently should we make each play?
Well, we need 1.8 per rotation from each since 40% of 4.5 is 1.8. Based upon some assumptions we made, the EV per PFR is 1.2375, the EV per 3bet/Cbet is 3.0825 per attempt.
1.8/1.2375 means that we need 1.4545 times more than the preflop raise gets per rotation. Or 1.4545 raises per 9 hands or 1.4545/9=~16.16% of hands dealt should be raises. 1.8/3.0825=.583942 means we need only ~58.4% of the EV we get from a steal or we can 3bet 58.4% of all rotations or about .583942/9=~.06488% of all hands dealt should be 3bets.
Since not every hand we get will both be strong enough to 3bet AND not be 4bet before it gets to us we should be willing to raise more than 6.9% of all hands on average, and we should adjust this based upon the position and hand range of the initial raiser. An early position raise indicates more strength, late position raise indicates less such that given optimal opponents we should still 3bet a tighter range vs an early position raiser and a looser range vs a late position raiser.
Also, since it will not fold to us every time we have a raising hand that isn't strong enough to 3bet, we need to widen our preflop range and adjust for position as well.
Overall though, coming up with a preflop raise on 16.16% of hands dealt and a 3bet on 6.5% of hands dealt is definitely attainable. Picking up chips from isolation raise+Cbets or dead money grabs after multiple limbpers and blind defends and flat calls in position of course has to also be done enough and profitably to meet the approximate quota as well.
Additionally the success rate and expected value of each move will change, and the varience caused by a 3bet or large isolation raise may make it less desirable to make as frequently as implied.
So in reality you might 3bet far more frequently when you have over 40 big blinds and raise less often, particularly at a more active table and particular as specific spots come up than implied, but you may make up for it later by not 3betting frequently at all around 20-30 big blinds and then once again you may shift when a 3bet is all in and a PFR gives your opponent the perfect shoving stack such that you have to tighten up your range once again.
Additionally, who knows if your raise will succeed 20% of the time or 80% of the time at a given table, and possibly your Cbet will succeed much more often, or much less often than 50%. Certainly it's possible to set up a spreadsheet or more of these calculations to try to get a better picture of individual situations that favor either one or the other, or where the steal attempt is less profitable. It may also be more accurate to adjust the EV as you increase the frequency of hands since our showdown value and table image will be different and the response should be different.
But ultimately this post is just to get you to understand and respect the fact that if you are profitable enough with just the right amount of activity in the right way at a table, you can in theory dramatically reduce your chances of having to be all in. Certainly if you are more active you can accumulate more chips and as such when you finally get it all in your stealing attempts are so profitable that you have everyone outchipped and you can still recover and accumulate until the next all in you have everyone out chipped and so the next all in you can survive until eventually you win one of those. Or you could get it all in a few times and be much more patient and steal much less often.
The more capable you are of maintaining your big blinds or even staying ahead of them, the more willing you can be to make big laydowns in big pots when you know you have the best of it, when you should fold when you have great pot odds because the pot is inflated to the point where you don't need that varience to advance deeply and when you can continue to apply pressure and at times not care about your two cards as much as the situation.
In reality though, there is ALWAYS varience, and even low varience can force you to take on higher varience or play less active in your 3bets+Cbets or less active in the hands you make a preflop raise with.
Are we optimistic?
Accumulating chips at a high rate has to be done to win a tournament. Two steals per rotation is 2/9 hands which is 22/100 and these aren't big blinds but "M". That translates into 33.33bbs/100 before the antes and 50bbs/100 afterwards. Even though people underplaying the ante stages and overvaluing their survival which allows for consistent accumulation, it PROBABLY isn't enough to maintain that win rate over any very long term period of time with low varience...
That doesn't mean that attempting to do so won't frequently produce enough accumulation plus adding in some all ins with an edge that can give you a pretty darn good shot overall at making a deep run and giving yourself a chance to win.
Given our assumptions on blind structure and hands per hour, with 40% chips coming from preflop raises plus postflop action, 40% of chips coming from 3bets plus postflop action, and remaining 20% of chips coming from: blind defends, dead money grabs, squeeze plays, blind defends, walks, flat calls, etc. we can theoretically sustain our chipstack for an entire tournament without ever being all in with a preflop raise on 16.16% of hands dealt and a 3bet on 6.5% of hands. Variance and the assumptions not always being consistent with reality will force us to call off most tournaments in reality, but it's a good starting point to understand the value of applying consistent pressure.
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The interesting aspect of tournaments, is that if you have a high enough win rate at low enough variance, you can in theory avoid ever being all in. At a minimum, if you maintain a pretty high winrate at relatively low variance, you can at least prolong the all in for a considerable amount of time... This can result in an enormous boost to your chances of doing well in a tournament. It's not uncommon for me to triple up my starting stack before I'm all in, and at slower structures I could probably go much longer, but I have a tendency to make a very infrequent mistakes that are very, very large in magnitude, as it can be difficult for me to focus for more than 5 hours.
In a few tournaments I have analyzed, you can avoid an all in if you can steal 3 blinds AND antes successfully per rotation. You can get very close with 2 steals and in slower structures, 2 steals may be enough if the speed of play is fast enough (around 80-120 hands per hour rather than 60-80).
The WSOP And Other Big Events are the Exception, not the rule
You should adapt to structure, but the WSOP main event is obviously the exception to the rule. This level has 2 hours before blinds go up and you start with 300 big blinds and the blinds rise at a rate of about 0.40% per hand on average after the first couple levels of the antes. This tournament is such a slow structure that you can for a very long time till have an enormous chipstack relative to the blinds if you just maintain your chips or even if you lose your chips gradually over time. You may not even need to maintain the number of big blinds to get deep, you can just play a few big hands and get a few decent pots every rare once every so often. If you autofold I estimate that you will see 440 hands before you exit the tournament. If you steal one per rotation to maintain your chips until the antes gets involve, then steal 1.3 times per rotation successfully after you get down to 25 big blinds, you will hover above 20 big blinds for the entire tournament until you win if variance doesn't get you. In a tournament like this, coolers and high variance gets in the way and it's sometimes a liability to have good cards in some ways since it keeps you in the hand in an inflated pot that you would prefer to just take down or fold.If good hands are such a liability, why not just fold if the pot gets too big? Because as much as you'd love to get through an entire tournament without ever being all in, eventually you will. Plus if you don't occasionally show them a big hand your raises may not get as much respect after awhile.
Certainly an average gain equal to 2 steals per rotation plus a few good hands and the very occasional spot where you have a premium hand AND an opportunity to double up is usually enough to have a great ROI. You can still dramatically reduce your chances of elimination, which will translate into a huge win percentage.
Requiring 2 steals per rotation does not mean you should raise 2 times per rotation because your attempts aren't 100% successful. So how many blind steals should you attempt? That really depends on the probability of success.
If you successfully get everyone to fold 80% of the time, expected value of 4.5 big blinds requires that you steal 2.8846 times per rotation or raising about 32% of the time total.
If you get through 70% of the time you need to come up with a steal attempt 46% of the time, and if it works 60% of the time, you need to come up with a steal attempt a whopping 80.65% of the time.
But hold on, This is assuming that your failed steal atempts always lose. If you are called, you will be forced to muck and never flop a good enough hand to stay, and if you are raised, you will never have a good enough hand to stay.
However, I would say that if you KNEW for a fact that you could steal the blinds his frequently, you probably SHOULD never play a big pot, because you can win without conflict. Why take a 30% chance of elimination if you literally never need to. But you never will have that knowledge with certainty, so even if you are 80% confident, you still must have some threshold since there is a chance you are overconfident, and there is still the 20% of the time that you factored in that things won't go your way.
Obviously if opponents recognized this strategy, they'd reraise more actively, your success would decline and it wouldn't be worth folding, and most importantly, you never KNOW that the conditions will remain. In fact, they probably won't... As such, the idea that you can play that perfect tournament 100% of the time and never be all in is probably nothing more than a deluded fantasy. Nevertheless, it's one in which we still should determine correct play IF it were true, so we can adjust from there.
Often times you may get knocked out after getting short and forced to take a less premium hand and regret not calling off with the premium hand earlier. That doesn't mean you shouldn't be aware of the strategy and try to adjust strategically based upon how close or far away from reality you think this is.
It certainly is a worthy calculation to determine how frequently you need to come up with chips to avoid all ins. Since you are all ins, accepting a lower win rate is perfectly acceptable, but not too much lower.
So you certainly should plan on having some threshold where you will fight back if you flop good enough, you certainly will see some rivers, and you certainly will pick up aces and it will be worth playing to a reraise...
One side of the argument is that you will be 3bet, you will be called and faced with calls more often, and opponents will raise ahead of you enough that you couldn't possibly steal that many blinds if you raised when folded to 100% of the time. The other side is that when called or raised, you have more equity than is calculated. You can still maintain relatively low varience chip accumulation with high percentage Cbets, occasional 4bets when facing 3bets, occasionally calling 3bets, occasionally 3betting yourself (plus a Cbet), and occasionally you will see showdowns and have a chance to win, plus implications of the turn and river.
So let's imagine instead you are called 80% of the time instead of 20%, but your Cbet succeeds 50% of the time. Let's imagine there is no raising by your opponent, and that when your Cbet fails you still have 25% equity in the hand. Let's also assume that if your Cbet is called that the turn and river are always checked.
In this scenario, you need to come up with a steal ATTEMPT plus a Cbet attempt about 40.4% of all hands dealt to be able to sustain your umber of big blinds in the ante stages.
But what if only 40% of your chips came from steal+Cbets and another 40% came from 3bets and 20% came from a mixture of walks, flat calling in position and big and small blind defenses and maybe a few turn and river takedowns and showdown wins? That certainly would require us to steal less often.
So let's first try to factor in your 3bets. In a 3bet you are going to be risking 2.5 times the standard raise of we'll say 2.25xBBs for a total of 5.625BBs to win 4.5xBBs when opponent folds. The intention is not to always get a fold, but set up a profitable Cbet in an inflated pot and taking a pot where you have position throughout the hand.
So we will assume your 3bet works more effectively and that you do this with fewer hands, and as such your Cbet is more effective. We will say that you win the hand 25% of the time when your Cbet fials still. If you were to only 3bet/Cbet because table never folds to you, you only need to succeed 16.22% of the time. But there's a HUGE caveat in that you are personally putting over 12 big blinds into the play when you Cbet and in reality probably more. The strategy can no longer REALLY be said to be all that low varience, so there is a definate tradeoff that occurs. Nevertheless, a preflop raise plus a Cbet risks as much as 5.6 big blinds. So if you have 30 big blinds that's still 18.67% of your stack.
The equivalent of risking potentially 18.67% of your stack means that if you 3bet/Cbet at 66 big blinds, it is about the same as a raise+Cbet is at 30 big blinds. At 20 big blinds a PFR+Cbet is about the same as a 3bet/Cbet is at 44 big blinds. Since the 3bet can be done less frequently with a stronger hand and is thus more successful and has with it a slightly bigger edge, in terms of risk/reward you can actually say that it's more preferable to make. As such, it may be about the same risk/reward profile at 30-50 big blinds as a PFR/Cbet is at 20-30BBs.
Since the result of not accumulating chips early on in the ante stages will inevitably result in fewer chips which will force you to raise more liberally anyways, it may make sense to 3bet in the 30-50BBs range before you are forced into a position to take on that amount of risk, and potentially more. You never know if your opponents will fold to you often enough to keep up with big blinds.
So if we get 40% of the 4.5 per rotation we need from PFR+Cbets, 40% from 3bets and 20% from "other", how frequently should we make each play?
Well, we need 1.8 per rotation from each since 40% of 4.5 is 1.8. Based upon some assumptions we made, the EV per PFR is 1.2375, the EV per 3bet/Cbet is 3.0825 per attempt.
1.8/1.2375 means that we need 1.4545 times more than the preflop raise gets per rotation. Or 1.4545 raises per 9 hands or 1.4545/9=~16.16% of hands dealt should be raises. 1.8/3.0825=.583942 means we need only ~58.4% of the EV we get from a steal or we can 3bet 58.4% of all rotations or about .583942/9=~.06488% of all hands dealt should be 3bets.
Since not every hand we get will both be strong enough to 3bet AND not be 4bet before it gets to us we should be willing to raise more than 6.9% of all hands on average, and we should adjust this based upon the position and hand range of the initial raiser. An early position raise indicates more strength, late position raise indicates less such that given optimal opponents we should still 3bet a tighter range vs an early position raiser and a looser range vs a late position raiser.
Also, since it will not fold to us every time we have a raising hand that isn't strong enough to 3bet, we need to widen our preflop range and adjust for position as well.
Overall though, coming up with a preflop raise on 16.16% of hands dealt and a 3bet on 6.5% of hands dealt is definitely attainable. Picking up chips from isolation raise+Cbets or dead money grabs after multiple limbpers and blind defends and flat calls in position of course has to also be done enough and profitably to meet the approximate quota as well.
Additionally the success rate and expected value of each move will change, and the varience caused by a 3bet or large isolation raise may make it less desirable to make as frequently as implied.
So in reality you might 3bet far more frequently when you have over 40 big blinds and raise less often, particularly at a more active table and particular as specific spots come up than implied, but you may make up for it later by not 3betting frequently at all around 20-30 big blinds and then once again you may shift when a 3bet is all in and a PFR gives your opponent the perfect shoving stack such that you have to tighten up your range once again.
Additionally, who knows if your raise will succeed 20% of the time or 80% of the time at a given table, and possibly your Cbet will succeed much more often, or much less often than 50%. Certainly it's possible to set up a spreadsheet or more of these calculations to try to get a better picture of individual situations that favor either one or the other, or where the steal attempt is less profitable. It may also be more accurate to adjust the EV as you increase the frequency of hands since our showdown value and table image will be different and the response should be different.
But ultimately this post is just to get you to understand and respect the fact that if you are profitable enough with just the right amount of activity in the right way at a table, you can in theory dramatically reduce your chances of having to be all in. Certainly if you are more active you can accumulate more chips and as such when you finally get it all in your stealing attempts are so profitable that you have everyone outchipped and you can still recover and accumulate until the next all in you have everyone out chipped and so the next all in you can survive until eventually you win one of those. Or you could get it all in a few times and be much more patient and steal much less often.
The more capable you are of maintaining your big blinds or even staying ahead of them, the more willing you can be to make big laydowns in big pots when you know you have the best of it, when you should fold when you have great pot odds because the pot is inflated to the point where you don't need that varience to advance deeply and when you can continue to apply pressure and at times not care about your two cards as much as the situation.
In reality though, there is ALWAYS varience, and even low varience can force you to take on higher varience or play less active in your 3bets+Cbets or less active in the hands you make a preflop raise with.
Are we optimistic?
Accumulating chips at a high rate has to be done to win a tournament. Two steals per rotation is 2/9 hands which is 22/100 and these aren't big blinds but "M". That translates into 33.33bbs/100 before the antes and 50bbs/100 afterwards. Even though people underplaying the ante stages and overvaluing their survival which allows for consistent accumulation, it PROBABLY isn't enough to maintain that win rate over any very long term period of time with low varience...
That doesn't mean that attempting to do so won't frequently produce enough accumulation plus adding in some all ins with an edge that can give you a pretty darn good shot overall at making a deep run and giving yourself a chance to win.
Saturday, August 8, 2015
Unexploitable Bubble Factor Call off for 20 and 30 big blinds
Based upon the pot odds you are getting when facing a shove for your tournament life, the hands you call off with will depend upon your "bubble factor" in a tournament. Bubble factor is basically the multiple of the pot odds you need to call off your tournament life assuming equal skill and a bunch of other assumption the ICM makes. The ICM usually will calculate an ICM close to 1 near tournament starts and it drops somewhat close to one following the money bubble burst when you are far from the final table. It rises to around 1.6 near money bubble and again just above 1.6 at final table bubble, or closer to 2.0 if the money bubble and final table bubble are the same in a top heavy payout.
Utility theory and opportunity cost theory may attempt to adjust these factors based upon the assumptions of there being skill involved. Both try in their own way to determine how to adjust those bubble factors given the skill.
The Utility Theorists believe the skill you have is proportional to the number of chips you have. A larger number of chips creates higher bubble factors for opponents who face you, and thus more fold equity and a greater probability of accumulating more chips without as great of risk on your tournament life, and greater probability of forcing other people to risk their tournament life.
The opportunity cost theorists believe that players do not respect ICM and thus will knock each other out sooner as well as provide much more "future value" which means survival is more important than expected value. An all in not only risks your tournament life which is more valuable if you do have skill, but that it also costs you the opportunity to see more profitable spots in the future plus all the hands you would have been dealt if you were not eliminated. If you still have plenty of room to accumulate chips, all in becomes unnecessary, particularly since it's possible you may not have to be all in to win a tournament.
Also, as blinds and antes rise proportional to everyone's chips, not only do you stand a better chance of getting called, possibly getting called twice and tripling up.... You also have the additional fold equity from someone raising another player out of the pot and the ability to wait for a dominant hand. Youalso build up a tight image that becomes relevant if/when you win a double up that increases your chances of additional blind steals when blinds are much, much higher than whatever they were when you passed up an edge. It also increases your probability of survival deep, and requires fewer steals or more hands before you have to double up before you can get back to where you were before you started blinding off.
I believe both have some merit. Between 15-30 big blinds there's an argument for taking slightly more risks than the ICM suggest to gain utility and make up for the edge you may give up by stolen pots in the future. There's also the argument for taking some risks vs some good players and loose aggressive players to your immediate left that otherwise might hinder your ability to accumulate chips.
Between 5-25 there's the argument that because of the antes rising, and blinds rising, you can win around 20% more on a blind steal a level later which allows for a tighter strategy to still be profitable, but also that ensuring your survival and increasing the probability of a double up and triple up when you do get that hand.
Because of theses bubble factors dictating a different "call off" range, it should change the opening range if you want to avoid being exploitable to a raise.
So the first step is determining a few guidelines for the "call off" percentages. These can be determined by a formula that relates the pot odds and bubble factors to the win percentages. Once we have these, we can assume that opponents 3bet such that you have a 50% chance of being 3bet by one opponent. We then need to calculate which hands have the equity to call off. When we have the "call off" range we can extrapolate the raise percentage.
The raise percentage must not only be unexploitable, but also compensate for bubble factors in which the chips we lose or may lose are worth more than the chips we gain.
The assumption is that when opponents are faced with a raise where the iniaial raiser had this many players left to act, they 3bet with the following:
8 8.3% 88+, AJ+,ATs+,KTs+,QJs
7 9.43% 88+, AJ+, KQ, A9s+,KTs+,QJs,JTs
6 10.91% 66+, AJ+, KQ, A9s+,KTs+,QTs+,JTs,T9s
5 12.95% 66+, AJ+, KQ, A9s+,K9s+,Q9s+,J9s+,T8s+,98s,87s,76s,65s,54s
4 15.91% 66+, AJ+, KQ,QJ,JT, A8s+,KTs+,QTs+,J9s+,T8s+,97s+,87s,76s,65s,54s
3 20.63% 55+, AT+,KT+,QT+,JT,A7s+,KTs+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
2 29.29% 22+, A9+,KT+,QT+,JT,T9,98,87,76,65,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
1 50% 22+,A2+,K4+, Q8+, J9+,T8+,98,A2s+,K2s+,Q2s+,J5s+,T6s+,96s+,85s+,75s,64s+,54s
I only ran the calculations for 8 players, 5 players, and 2 players since I think having optimal call off vs 8.3% 3bet range, 12.95% range and 29.3% range is enough to get an idea. I may also add in a tighter range like top 4% later just because tighter 3bets are certainly common, especially with regards to shoves.
Keep in mind this is just as a means to calculate our opening strategy though so we aren't easily exploitable relative to our call off. I believe our call off range should actually be tighter because they 3bet less often than they should and because they are exploitable enough with raises that exploiting with calling 3bets is less necessary.
So with 30 BBs and a 0.8 bubble factor we need to be 36.69% to win (raise 2.25x BBs with antes)
So with 30 BBs and a 0.8 bubble factor we need to be 39.15% to win
So with 20 BBs and a 1.0 bubble factor we need to be 42.01% to win
So with 30 BBs and a 1.0 bubble factor we need to be 44.58% to win
So with 20 BBs and a 1.2 bubble factor we need to be 46.51% to win
So with 30 BBs and a 1.2 bubble factor we need to be 49.11% to win
So with 20 BBs and a 1.4 bubble factor we need to be 50.35% to win
So with 30 BBs and a 1.4 bubble factor we need to be 52.97% to win
So with 20 BBs and a 1.6 bubble factor we need to be 53.69% to win
So with 30 BBs and a 1.6 bubble factor we need to be 56.27% to win
So for example, if we raise UTG with 30 BBs and are shoved on and call with QQ+ and assume our opponents have a range of 88+,AJ+,ATs+,KTs+,QJs, then we are collectively are 72.568% to win vs that range. So 72.568% of the time we win say 32.5 and the remaining 27.432% we lose 48 (adjusting for bubble factors of 1.6 the chips we lose are worth 1.6 times more). Overall we can multiply .72568*32.5 plus .27432*-48. This is about 10.4.
What that means is that we can raise and fold X times and break even without being exploited. The X is what we have to solve for. Keep in mind that when we are raising, although we are losing 2.25 BBs when reraised, we actually are losing 1.6x more accounting for bubble factors. So we are risking in effect 3.6BBs on our raises and when we call, we gain an average of 10.40. So this means we can raise fold with 10.4/3.6=~2.89 times and call on the next one. Or we need to have QQ+ 1/3.89 times that we raise in this spot. Or we can raise 3.89 times more than we are willing to call off with, or with about 5.28% of hands
That translates into an opening hand range UTG 9 handed on the stone cold bubble with 30 big blinds of about 5.3% (roughly 88+,AQ). The actual call off range should try to account for the opponent because we need to be 56.27% to win a 30BB shove, but only 53.69% vs a 20BB shove. If a shorter stack shoves the bubble factors might even change and also, the opponent's hand range are most likely tighter than "cash game optimal" and a raise is probably profitable all of which means we should play tighter when calling off (and perhaps slightly looser when raising).
Nevertheless this is all work to establish a reasonable BASELINE to give us a better feel of approximately correct play.
What you have to understand about the bubble is IF opponents adjust and tighten up their 3bet range, you can profitably open much wider and call off very tight to the point if you want to exploit opponents. Even to the point where you are very exploitable such as raising 70% of hands and only calling off with KK+. Obviously if opponents even 3bet you once you should dramatically reduce your raise percentage and reevaluate after a couple more raises on whether or not you should tighten or loosen it up. If on the other hand you are seeing opponents 3bet shove every single hand, you should call off much looser (remember a 30BB shove you should be 56.27% to win on the bubble, so 57% over a random hand vs any two shover ), but basically only open with a hand that you are willing to call off with.
30BBs opening range and call off
(before separator are hands you are willing to call off a shove with)
0.80 bubble factor
8 players left to act (vs 8.3% reraise shove range)
99+,AJ+,KQ+|28.13%
4 players left to act (vs 15.91% reraise shove range)
77+,A3+,A2s+,K9o+,K6s+,QTo+,Q8s+,JTo+,J9s+,T9s|71.25%
2 players left to act (vs 29.29% reraise shove range)
22+,A2+,K2+,Q3+,Q2s+,J6o+,J3s+,T8o+,T6s+,98o+,96s+,86s+,76s|100%
1.0 bubble factor
8 players left to act (vs 8.3% reraise shove range)
TT+,AQ+,AJs+|17.65%
4 players left to act (vs 15.91% reraise shove range)
88+,ATo+,A8s+,KJo+,KTs+,QJs|33.33%
2 players left to act (vs 29.29% reraise shove range)
44+,A3o+,A2s+,K7o+,K3s+,Q9o+,Q7s+,JTo,J9s+,T9s|67.36%
1.2 bubble factor
8 players left to act (vs 8.3% reraise shove range)
JJ+,AQ+ | 11.18%
4 players left to act (vs 15.91% reraise shove range)
99+,AQ+,ATs+,KQs|19.23%
2 players left to act (vs 29.29% reraise shove range)
66+,A9o+,A5s+,KTo+,K9s+,QTo+,QTs+,JTs|31.45%
1.4 bubble factor
8 players left to act (vs 8.3% reraise shove range)
JJ+ | 6.89%
4 players left to act (vs 15.91% reraise shove range)
TT+,AKs | 10.56%
2 players left to act (vs 29.29% reraise shove range)
77+, ATo+,A9s+,KQo+,KTs+,QJs |20.49%
1.6 bubble factor
8 players left to act (vs 8.3% reraise shove range)
QQ+ | 88-JJ,AQ+
4 players left to act (vs 15.91% reraise shove range)
TT+|77-99,AQ+A9s+,KQs,87s,54s
2 players left to act (vs 29.29% reraise shove range)
88+,AQ+,ATs+ | open with 13.7% of hands
20 BB opening range and call off
0.80 bubble factor
8 players left to act (vs 8.3% reraise shove range)
99+,AJo+,ATs+,KQo+,KTs+|23.11%
4 players left to act (vs 15.91% reraise shove range)
66+,A2o+,K7o+,K2s+,Q9o+,Q2s+,J9o+,J9s+,T8s |100%
2 players left to act (vs 29.29% reraise shove range)
22+,A2+,K2+,Q2+,J3o+,J2s+,T6o+,T2s+,96o+,94s+,87o+,85s+,75s+,65s,54s|100%
1.0 bubble factor
8 players left to act (vs 8.3% reraise shove range)
TT+,AJ+,KQs|14.05%
4 players left to act (vs 15.91% reraise shove range)
88+,A8o+,A2s+,KTo+,K9s+,QJo+,Q3s+,J8o+,J7s+,T8s+,98s|46.21%
2 players left to act (vs 29.29% reraise shove range)
33+,A2+,K4+,K2s+,Q6o+,Q3s+,J8o+,J7s+,T8s+,98s|41.64% (note: I used propoker tools to determine the call off range, and pokerstove to do the remaining math.... In propoker tools J9s means J9s,Jts,Q9s,QTs,QJs,K9s,KTs,KJs,KQs where as I've always interpreted it as only J9s,JTs. As a result, whenever low suited one gap connectors or low offsuit cards like 97o+ were in the calculation it include more than I intended like Q7o so it messed with some of the results like this one. In most cases, it didn't change the results very much if at all unless facing a wide 3bet range.)
1.2 bubble factor
8 players left to act (vs 8.3% reraise shove range)
TT+,AQ+|9.88%
4 players left to act (vs 15.91% reraise shove range)
88+,AT+,A9s+,KQo,KTs|17.94%
2 players left to act (vs 29.29% reraise shove range)
44+,A7o+,A2s+,KTo+,K9s+,QJo,QTs+,JTs|32.77%
1.4 bubble factor
8 players left to act (vs 8.3% reraise shove range)
JJ+,AK,AQs+|6.93%
4 players left to act (vs 15.91% reraise shove range)
99+,AQo+,AJs+,KQs| 11.51%
2 players left to act (vs 29.29% reraise shove range)
66+,A9o+,A7s+,KTo+,KTs+QJo,QTs+|18.94%
1.6 bubble factor
8 players left to act (vs 8.3% reraise shove range)
JJ+|4.42%
4 players left to act (vs 15.91% reraise shove range)
TT+,AKs|6.77%
2 players left to act (vs 29.29% reraise shove range)
77+,ATo+,ATs,KQo,KTs+|11.62%
===========================================================================
I believe I have provided enough of a context for you to get a good idea of how to adjust based upon everywhere between these numbers or even outside of these ranges as a good approximation. But a 3bet range of TT+,AK,AQs may be more common from early or middle position. So
Early and middle position strategy for different bubble factors.
20 BBs
0.8 bubble factor
TT+,AK,AQs|12.41%
1.0 bubble factor
JJ+,AK|7.94%
1.2 bubble factor
JJ+|5.33%
1.4 bubble factor
QQ+|4.18%
1.6 bubble factor
QQ+|3.35%
30BBs
0.8 bubble factor
TT+,AK|15.55%
1.0 bubble factor
JJ+,AKs|9.54%
1.2 bubble factor
QQ+|6.82%
1.4 bubble factor
QQ+|5.22%
1.6 bubble factor
QQ+|4.02%
Note:Raising more often will probably still be profitable since opponents 3bet range is tighter, but because of complications about them potentially just calling in position, it's probably not that great.
The "optimal 3 bet range" we used was one in which opponents deny you the odds to profitably steal with any two, and thus it's a very wide range, particularly in bubble situations, and probably looser than is realistic. Thus in real life you probably can raise wider to exploit and fold tighter and assume opponents aren't trying to exploit. IF you get 3bet, you might reduce the raise percentage and increase the call off percentage and reevaluate later. On the other hand, It probably is correct on the bubble to 3bet much wider IF opponent's open with the same range and fold very tightly.
I think 88+,AJ+ is a common 3bet range vs a late position raiser plus maybe some rare bluffs we won't include because they aren't common enough and enough people will shove tighter than this. I will add this calculation in later.
Utility theory and opportunity cost theory may attempt to adjust these factors based upon the assumptions of there being skill involved. Both try in their own way to determine how to adjust those bubble factors given the skill.
The Utility Theorists believe the skill you have is proportional to the number of chips you have. A larger number of chips creates higher bubble factors for opponents who face you, and thus more fold equity and a greater probability of accumulating more chips without as great of risk on your tournament life, and greater probability of forcing other people to risk their tournament life.
The opportunity cost theorists believe that players do not respect ICM and thus will knock each other out sooner as well as provide much more "future value" which means survival is more important than expected value. An all in not only risks your tournament life which is more valuable if you do have skill, but that it also costs you the opportunity to see more profitable spots in the future plus all the hands you would have been dealt if you were not eliminated. If you still have plenty of room to accumulate chips, all in becomes unnecessary, particularly since it's possible you may not have to be all in to win a tournament.
Also, as blinds and antes rise proportional to everyone's chips, not only do you stand a better chance of getting called, possibly getting called twice and tripling up.... You also have the additional fold equity from someone raising another player out of the pot and the ability to wait for a dominant hand. Youalso build up a tight image that becomes relevant if/when you win a double up that increases your chances of additional blind steals when blinds are much, much higher than whatever they were when you passed up an edge. It also increases your probability of survival deep, and requires fewer steals or more hands before you have to double up before you can get back to where you were before you started blinding off.
I believe both have some merit. Between 15-30 big blinds there's an argument for taking slightly more risks than the ICM suggest to gain utility and make up for the edge you may give up by stolen pots in the future. There's also the argument for taking some risks vs some good players and loose aggressive players to your immediate left that otherwise might hinder your ability to accumulate chips.
Between 5-25 there's the argument that because of the antes rising, and blinds rising, you can win around 20% more on a blind steal a level later which allows for a tighter strategy to still be profitable, but also that ensuring your survival and increasing the probability of a double up and triple up when you do get that hand.
Because of theses bubble factors dictating a different "call off" range, it should change the opening range if you want to avoid being exploitable to a raise.
So the first step is determining a few guidelines for the "call off" percentages. These can be determined by a formula that relates the pot odds and bubble factors to the win percentages. Once we have these, we can assume that opponents 3bet such that you have a 50% chance of being 3bet by one opponent. We then need to calculate which hands have the equity to call off. When we have the "call off" range we can extrapolate the raise percentage.
The raise percentage must not only be unexploitable, but also compensate for bubble factors in which the chips we lose or may lose are worth more than the chips we gain.
The assumption is that when opponents are faced with a raise where the iniaial raiser had this many players left to act, they 3bet with the following:
8 8.3% 88+, AJ+,ATs+,KTs+,QJs
7 9.43% 88+, AJ+, KQ, A9s+,KTs+,QJs,JTs
6 10.91% 66+, AJ+, KQ, A9s+,KTs+,QTs+,JTs,T9s
5 12.95% 66+, AJ+, KQ, A9s+,K9s+,Q9s+,J9s+,T8s+,98s,87s,76s,65s,54s
4 15.91% 66+, AJ+, KQ,QJ,JT, A8s+,KTs+,QTs+,J9s+,T8s+,97s+,87s,76s,65s,54s
3 20.63% 55+, AT+,KT+,QT+,JT,A7s+,KTs+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
2 29.29% 22+, A9+,KT+,QT+,JT,T9,98,87,76,65,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
1 50% 22+,A2+,K4+, Q8+, J9+,T8+,98,A2s+,K2s+,Q2s+,J5s+,T6s+,96s+,85s+,75s,64s+,54s
I only ran the calculations for 8 players, 5 players, and 2 players since I think having optimal call off vs 8.3% 3bet range, 12.95% range and 29.3% range is enough to get an idea. I may also add in a tighter range like top 4% later just because tighter 3bets are certainly common, especially with regards to shoves.
Keep in mind this is just as a means to calculate our opening strategy though so we aren't easily exploitable relative to our call off. I believe our call off range should actually be tighter because they 3bet less often than they should and because they are exploitable enough with raises that exploiting with calling 3bets is less necessary.
So with 30 BBs and a 0.8 bubble factor we need to be 36.69% to win (raise 2.25x BBs with antes)
So with 30 BBs and a 0.8 bubble factor we need to be 39.15% to win
So with 20 BBs and a 1.0 bubble factor we need to be 42.01% to win
So with 30 BBs and a 1.0 bubble factor we need to be 44.58% to win
So with 20 BBs and a 1.2 bubble factor we need to be 46.51% to win
So with 30 BBs and a 1.2 bubble factor we need to be 49.11% to win
So with 20 BBs and a 1.4 bubble factor we need to be 50.35% to win
So with 30 BBs and a 1.4 bubble factor we need to be 52.97% to win
So with 20 BBs and a 1.6 bubble factor we need to be 53.69% to win
So with 30 BBs and a 1.6 bubble factor we need to be 56.27% to win
So for example, if we raise UTG with 30 BBs and are shoved on and call with QQ+ and assume our opponents have a range of 88+,AJ+,ATs+,KTs+,QJs, then we are collectively are 72.568% to win vs that range. So 72.568% of the time we win say 32.5 and the remaining 27.432% we lose 48 (adjusting for bubble factors of 1.6 the chips we lose are worth 1.6 times more). Overall we can multiply .72568*32.5 plus .27432*-48. This is about 10.4.
What that means is that we can raise and fold X times and break even without being exploited. The X is what we have to solve for. Keep in mind that when we are raising, although we are losing 2.25 BBs when reraised, we actually are losing 1.6x more accounting for bubble factors. So we are risking in effect 3.6BBs on our raises and when we call, we gain an average of 10.40. So this means we can raise fold with 10.4/3.6=~2.89 times and call on the next one. Or we need to have QQ+ 1/3.89 times that we raise in this spot. Or we can raise 3.89 times more than we are willing to call off with, or with about 5.28% of hands
That translates into an opening hand range UTG 9 handed on the stone cold bubble with 30 big blinds of about 5.3% (roughly 88+,AQ). The actual call off range should try to account for the opponent because we need to be 56.27% to win a 30BB shove, but only 53.69% vs a 20BB shove. If a shorter stack shoves the bubble factors might even change and also, the opponent's hand range are most likely tighter than "cash game optimal" and a raise is probably profitable all of which means we should play tighter when calling off (and perhaps slightly looser when raising).
Nevertheless this is all work to establish a reasonable BASELINE to give us a better feel of approximately correct play.
What you have to understand about the bubble is IF opponents adjust and tighten up their 3bet range, you can profitably open much wider and call off very tight to the point if you want to exploit opponents. Even to the point where you are very exploitable such as raising 70% of hands and only calling off with KK+. Obviously if opponents even 3bet you once you should dramatically reduce your raise percentage and reevaluate after a couple more raises on whether or not you should tighten or loosen it up. If on the other hand you are seeing opponents 3bet shove every single hand, you should call off much looser (remember a 30BB shove you should be 56.27% to win on the bubble, so 57% over a random hand vs any two shover ), but basically only open with a hand that you are willing to call off with.
30BBs opening range and call off
(before separator are hands you are willing to call off a shove with)
0.80 bubble factor
8 players left to act (vs 8.3% reraise shove range)
99+,AJ+,KQ+|28.13%
4 players left to act (vs 15.91% reraise shove range)
77+,A3+,A2s+,K9o+,K6s+,QTo+,Q8s+,JTo+,J9s+,T9s|71.25%
2 players left to act (vs 29.29% reraise shove range)
22+,A2+,K2+,Q3+,Q2s+,J6o+,J3s+,T8o+,T6s+,98o+,96s+,86s+,76s|100%
1.0 bubble factor
8 players left to act (vs 8.3% reraise shove range)
TT+,AQ+,AJs+|17.65%
4 players left to act (vs 15.91% reraise shove range)
88+,ATo+,A8s+,KJo+,KTs+,QJs|33.33%
2 players left to act (vs 29.29% reraise shove range)
44+,A3o+,A2s+,K7o+,K3s+,Q9o+,Q7s+,JTo,J9s+,T9s|67.36%
1.2 bubble factor
8 players left to act (vs 8.3% reraise shove range)
JJ+,AQ+ | 11.18%
4 players left to act (vs 15.91% reraise shove range)
99+,AQ+,ATs+,KQs|19.23%
2 players left to act (vs 29.29% reraise shove range)
66+,A9o+,A5s+,KTo+,K9s+,QTo+,QTs+,JTs|31.45%
1.4 bubble factor
8 players left to act (vs 8.3% reraise shove range)
JJ+ | 6.89%
4 players left to act (vs 15.91% reraise shove range)
TT+,AKs | 10.56%
2 players left to act (vs 29.29% reraise shove range)
77+, ATo+,A9s+,KQo+,KTs+,QJs |20.49%
1.6 bubble factor
8 players left to act (vs 8.3% reraise shove range)
QQ+ | 88-JJ,AQ+
4 players left to act (vs 15.91% reraise shove range)
TT+|77-99,AQ+A9s+,KQs,87s,54s
2 players left to act (vs 29.29% reraise shove range)
88+,AQ+,ATs+ | open with 13.7% of hands
20 BB opening range and call off
0.80 bubble factor
8 players left to act (vs 8.3% reraise shove range)
99+,AJo+,ATs+,KQo+,KTs+|23.11%
4 players left to act (vs 15.91% reraise shove range)
66+,A2o+,K7o+,K2s+,Q9o+,Q2s+,J9o+,J9s+,T8s |100%
2 players left to act (vs 29.29% reraise shove range)
22+,A2+,K2+,Q2+,J3o+,J2s+,T6o+,T2s+,96o+,94s+,87o+,85s+,75s+,65s,54s|100%
1.0 bubble factor
8 players left to act (vs 8.3% reraise shove range)
TT+,AJ+,KQs|14.05%
4 players left to act (vs 15.91% reraise shove range)
88+,A8o+,A2s+,KTo+,K9s+,QJo+,Q3s+,J8o+,J7s+,T8s+,98s|46.21%
2 players left to act (vs 29.29% reraise shove range)
33+,A2+,K4+,K2s+,Q6o+,Q3s+,J8o+,J7s+,T8s+,98s|41.64% (note: I used propoker tools to determine the call off range, and pokerstove to do the remaining math.... In propoker tools J9s means J9s,Jts,Q9s,QTs,QJs,K9s,KTs,KJs,KQs where as I've always interpreted it as only J9s,JTs. As a result, whenever low suited one gap connectors or low offsuit cards like 97o+ were in the calculation it include more than I intended like Q7o so it messed with some of the results like this one. In most cases, it didn't change the results very much if at all unless facing a wide 3bet range.)
1.2 bubble factor
8 players left to act (vs 8.3% reraise shove range)
TT+,AQ+|9.88%
4 players left to act (vs 15.91% reraise shove range)
88+,AT+,A9s+,KQo,KTs|17.94%
2 players left to act (vs 29.29% reraise shove range)
44+,A7o+,A2s+,KTo+,K9s+,QJo,QTs+,JTs|32.77%
1.4 bubble factor
8 players left to act (vs 8.3% reraise shove range)
JJ+,AK,AQs+|6.93%
4 players left to act (vs 15.91% reraise shove range)
99+,AQo+,AJs+,KQs| 11.51%
2 players left to act (vs 29.29% reraise shove range)
66+,A9o+,A7s+,KTo+,KTs+QJo,QTs+|18.94%
1.6 bubble factor
8 players left to act (vs 8.3% reraise shove range)
JJ+|4.42%
4 players left to act (vs 15.91% reraise shove range)
TT+,AKs|6.77%
2 players left to act (vs 29.29% reraise shove range)
77+,ATo+,ATs,KQo,KTs+|11.62%
===========================================================================
I believe I have provided enough of a context for you to get a good idea of how to adjust based upon everywhere between these numbers or even outside of these ranges as a good approximation. But a 3bet range of TT+,AK,AQs may be more common from early or middle position. So
Early and middle position strategy for different bubble factors.
20 BBs
0.8 bubble factor
TT+,AK,AQs|12.41%
1.0 bubble factor
JJ+,AK|7.94%
1.2 bubble factor
JJ+|5.33%
1.4 bubble factor
QQ+|4.18%
1.6 bubble factor
QQ+|3.35%
30BBs
0.8 bubble factor
TT+,AK|15.55%
1.0 bubble factor
JJ+,AKs|9.54%
1.2 bubble factor
QQ+|6.82%
1.4 bubble factor
QQ+|5.22%
1.6 bubble factor
QQ+|4.02%
Note:Raising more often will probably still be profitable since opponents 3bet range is tighter, but because of complications about them potentially just calling in position, it's probably not that great.
The "optimal 3 bet range" we used was one in which opponents deny you the odds to profitably steal with any two, and thus it's a very wide range, particularly in bubble situations, and probably looser than is realistic. Thus in real life you probably can raise wider to exploit and fold tighter and assume opponents aren't trying to exploit. IF you get 3bet, you might reduce the raise percentage and increase the call off percentage and reevaluate later. On the other hand, It probably is correct on the bubble to 3bet much wider IF opponent's open with the same range and fold very tightly.
I think 88+,AJ+ is a common 3bet range vs a late position raiser plus maybe some rare bluffs we won't include because they aren't common enough and enough people will shove tighter than this. I will add this calculation in later.
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