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.
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