Tournament Planning 2

A more thorough way to plan tournament strategy around the blind structure is to factor in more or less your entire strategy. You may prefer to have a goal to make the final table and from there just use ICM. ICM is terrible for entire tournaments but when you have 5 big blinds and everyone is short stacked (5-10 big blinds) it's all in or fold anyways. Skill may exist but it is really limited. Skilled players might fold a bit more or recognize when jamming slightly wider or slightly less often is better based upon how opponent's are playing and how well they know ICM shoves based upon payout structure.
Say a tournament has 500 hands until 5 handed. You can determine this by the following calculation
1)Number of entrants times average chips per player (starting stack plus add on plus rebuys per person) equals total chips in play.
2)Total chips in play divided by 5 players equals average stack at that stage.
3)average stack at that stage divided by the average number of big blinds like 10 equals the rough approximate blind
That equals the rough estimate of what the big blind is with 5 players left.
Once you know at what blind level, you simply need to know an estimate of hands per blind level. Usually live play is around 30 hands per hour and online is around 100 hands per hour. In other words 30 hands per 60 minutes or 1 hand every 2 minutes( 0.5 hands per minute) live and 100 hands per 60 minutes or 1.667 hands per minute. So if there are 30 minute blind levels live it is about 15 hands per blind level. So 15 times the number of blind levels until the big blind is where you anticipate 5 handed let's say 34 times 15=510 hands per tournament of this nature.

Once you know the number of hands, you can determine how many big blinds per blind level you need to win to avoid getting too short stacked. Your skill edge may diminish under 20 big blinds OR your risk will increase. I would prefer to raise more and take more risk unless I can coast into higher payouts if skill diminishes too much the blinds will catch you and then you have to get multiple double ups just to survive and resort to multiple all ins. If you take too much risk you may end up unnecessarily getting eliminated. There is a difficult balancing act.

Let's say for example you need to steal 3 times per blind level or win about 6.5 blinds per blind level on average whether that is one hand or 10 hands to avoid all ins. You can simply determine what hand range you need to play such that you have a more than 50% chance of getting this hand range 34 times or more.34 because 510/34=15. But with each hand you play you will have to gain 6.5 big blinds. Let's be honest that may be a little high so you will want to widen your range overall or be willing to risk all your chips a time or two or three with superior hands.

Unfortunately you may find out even if you execute this plan, you will spend about half the tournament between 15-20 big blinds.

If the goal is to avoid being all in, chances are this isn't a fast enough rate of chip accumulation given the higher variance that will occur in the 15-20 big blind range and the possibility for hands not coming as regularly, or earnings not maintaining a high enough rate... plus given the action before you act, you may prefer to fold. Foretunately the math is for more than 50% chance of 34 hands OR MORE so it allows us to fold a time or two and still have a good chance of doing very well with manageably limited risk.

But we can still use this hand range as a baseline and build a strategy around it.

So what is the hand range that in 510 hands we will get 34 times or more?
77+,AQo+,ATs+,KQs

Take a situation where it folds to you in Middle position and you raise with this range... We may want to be slightly tighter in early position and looser in late position and tighter when reraising. We also will want to look for any situation that has a better or similar low risk to high reward to a middle position raise equivalent to this.

I believe this strategy becomes most flawed in the ante stages and later on as it's lower risk to fight just a little harder to preserve chips to maintain a large enough stack to avoid anything that could even cause you to approach a stack where an all in may become necessary.

So how about this.

Pre ante stages: when it folds to you
Early position: raise 88+,AKo,AQs
Middle position: 77+,AQo+,ATs+,KQs
Late position:22+,AJo+,KQo,A2s+,[45s-KQs]
When facing a raise from
Early position: raise QQ+,call JJ, bluff raise AKs
Middle position:raise JJ+,call AKo,88-TT, bluff 22-77,AJo+, KQo,X9s (any 2 suits cards with low card 9 or higher)
Late position: raise 88+,AKo,AQs. Call 44-77,AJo,AQo,ATs,AJs,KJs+. Bluff X9o+,X6s+,Q2s+,K2s+,A2s+

Bluffs only done half the time or less unless there is knowledge that opponent folds too often.

Ante stages most people don't play enough hands in my opinion. There is math to back it up. Basically you will get the pot odds to call a raise. In this model the reason we become struggling to avoid all ins is because the blinds catch up to us and the antes are costly. Going card dead late has the most severe consequences and losing a hand or having to fold has greater consequences late.

So how do we adjust to the antes?
Early position: 55+,AQo+,AJs
Middle: 22+,AJo+,KQo,A8s+,K9s+,Q9s+J9s+,T8s+,97s+,76s,65s,54s
Late: 22+,A9o+,KTo+,QJo,JTo,T9o,A2s+,K2s+,Q8s+,J7s+,T6s,96s+,85s+,75s,64s+,54s

When faced with a raise in the ante stages every single hand in the "bluff" range you could call with, but I will say bluff with that range half the time and call the other half in the ante stages. The other details don't change because opponents don't adjust to the antes enough.

In addition, you are always looking for opportunity

For everything else keep risk mitigated to under 2x the Kelly bet such as a short stack jamming.


Adapting: Not every tournament will deliver enough hands and sometimes you may lose a big enough pot to where you are running way behind expectations. As you go below expectations I like to take additional risk (but calculated). If I haven't played a hand in 2 rotations I will raise any two halfway decent cards and if the blind steal fails I will be really cautious and usually check/fold as opposed to continuing. Save the cbets for playable hands. I also might minbet all 3 streets to virtually guarentee a call. This gives up a little bit of value and increases chance of suckouts for a high probability of decent chip accumulation. When you are barely hovering above 10 big blinds or even as you dip below 20 I think minbetting is a reasonable risk and giving up some value in exchange for a high probability of getting back in control is worth an increased chance of allowing a suckout as long as you can fold when they raise and adapt as needed.
Unless there is value from folding your way up a few blind levels, dont fear the all in, we strategize around it but if you are blinding down there, you need to take some chances to get back to manageable. I will usually minraise more frequently say around 7-16 big blinds or consider jamming after a few limpers or a small raise with a wider range.

Tournament Strategy Design

One way to model tournaments is to look at the blind levels and have an assumed/estimated rate of chip accumulation. You may accumulate more on different levels based upon your expected chip stack in big blinds, the size of the antes and what stage of the tournament.



Then you can determine you need to double up 3 times throughout the tournament in about 187 hands. You can then determine the probability that you are dealt a given hand X or more times.



Based on this information we need to double up about 3 times given the structure and we have a 64.8% chance of being dealt JJ or better 3 times or more and a 46.2% chance of being dealt QQ+. As you have gone through more hands without doubling up or if you are behind on the rate of chip accumulation you might decide you need to widen your range. you should constantly adjust based upon projected hands left. You can try to double up more or less than this amount and you could easily be dealt 99 and have it be stronger than JJ in certain conditions plus you have postflop to consider, but it's worth thinking about. So let's say you haven't doubled up and have accumulated chips at the expected rate minus a double up and you have 120 hands left projected. Now you can widen your hand selection. Or perhaps you've doubled up and only need to double up 2 more times, you can narrow your hand range or widen it depending on hands left. This is one way to approach risk. Perhaps you want a greater probability of cashing first and so you want a stronger hand and a greater probability of surviving. Or perhaps you want a greater probability of winning and think you can parlay an earlier double up into a greater edge and less risk overall. You can make adjustments. Perhaps there are lots of postflop situations and can get your money in better. Perhaps you aren't likely to get action with your big hand so you need to widen your range or find a way to increase your edge. But this is a good baseline to start with. Slower structures you can be more selective assuming you can still get paid off when you have a hand.

how to calculate Jam or fold ICM

ICM is a valuable calculation in all in or fold scenarios because it can tell you concretely and objectively how much a decision is worth like jamming vs folding.
I have theories about in MTTs how deeper stacks allow players to apply a skill and the opportunity cost of survival to see more hands and find better spots is also greater, but with short stacks when everyone is short stacked near the end of tournaments or near the end of supersattelites or even on the bubble or in sit N Gos ICM is the most relevant because the other stuff doesn't come into play as much.

I would favor an alternative model that requires a lot of guess work for the tournaments that have more playability but ICM is really relevant in super short stacked situations.

Say for instance there are 13 players left in a super satellite that pays 11 places and 11th it pays 180 and 10th or less it pays 250. You have only 3 big blinds or 3000 in chip value with blinds 500/100 and 1000 ante but there are 2 players with fewer chips than you have. You are dealt QQ. It folds to you in the small blind. Folding is better than jamming. How do I know this?
ICM calculation.

There are ICM calculators online that will tell you how much a given chipstack is worth given you also plug in how much your opponents have so they know what percentage of chips you have. In an example I looked at, if you shove and opponent folds 20% of the time you go from 3000 (which is worth $183.05) to 5100 in chips (which is worth $221.71 in ICM) if they fold. But if the big blind calls and you win you go up to 7100 (which is worth $236.20).
So... if you are 75% to win with QQ
(.20*221.71)+(.52*236.20)+(.28*0)=
(44.34)+(122.82)+(0)=167.16
Since folding is worth 183.05, folding is better than jamming. Limping in for half a big blind might be okay provided you examine the very complex decision tree and possible outcomes of each decision and it proves to be more profitable than folding, but that requires a lot of information that you really can't be too confident about.
Folding QQ not only is better than jamming but making it puts $16 in your pocket vs the alternative. Your opponent should NOT be calling so widely, but if he is it hurts both you and your opponent. There is a weird dynamic where if you and your opponents are even in chips you can jam with any two and they might even be correct to fold aces, but as they widen their hand range they hurt themselves and hurt you too to and that continues as they widen their hand range the point where you possibly would be correct to fold aces if they are going to always call you.

You have to consider this as a possibility and look at other calling ranges and the value and weight them by probability of being correct.
If folding QQ with only 3 big blinds is worth that much think of how valuable folding other hands that you might normally want to push on the bubble with deeper stacks. If your opponent folds a lot more often which is possible you can come up with a different equation and when called your odds of winning might decline but you may make enough when opponent folds for it to increase in value and possibly be worth more than folding. Different payout structures may suggest a different strategy as well. You should be aware of the payout structure given X number of opponents and see how it changes and calculate for varying amounts approaching the bubble and on the bubble or have some method to come up with crude approximations because it can put extra money in your pocket.

How Often Opponents Need To Defend (or more) to Deny Bluffs profit

This assumes that when called, hands are flipped face up and shown down to the river.

Bluffing

When you choose to bluff you want to have a hand not strong enough to call because you have value to continue by just calling. However, you can still bluff with the bottom end of your hand range that has value in calling and you especially can do so with hands with bad reverse implied odds and only marginal value to call. Hands like low pocket pairs has value vs one bet but not vs multiple if opponents narrow their range with streets and that prefer not to see multiple streets where play becomes more difficult you can consider raising as a bluff.

Assume opponent has 55+,AQo+,AJs+,KQs and he raises 2.2 in the ante stages in a tournament.
You can technically call if you are 32.26% to win.
That means you can call the raise with:
44+,A9o+,KTo+,QTo+,J9o+,T9o,A2s+,K6s+,Q8s+,J7s+,T7s+,97s+,87s

If our opponent will call a 3bet with tighter than TT+,AKo,AQs+ we can raise with any two profitably assuming we bet pot

If our opponent plays exactly this range we'd probably only want value over the calling range which may only be TT,JJ,AQs and sometimes AK, sometimes, AKs and sometimes QQ.

bluff equity vs opponents assumed calling range for reference:
33 35.898%
22 35.318%
Q7s 32.359%
Q6s 32.609%
Q5s 32.504%
Q4s 32.224%
Q3s 31.851%
Q2s 31.474%
K5s 31.452%
54s 31.429%
65s 31.382%
K4s 31.157%

76s 31.087%
J6s 30.983%
75s 30.174%
K3s 30.763%
K2s 30.366%
64s 30.033%
53s 29.973%
86s 29.903%
43s 29.689%
Q9o 29.890%
J8o 29.002%
85s 28.911%
74s 28.746%
96s 28.558%
T6s 28.231%
32s 27.844%

A8o 27.079%
K9o 27.776%
T8o 26.098%98o 25.545%


If our opponents make more mistakes after the flop we can bluff raise with a wider range.


On the flop:
On the flop bluff raising is a little bit different, but let's take a J72 board with 2 spades and one heart and let's look at an opponent who bets something like:
66+,22,A9s+,A5s,A2s,AJo+, J9 or a better jack J7s+,K7s,T9s,T7s,97s+,87s,57s,67s

All flushdraws we can mostly call and sometimes raise as a semibluff.

all    22    89.19%    most often raise, occasionally call
all    JJ    93.23%    most often raise, occasionally call
all    77    90.75%    most often raise, occasionally call
all    QQ    68.26%    usually raise, sometimes call
all    KK    72.54%    usually raise, sometimes call
all    AA    76.59%    usually raise, sometimes call
all    AJ    66.71%    call mostly, sometimes raise
all    A2    33.70%    almost always call
all    88    35.10%    almost always call
all    99    38.59%    almost always call
all    TT    42.11%    call
all    AA    76.59%   
all    a7    40%    call
backdoor spades (highcard)    AK    31.42%    mostly call, rarely raise
backdoor spades (lowcard)    AK    30.75%    mostly call, rarely raise
backdoor spades (suited hearts)    AK    30.56%    mostly call, rarely raise
backdoor spades (highcard)    t9    28.52%    mostly call, rarely raise
backdoor spades (lowcard)    t9    28.52%    mostly call, rarely raise
backdoor spades (suited hearts)    t9    28.52%    mostly call, rarely raise
backdoor spades (suited hearts)    t8    27.22%    mostly call, rarely raise
backdoor spades (highcard)    t8    27.09%    mostly call, rarely raise
backdoor spades (suited hearts)    98    27.06%    mostly call, rarely raise
no draw    AK    27.04%    mostly call, rarely raise
backdoor spades (highcard)    98    26.92%    mostly call, rarely raise
backdoor spades (lowcard)    t8    26.84%    mostly call, rarely raise
backdoor spades (lowcard)    98    26.64%    mostly call, rarely raise
backdoor spades (highcard)    AQ    25.91%    mostly call, sometimes raise
backdoor spades (suited hearts)    AQ    25.44%    mostly call, sometimes raise
no draw    t9    25.38%    mostly call, sometimes raise
backdoor spades (lowcard)    AQ    25.18%    mostly call, sometimes raise
all    66    24.56%    usually bluff raise
all    55    24.18%    usually bluff raise
no draw    t8    24.02%    float or bluff raise mixture
all    33    23.89%    usually bluff raise
no draw    98    23.84%    float or bluff raise mixture
all    44    23.46%    usually bluff raise
backdoor spades (highcard)    AT    22.63%    float or bluff raise mixture
backdoor spades (highcard)    kt    22.17%    float or bluff raise mixture
backdoor spades (suited hearts)    kt    22.05%    float or bluff raise mixture
backdoor spades (suited hearts)    AT    21.95%    float or bluff raise mixture
backdoor spades (suited hearts)    qt    21.87%    float or bluff raise mixture
backdoor spades (highcard)    qt    21.75%    float or bluff raise mixture
backdoor spades (lowcard)    kt    21.62%    float or bluff raise mixture
no draw    AQ    21.58%    float or bluff raise mixture
backdoor spades (lowcard)    AT    21.56%    usually bluff raise, sometimes fold
backdoor spades (lowcard)    qt    21.46%    float or bluff raise mixture
backdoor spades (highcard)    A9    21.09%    usually bluff raise, sometimes fold
backdoor spades (highcard)    A8    20.88%    usually bluff raise, sometimes fold
backdoor spades (suited hearts)    A9    20.55%    usually float, sometimes bluff raise, sometimes fold
backdoor spades (highcard)    k9    20.40%    usually float, sometimes bluff raise, sometimes fold
backdoor spades (suited hearts)    k9    20.33%    usually float, sometimes bluff raise, sometimes fold
backdoor spades (suited hearts)    A8    20.30%    usually float, sometimes bluff raise, sometimes fold
backdoor spades (suited hearts)    q9    20.17%    usually bluff raise, sometimes float, sometimes fold
backdoor spades (highcard)    q9    20.01%    usually bluff raise, sometimes float, sometimes fold
backdoor spades (lowcard)    A9    20%    usually bluff raise, sometimes float, sometimes fold
backdoor spades (lowcard)    k9    19.87%    bluff raise or fold
backdoor spades (lowcard)    q9    19.74%    bluff raise or fold
backdoor spades (lowcard)    A8    19.42%    bluff raise or fold
backdoor spades (highcard)    A5    19.05%    usually float, sometimes bluff raise, sometimes fold
backdoor spades (highcard)    A4    18.70%    usually float, sometimes bluff raise, sometimes fold
backdoor spades (highcard)    A3    18.70%    usually float, sometimes bluff raise, sometimes fold
backdoor spades (suited hearts)    A5    18.47%    usually float, sometimes bluff raise, sometimes fold
no draw    kt    18.31%    sometimes bluff raise, sometimes fold
no draw    AT    18.15%    sometimes bluff raise, sometimes fold
no draw    qt    18.14%    sometimes bluff raise, sometimes fold
backdoor spades (suited hearts)    A4    18.10%    usually fold, sometimes mixed bluff raise or fold
backdoor spades (suited hearts)    A3    18.10%    usually fold, sometimes mixed bluff raise or fold
backdoor spades (highcard)    A6    17.88%    usually fold, sometimes mixed bluff raise or fold
backdoor spades (suited hearts)    A6    17.30%    usually fold, sometimes mixed bluff raise or fold
backdoor spades (lowcard)    A5    17.25%    usually fold, sometimes mixed bluff raise or fold
backdoor spades (lowcard)    A4    16.90%    usually fold, sometimes mixed bluff raise or fold
backdoor spades (lowcard)    A3    16.90%    usually fold, sometimes mixed bluff raise or fold
no draw    A9    16.64%    usually fold, sometimes mixed bluff raise or fold
no draw    k9    16.47%    usually fold, sometimes mixed bluff raise or fold
no draw    A8    16.43%    usually fold, sometimes mixed bluff raise or fold
no draw    q9    16.33%    usually fold, sometimes mixed bluff raise or fold
backdoor spades (lowcard)    A6    16.10%    usually fold, sometimes mixed bluff raise or fold
backdoor spades (suited hearts)    86    15.42%    mostly fold very rarely float
backdoor spades (highcard)    86    14.86%    mostly fold very rarely bluff raise
backdoor spades (lowcard)    86    14.68%    mostly fold very rarely bluff raise
no draw    A5    14.64%    no draw
backdoor spades (suited hearts)    45    14.44%    mostly fold very rarely float
backdoor spades (suited hearts)    65    14.38%    mostly fold very rarely float
no draw    A4    14.30%    mostly fold very rarely bluff raise
no draw    A3    14.30%    mostly fold very rarely bluff raise
backdoor spades (suited hearts)    96    14.13%    mostly fold very rarely float
backdoor spades (suited hearts)    95    13.98%    mostly fold very rarely float
backdoor spades (highcard)    96    13.77%    mostly fold very rarely bluff raise
backdoor spades (highcard)    45    13.76%    mostly fold very rarely bluff raise
backdoor spades (lowcard)    45    13.75%    mostly fold very rarely bluff raise
backdoor spades (highcard)    65    13.72%    mostly fold very rarely bluff raise
backdoor spades (lowcard)    65    13.70%    mostly fold very rarely bluff raise
backdoor spades (highcard)    95    13.65%    mostly fold very rarely bluff raise
no draw    A6    13.38%    fold. only rare opponent specific decisions
backdoor spades (lowcard)    96    13.30%    fold. only rare opponent specific decisions
backdoor spades (suited hearts)    34    13.25%    mostly fold very rarely float
backdoor spades (lowcard)    95    13.12%    fold. only rare opponent specific decisions
backdoor spades (highcard)    34    12.48%    fold. only rare opponent specific decisions
backdoor spades (lowcard)    34    12.48%    fold. only rare opponent specific decisions
no draw    86    11.78%    fold. only rare opponent specific decisions
no draw    45    10.85%    fold. only rare opponent specific decisions
no draw    65    10.80%    fold. only rare opponent specific decisions
no draw    96    10.60%    fold. only rare opponent specific decisions
no draw    95    10.20%    fold. only rare opponent specific decisions
no draw    34    9.57%    fold. only rare opponent specific decisions

Some opponents fold often enough on the flop or on prior streets for you to profitably be able to bet any 2 cards but even so, you don't want to give opponent reason to adjust so unless you specifically know this opponent isn't capable of adjusting or only very occasionally mix in these bluffs when you haven't bluffed in awhile, you haven't played a pot with this opponent in awhile, your opponent maybe hasn't been tilted and doesn't have a reason to change his play and you haven't had a spot where you can bluff anyone in awhile especially this opponent. In that case the cards really don't matter but even so, I see no reason why you can't at least have some standards just in case your assumptions are wrong.... At least on the flop. By the river hands will approach zero equity or 100% and have much fewer hands between. On the turn there will still be some longshot draws with one card to improve and hands like KQ that could hit the top pair and still not be good but have at least some chance (like under 10%) of winning when called.

on say a J728 board with 2 suits you might bluff hands like:
KQ with flush draw
A2-A6 with flush draw.
A9
AT
KQ no flush draw
A7
A2

Value hands after 2 streets of betting go down.

On the river it's more about which river cards you bluff and how often then what hand since bluffs will have pretty close to zero chance of winning when called. Bluffs should be much less frequent on the river than on the flop and even than on the turn.



Theoretical bluff to value ratio looks something like this. For a half the pot bet you are giving your opponents 3 to 1 and therefore they only need to be right 1/4 times. You should bluff such you are indifferent to whether or not they call because if you bluff more often they can always call and if you bluff less often they can always fold bluff catchers.
So on the river you should bluff 25% of the time to make them right on 1/4 calls.
On the turn you get to leverage the possibility of multiple bets and hands that are value on the turn may lose value when facing a n additional bet so you can bluff more as some bluff hands will improve and become value hands and some value hands will decline. The purpose of bluffing more is so that the river frequency matches the ratio needed and to have balance for multiple possible rivers to represent.
So you should actually bluff if you intend on 2 half the pot bets 1-(.75*.75)=43.75% and on the flop
1-(.75*.75*.75) =57.8125% on the flop.
With larger bets your opponents get worse pot odds and therefore have to call less often so you can bluff more often and still force opponent to break even. However, keep in mind this % is not of total hands that you have, but total hands that you bluff. So given your opponent can fold more often, fewer hands have value when called and therefore, fewer bets for value and so the total % of hands you bluff might not be any larger and may even be smaller if you bet bigger.

Minimum defend frequency=bluff catching.

Your opponent has to defend some percentage of the time to prevent you from bluffing profitably with any two cards so on the river they need to call you based upon the price you get when you bet. You are risking 1 half bet to get 2 halfbets on a half pot bet so opponents must defend you 50% of the time by calling or raising.

I don't know how it works on the river, but let's just assume it procedes similarly to how we can bluff more. I believe if we bluff more our opponent can continue more (and rebluff more). So I believe if we bet half pot bet our opponent should defend 87.5% on the flop, 75% on the turn and 50% on the river to deny us the ability to parlay multiple bets and bluff successfully with any two.

That may be a little high, but certainly if our opponent defends a pot size bet less than 50% on any street we can profitably bluff with any two and many of the bluffing hands will have some equity on earlier streets so we can bluff pretty widely and should defend at least some percentage more than 50% when our opponent bets half the pot. We not only have to protect our hands but also protect multiple streets of multiple hands and force our opponent to consider a wide range of hands that we can have.

I think to confirm this we can run a simulation but I will do that later perhaps..

You never should bluff more than 50% on the river unless you know opponent folds too often and won't adjust.

General poker principals:

General poker principals:
There are certain frequencies that opponents need to call with in order to prevent you from bluffing with any two. With multiple opponents they should at a minimum act in aggregate to call enough to force you to break even on bluff attempts. So if you are betting preflop for 2 times the pot or 3 big blinds into a 1.5 big blind pot when opponents fold they should each call at least this often given you raised with this many opponents. That will cause them to effectively fold about 2/3rds of the time. They should call slightly more than this, but this is a good baseline that you can apply on any street where you bet 2 times the pot.
1)33.33%
2)18.15%
3)12.50%
4)9.53%
5)7.7%
6)6.46%
7)5.56%
8)4.89%

When the antes kick in you are betting pot preflop (and sometimes minraise is less than pot) and your opponents must call you at least this often.

Defend range for a 1x pot bet:
1) 50%
2) 29.29%
3) 20.63%
4) 15.91%
5) 12.95%
6) 10.91%
7) 9.43%
8) 7.41%

For post flop considerations given the number of opponents you face let's also look at half pot and 1/3rd pot bets

Defend range for half pot bet:
1) 66.66%
2) 42.27%
3) 30.66%
4) 24.02%
5) 19.73%
6) 16.73%
7) 14.53%
8) 12.83%

For 1/3rd pot bet they need to collectively defend 75% of the time.

Some caveats to this.
The more streets left over, the more opponents can/should call, and the higher frequency you can/should bluff.
A toy game example by Matthew Janda showed 2/3rds pot betting where you bet 33% value and bluff 66% on the flop, then 49% bluff, 51% value on the turn, and then 30% bluff and 70% value on the river. I assume that also applies preflop. Also with an increased price such as in the big blind you can call more often to defend and you don't have to continue as often on the flop because of the pot odds you got on the prior round of betting. Also to be considered, in real poker hands that can draw to very strong hands or be used in bluffs when they miss are more valuable while hands with weak kickers, low cards that can be outkicked and out drawn and marginal hands that can only be used to bluff catch lose value.... particularly those that are not always strong enough to beat bluffs when we bluff catch.

If you actually work out hands, you need to use equity calculators to determine which specific hands these are on specific flops, and how opponents can shed these hands on each street with a round of betting.

Given this defend range, you want to only raise with hands that have value. If opponents call too often you don't really want to add in bluffs but if opponents call more than this the value hands go up and the hands that were considered bluffs now have value.

You only need about 33% equity to call a preflop raise of 2.2 big blinds when the blinds and antes are involved which means you can flat call very widely. While technically we have your opponent defending much less often, that is the minimum threshold to where bluffing with zero equity assuming the betting ends after the hand is profitable.

Nevertheless, we can consider anything that has equity when you call a bet to also be of value to bet. technically we may prefer a smaller pot with hands with 33% to 50% equity but raising gives us a chance at the blinds so in my mind this is close enough. Technically we'd probably have a mixed strategy and sometimes want to just call with the mediums strength hands plus occasionally stronger hands to protect it.

So what hands have equity?
Given we raise with number of opponents left and opponents defend often enough to force our bluffs to break even.
Pre-Ante stage:
1: 22+, A2+, K3+, Q8+, J9+, Q4s+, J7s+, T7s+, 98s, 87s
2: 22+, A4+, KT+,QJ,A2s+, K8s+,Q9s+,J9s+,T8s+,98s
3: 44+,A9o+,KQo,A7s+,KTs+,QTs+,JTs
4: 55+, AT+,KQ, A8s+, KTs+,QTs+,JTs
5: 77+, AQ+, ATs+, KQs
6: 88+, AK, AQs+
7: 99+, AK, AQs+
8: TT+, AK, AQs+

I would personally want to shed hands with kicker troubles and insert hands with more drawing potential. I would be very comfortable flat calling with this range as well if an opponent bet from a given spot with a number of opponents left before he raised.
Nevertheless, we can also bluff. We may wish to bluff with those hands not quite strong enough to flat call, or use those hands just on the bottom end of the range, particularly those without great drawing potential but that might make a lot of stronger kicker hands to fold like A2 or K3 or KJ or A9 or suited connectors or suited jacks, queens and kings (as opposed to suited aces which can draw to the best possible flush).

I would totally be comfortable playing an equal amount of value bet to bluff ranges. If we double our hand range total we roughly end up with the following hands:

value plus bluffs:
1: Any 2 (minus some bad hands)(85%)
2:22+,A2s+,K2s+,Q2s+,J2s+,T6s+,96s+,85s+,74s+,63s+,52s+,42s+,32s,A7o+,K9o+,Q9o+,J9o+,T7o+,97o+,86o+,75o+,64o+,54o,43o,32o (52%)
3:22+,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,86s+,75s+,64s+,53s+,42s+,32s,A9o+,KTo+,QTo+,J9o+,T9o,98o
(29.4%)
4:22+,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,86s+,75s+,64s+,53s+,42s+,32s,AJo+,KJo+,QJo,JTo (23.2%)
5: 44+,A9s+,K9s+,Q9s+,J8s+,T8s+,97s+,86s+,75s+,64s+,53s+,43s,32s,AQo+,KQo (16.4%)
6: 55+,A2s+,KJs+,QTs+,J9s+,T8s+,97s+,86s+,76s,65s,54s,43s,AKo (13.9%) - sometimes fold the weaker hands
7: 66+,ATs+,KQs,QJs,JTs,T8s+,98s,87s,76s,65s,54s,43s,32s,AKo (9.8%) - sometimes fold weaker hands
8: 77+,AQs+,A5s,KQs,QJs,JTs,T9s,98s,87s,76s,65s,54s,AKo (8.1%) (sometimes fold weaker hands)

But remember, we can probably bluff a little more than this, but if our opponents call too often we don't need to bluff (we could if our opponents also make post flop errors) and if they fold too often we can always bluff with as many as possible. Given the possible postflop errors if our opponents fold too often we can actually play any two. If our opponents call too often we have to have sufficient pot odds and implied odds to  make up for the hands that are behind to call which means we can't really play any two without being really deep and to do so profitably will require more variance than is helpful in the early stages of tournaments. But we can play a wider range against worse opponents in general but it's also profitable to play a tighter range against loose opponents as we will get more value.

Ante stages: In the ante stages the eqution changes.
This is our value range vs what should be looser opponents:
equity to have value: 33%
1:22+,A2o+,k2o+,q2+,j2o+,T3o+,95o+,85o+,75o+,64o+,53o+ (85.5%)
2:22+,A2o+,K2o+,
3:22+,A2o+,K2o+,Q8o+,J8o+,T9o+,98o,87o,76o,A2s+,K2s+,Q2s+,J4s+,T6s+,95s+,84s+,74s+,63s+,52s+,43s (55.4%)
4:22+,A2o+,K8o+,QTo+,A2s+,K2s+,Q4s+,J8s+,T7s+96s+,85s+,74s+,63s+,53s+,43s (38.8%)
5:22+,A2o+,KTo+,QTo+,A2s+,K2s+,Q8s+,J8s+,T7s+,96s+,85s+,75s+,64s+,53s+,43s (35.1%)
6:22+,A2o+,KTo+,QJo,A2s+,K2s+,Q8s+,J8s+,T8s+,97s+,86s,76s,65s,54s (32.1%)
7:22+,A2o+,Kto+,A2s+,K4s+,Qts+,J9s+,T8s+,97s+,87s,76s,65s,54s (29.4%)
8:22+,ATo+,KTo+,A2s+,K5s+,QTs+,JTs,T9s,98s

We could probably play any two cards most of the time if we wanted to and we wouldn't have to have that wide of a preflop bluff range to do so.

value+bluffs when bluffs equal value
1:100%
2:100%
3:100%
4:77.6%
5:70.2%
6:64.2%
7:58.8%
8:39.6%


However, this doesn't quite consider how we might counter light 3betting and as a result it becomes more intricate to analyze and so we're better off  probably playing a little bit tighter.

When our opponents bet we can 3bet as well. In general, if our opponents fold often enough we can 3bet any two, if they fold or call we want to have the bottom end of our calling range (or just slightly worse) in adddition to our strongest hands. If they tend to call widely we could 3bet for thin value with suited broadway strong aces and mid pair or better.

With one opponent, when we get to the river after 3 streets of large betting we need to have trips, two pair, straights and flushes if we fold such that we force our opponent to break even on bluffs on each street. But we should be calling with most pairs and most draws and even backdoor draws on certain flops, then we need to improve to a strong pair or a pair with a draw or top pair or better and then we need to have the big hands by the river. We can probably be a little bit looser than this because our opponent should bluff more on the flop and turn than on the river. With smaller betting overpair and top pair is probably good enough to call.

The above is all solid poker fundamentals. There are two more things to consider, bluff catching vs bluff frequency.
If we arrive on the river and we have the nuts or a total bluff, we want to bluff with a frequency that will cause our opponent to break even on bluff catches. If we were to bluff any more than this, our opponent should always call and profit off doing so. If we were to bluff less than this, our opponent would never call.
Conversely, our opponent should call such that he forces our bluff to break even. If he were to call more than this we should never bluff and if he folds more than this we should always bluff.

So if we bet the pot our opponent is getting 2 to 1 on his calls. If he bluff catches he can call twice and lose and be right on the 3rd and break even. So we should make him right exactly 1/3 and we should bet with a bluff 33% of the time and with value 66% of the time.

If we bet half the pot our opponent is getting 3 to 1, we should make him right exactly 1/4 times or bluff 25% of the time, value 75% of the time.

If we bet 10 times the pot our opponent, we should bluff 10/2.
We should never bluff more than half the time unless we know our opponent folds more than he should.

Our opponent should call a pot sized bet 50% of the time, a 1/2 pot sized bet 2/3rds of the time, a 2x pot bet 1/3rd of the time a 10x pot bet 1/11th of the time, a 1/10th pot sized bet 10/11 of the time. If our opponents call less often we can profitably bluff with any two and should find ways to enter this situation more often if possible. If our opponents call more often, we should try to eliminate hands that will end up only being bluffs and we should avoid bluffing.

This is how great poker is played, by working out the perfect strategy, determining how strategy changes as frequencies are higher or lower, and knowing what it looks like so when we see an opponent call down with only a pair we know he calls one or more streets too often and we can bluff less against him and value bet more. Our profit comes from mistakes by opponents.

TOURNAMENT POKER

Tournament poker is a little bit different. Accumulating 100% of the chips does not yield 100% of the prize pool but more like 20% of the prize pool. According to some poker theorists this means that the chips we stand to win are not worth the chips we risk losing. I think the opposite is true to the degree by which you sufficiently manage to reduce your chip varience to where you aren't at risk of ruin or elimination.

This is how a positive expected value risk effects return as risk increases. This is what it looks like:
https://forexboat.com/wp-content/uploads/2015/03/Slide2-1024x576.png

We can get a better return to volatility with lower risk. Since a 10% decline requires an 11% gain to get back to even, a 20% loss requires a 25% gain to get back to even and a 90% loss requires a 1000% gain to get back to even and a 95% loss requires a 2000% gain to get back to even we want to reduce volatility if we can do so, especially since there is a minimum bet that actually increases. We can't afford the chip volatility, at least while we still have a choice. Eventually there should be some tradeoff.

We should take on as much risk as we can without reducing our edge or unnecessarily increasing our volatility. Eventually, we run out of options without taking risk and accumulating chips with no risk of ruin becomes impossible. Knowing this, there is some logic in seeking excess risk even with a negative return with the idea being that when we survive we will gain the ability to accumulate more chips for longer that will hopefully pay for the cost of the unnecessary risk when we don't survive. The chips we are able to accumulate following a double up are worth more than the chips we risk, meaning that with 60 big blinds we can accumulate chips safely at a faster rate with less risk than the alternative of not taking that risk so that it probably is worth more. A skilled player in the right structure can parlay a well timed double up into never having to be all in for the rest of the tournament! Conversely, early on in the tournament, a skilled player can parlay an increased chance of survival into significantly more chips without ever being all in and continue to grow until the blinds become say 20% of the starting stack or more. Survival is clearly super valuable early on, but when we get too short stacked the remainder of the tournament we will resort to more of a luckfest if we don't double up and if we do we can then make small constant, continuous pressure to accumulate chips. Therefore, making a just slightly a little bit too reckless bluffs and shoves and all in calls to stay above certain levels knowing that if we get caught we still have a decent chance of doubling up and once we do we will be hard to deny a final table may actually be the best strategy. It's hard to know for sure as under a certain amount of big blinds I actually think being tighter than 99% of tournament pros not named Phil Hellmuth suggest is actually correct. The chances of tripling up go up and although a top skilled player's EV increases from 40 big blinds to 80 big blinds and higher there's a certain spot as a short stack where you have no leverage and so going from 8 big blinds to 16 doesn't do you much good, but going from 6 big blinds to 4 actually does because you now have a larger side pot and leverage of opponents stack to push other players out with a chance to more than triple up with a big favorite to win if you are patient enough.Sit a pro in with 20 big blinds and he might be able to have a decent win rate. Stick one in with 10 big blinds and antes and way more hands become way more profitable. To some players this means they can't pass up any opportunity to profit but I say they should pass up more because they will get even more profitable opportunity if they don't risk elimination on only a slightly profitable shove like 98s or K6 or something.

Let's look at the kelly criterion (risk management) based strategy for accumulating chips as our stack declines and we have to creatively come up with new ways to maintain an edge without variance.

No Ante:

Above 150 Bbs you can raise 3BBs and 2/3rds pot bet 3 streets of value

100-150Bbs raise 3BBs and pot bet 2 streets of value or 3.5BBs 50% pot 3 streets of value

60-100BBs raise 3BBs and 2/3rds pot bet 2 streets of value OR 2BB 50% pot 3 streets of value

40-60BBs raise 2BBs and 2/3rds pot bet 2 streets of value Or 40% pot 3 streets

30-40BBs raise 2BBs and ½ pot bet 2 streets of value. OR 30% pot 3 streets of value

20-30BBs raise 2BBs and 40% pot bet 2 streets of value. Or 20% pot 3 streets

Antes:
80-150BBs 3bet 6BBs+2 streets of value half pot.
50-80BBs minraise+3 streets of value 55% pot down to 40%
~50BBs 3bet 2.75, Cbet steal attempt
25-50BBs minraise+2 streets of value 70% pot down to 40%
25BBs-50BBs minraise+ overbet one street 2.5x pot down to 1x pot. or check back and minraise 1 street 1.25pot down to .50 pot.
15-25BBs minraise+2 streets 40% pot down to 20% pot
12.5BBs-15BBs minraise min bet 3 streets
10BBs-12.5BBs minraise min bet 2 streets
7-10BBs minraise min bet 1 street
7-15BBs minraise steal muck if wrong 

MOVES given # of blinds:
75-50 3 bet bluff and continuation bet
35-50 bluff raise flop (no ante) after a 3BB call
35-50 3bet bluff with greater discretion and more selective 3betting
30-50 bluff raise flop (ante) after a 2BB call.
25-45 minraise flop & Cbet bluffs (ante)
25-40 check behind your backdoor draws and gutshot on the flops and bluff raise turn with low pair and some kind of draw by the turn as a semibluff. You will also be checking for pot control most of the time with good hands anyways.
20-30 Float flop wide to bluff after a minraise preflop
15-25 check back flop and float turn wider rather than bluff raise and bluff some rivers when checked to
12-25 minraise+really selective cbet bluffs. You won't be Cbetting often and when you do Cbet you will often check back the turn instead, but you can occasionally Cbet bluff if you are really selective about it.
7-30BB minraise steal attempt with no plans to continue

-----------------------------
[Ideally you never have to enter the wildly volatile strategy that risks your entire chips or even close to it but realistically you will. As such, at some stage that is way before it becomes a shovefest I believe it's acceptable to accept a wildly voltile strategy willing to risk it all once and go back to more profitable, lower risk chip accumulation. It's better to risk it all once while you have a lot of chips and can gain a lot of chips for a lot more levels of increasing blinds than have to get it all in 3 times with the best hand. A 60% favorite only has a 21.6% chance of advancing after 3 all ins]. If during volatile play you get knee capped or you decide you're better off waiting it out until conditions change you have a little bit of wiggle room left and looking to triple up rather than double up and you are more looking to protect survival with only the best cards you can wait for. Knowing the best situation you can wait for given your edge and the blind structure, I would be willing to risk it all with a hand that was As strong as I could expect 50% of the time to see at least once given the hands left. I would ideally want to adjust this for flops turns and rivers as well as preflop but you can only do what you can do.
----------------------------------------
Let's discuss the moves.
In order to bluff you have to identify someone that can fold. When that's the case you want hands just at the bottom or just below the hands that have value to call so that you either aren't giving up that much, or you aren't giving up anything at all in exchange for using them to bluff... Preflop that's probably going to be any ace, King6-King 9, Queen4-Queen 8, JT,JT suited 2 and 3 gap connectors, low suited connectors, suited K2-K5 and Q2-Q5 and J5-J8 and unsuited connectors and unsuited mid and high gappers (J9,T8,97,86) plus maybe weak broadway hands. That does NOT mean by any means to ALWAYS use these hands to bluff. But when you have these hands it's better to use them to bluff than others and you probably don't have to worry about missed opportunity as there will be plenty of opportunity to come.
So you want to look for a loose preflop raiser capable of folding to aggression and either passive or straight forward after the flop in case you get caught so you at least have some ways to win if/when you decide to.

After the flop if you are going to bluff raise you want to remove all the hands that are capable of calling except maybe the bottom end of them. That is, bottom pair, lowe pocket pair, gutshot draws. And then you are going to look for the high end of hands that you have decided to fold. Backdoor straight & flush draws, ace high with a backdoor gutshot, backdoor 3 to straight draws backdoor straight flush draws with 1 gap (45 with a 7 and the suit to a flush) and other nuances.

This is your "trickery" range. Your "trickery range" is what you are willing to use to float or bluff with IF the conditions are right but you may prefer to fold some or most of the time. Your trickery range is where you either bluff raise or call to represent something and bluff raise some percentage of turns given some specific action and specific cards. You are going to take a free card on most good draws while bluffing most longshot draws and improved to one pair and you are going to give up some cards and you are going to bluff on some scare cards as well.

You might sometimes float more widely if the opponent always Cbets and folds too often on the turn or if he never check raises the turn and has some combination of checking a lot, check/folding a high % of the time he checks, betting the flop too widely or having too many weak hands preflop that he has to get rid of somewhere after the flop.

Everything else is knowing your situation, knowing the flop, knowing your opponent, knowing what to look for and then just taking advantage of it. You should know what percentages opponents should call you and then whether they call more or less and as a result what that might look like on the flop or turn, and what your action might be on each street as a result. You should know your percentages as well

You should know the structure and identify soft spots where the ante is larger relative to the small blind such as 1/3rd the small blind and also where large increases in the amount to steal is and you should be aware of where the final table is. If the final table occurs with an average stack of 15 big blinds, you simply take the number of chips in play divided by 9 for the average chips at the final table and then divide it by 15 to get the big blind you expect. You can figure out how many you have left by paying the blinds and antes plus or minus a low varience skill edge and see where that gets you and at what point you may have to take on more risk if you fall below a certain amount of chips. You may have to work a little harder and take a little more risk at risk of volatility/survival in order to maintain enough chips if the structure is fast enough. but figure this stuff out.

You also want to know aside from calling and bluffing frequencies that you should raise with the top and bottom parts of your range and check your medium strength hand but you should occasionally vary your play. Maybe 75% of the time you bet with the value range plus some percentage of bluffs and 25% you check/call those hands (or check/fold the bluffs), you may need to check raise bluff and check raise value bet some too which complicates things a little but as long as you have a general idea of when and why to do this, that's okay. If your opponent calls too widely you don't want to bluff but you instead increase your value range.

There's probably a lot of other details to know such as adjusting to tournament structure, adjusting to the bubble, 4betting vs 3betting range, 4bet bluffing, etc and in the money considerations but I'm a little unconventional about that stuff. I like to flat call more and manage the risk even with big hands so I end up trapping but I'm really not trying to as much as I'm trying to control pot size. If you constantly do this and opponents don't see you show down a big hand and you 3bet or 4bet for the first time in forever, they're going to assume you have a good hand if they're a thinking player capable of folding and so you probably can get away with a bluff, but at what cost? I could see an argument for playing this way just before the antes or just after or in a really big tournament where you know there's a lot of poker to be played and a fairly fast structure. Maybe some percentage of the time you get knocked out but when you don't you get a lot of chips and if you show a willingness to risk it all your opponents might not 3bet you anymore unless they want action or are willing to take risk themselves. Either way, that is an informational advantage and you gain fear equity that allows you to increase your rate of stealing. So I have seen players fold 30 hands in a row that then start raising every hand and then when they get 3bet they 4bet shove with 26off and they may even do it again. Sure, it's probably an unprofitable play but if you induce enough weak/tight play and a little bit wider range willing to risk it all (you'll get paid off when you have the absolute nuts) it's worth the cost of one hand, particularly if you can get such a big stack that risk no longer is a concern and you can play a pretty much max EV strategy until your stack reduces in size or others catch up.

Appendix GTO Numbers with tournament odds

1)Defend such that opponent is indifferent to bluffing. Meaning they cannot bluff profitably with any two and you have the best hand range possible without allowing them to bluff profitably with any two. Defend=call OR raise.
2)Bet/raise such that you have equity to call a bet plus an equal amount of bluffs. Meaning that if opponent defended properly by calling and it was checked to the river you would profit more than if you folded.
3) Tournaments mean opponents shouldn't defend as much and when they do we need more equity to have value (plus some bluffs)

Defend range of 2x pot bet:
1) 33.33%
2) 18.15%
3) 12.50%
4) 9.53%
5) 7.70%
6) 6.46%
7) 5.56%
8) 4.89%

Defend range for a 1x pot bet:
1) 50%
2) 29.29%
3) 20.63%
4) 15.91%
5) 12.95%
6) 10.91%
7) 9.43%
8) 7.41%

Defend range for half pot bet:
1) 66.66%
2) 42.27%
3) 30.66%
4) 24.02%
5) 19.73%
6) 16.73%
7) 14.53%
8) 12.83%

Equity range for 2x pot bet with 1 opponent:
1) 85%
2) 44.3%
3) 26.1%
4) 14.3%
5) 13.8%
6) 9.4%
7) 8.4%
8) 7.6%


Equity range for 1x pot bet with 1 opponent:
1) 100%
2) 100%
3) 100%
4)
5) 90%
6)
7) 80%
8)


tournament odds:
Opponents don't need to force opponents to break even in tournaments since they are willing to give up chips to fold their way up the money.
So if we risk 3 to gain 1.5 our opponents can fold more often since we are really risking some multiple of 3 to gain 1.5.

.80 tournament odds:
Opponents fold 2x pot 61.53845% of the time
Opponents fold 1x pot 44.444444% of the time
Opponents fold half pot 28.57142% of the time
Opponents fold 1/3rd pot 21.05% of the time

vs this range we need the following equity when called:
2x pot: 32%
1x pot: 26.67%
half pot: 20% equity
1/3 pot: 16% equity

1
Opponents fold 2x pot 66.66667% of the time
Opponents fold 1x pot 50% of the time
Opponents fold half pot 33.33333% of the time
Opponents fold 1/3rd pot 25% of the time

vs calling range (100%- above range) we need the following equity when called:
2x pot: 40%
1x pot: 33.333%%
half pot: 25% equity
1/3 pot: 20% equity

1.2
Opponents fold 2x pot 70.58823% of the time
Opponents fold 1x pot 54.54545% of the time
Opponents fold half pot 37.5% of the time
Opponents fold 1/3rd pot 28.57142% of the time

vs calling range (100%- above range) we need the following equity when called:
2x pot: 48%
1x pot: 40%
half pot: 30% equity
1/3 pot: 24% equity

1.4
Opponents fold 2x pot 73.68421% of the time
Opponents fold 1x pot 58.333333% of the time
Opponents fold half pot 41.17647% of the time
Opponents fold 1/3rd pot 31.81818% of the time

vs calling range (100%- above range) we need the following equity when called:
2x pot: 56%
1x pot: 46.6667%
half pot: 35% equity
1/3 pot: 28% equity

1.6
Opponents fold 2x pot 76.19047% of the time
Opponents fold 1x pot 61.53846% of the time
Opponents fold half pot 44.444444% of the time
Opponents fold 1/3rd pot 34.78260% of the time

vs calling range (100%- above range) we need the following equity when called:
2x pot: 64%
1x pot: 53.3333%
half pot: 40% equity
1/3 pot: 32% equity


Preflop defense .80 tournament odds 2x pot
1)38.46%
2)21.55%
3)14.94%
4)11.43%
5)9.25%
6)7.77%
7)6.70%
8)5.89%

Preflop defense .80 tournament odds 1x pot
1)55.56%
2)33.33%
3)23.69%
4)18.35%
5)14.97%
6)12.64%
7)10.94%
8)9.64%

Preflop defense .80 tournament odds 1/2 pot
1)71.42858%
2)46.55%
3)34.14%
4)26.89%
5)22.16%
6)18.84%
7)16.39%
8)14.50%

Preflop defense 1 tournament odds 2X pot
1)33.33%
2)18.15%
3)12.50%
4)9.53%
5)7.7%
6)6.46%
7)5.56%
8)4.89%

value vs this range:
1: 22+, A2+, K3+, Q8+, J9+, Q4s+, J7s+, T7s+, 98s, 87s
2: 22+, A4+, KT+,QJ,A2s+, K8s+,Q9s+,J9s+,T8s+,98s
3: 44+,A9o+,KQo,A7s+,KTs+,QTs+,JTs
4: 55+, AT+,KQ, A8s+, KTs+,QTs+,JTs
5: 77+, AQ+, ATs+, KQs
6: 88+, AK, AQs+
7: 99+, AK, AQs+
8: TT+, AK, AQs+

value plus bluffs:
1: Any 2 (minus some bad hands)(85%)
2:22+,A2s+,K2s+,Q2s+,J2s+,T6s+,96s+,85s+,74s+,63s+,52s+,42s+,32s,A7o+,K9o+,Q9o+,J9o+,T7o+,97o+,86o+,75o+,64o+,54o,43o,32o (52%)
3:22+,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,86s+,75s+,64s+,53s+,42s+,32s,A9o+,KTo+,QTo+,J9o+,T9o,98o
(29.4%)
4:22+,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,86s+,75s+,64s+,53s+,42s+,32s,AJo+,KJo+,QJo,JTo (23.2%)
5: 44+,A9s+,K9s+,Q9s+,J8s+,T8s+,97s+,86s+,75s+,64s+,53s+,43s,32s,AQo+,KQo (16.4%)
6: 55+,A2s+,KJs+,QTs+,J9s+,T8s+,97s+,86s+,76s,65s,54s,43s,AKo (13.9%) - sometimes fold the weaker hands
7: 66+,ATs+,KQs,QJs,JTs,T8s+,98s,87s,76s,65s,54s,43s,32s,AKo (9.8%) - sometimes fold weaker hands
8: 77+,AQs+,A5s,KQs,QJs,JTs,T9s,98s,87s,76s,65s,54s,AKo (8.1%) (sometimes fold weaker hands)

Preflop defense 1 tournament odds 1x pot
1)50%
2)29.29%
3)20.63%
4)15.91%
5)12.95%
6)10.91%
7)9.43%
8)8.30%

equity to have value: 33%
1:22+,A2o+,k2o+,q2+,j2o+,T3o+,95o+,85o+,75o+,64o+,53o+ (85.5%)
2:22+,A2o+,K2o+,
3:22+,A2o+,K2o+,Q8o+,J8o+,T9o+,98o,87o,76o,A2s+,K2s+,Q2s+,J4s+,T6s+,95s+,84s+,74s+,63s+,52s+,43s (55.4%)
4:22+,A2o+,K8o+,QTo+,A2s+,K2s+,Q4s+,J8s+,T7s+96s+,85s+,74s+,63s+,53s+,43s (38.8%)
5:22+,A2o+,KTo+,QTo+,A2s+,K2s+,Q8s+,J8s+,T7s+,96s+,85s+,75s+,64s+,53s+,43s (35.1%)
6:22+,A2o+,KTo+,QJo,A2s+,K2s+,Q8s+,J8s+,T8s+,97s+,86s,76s,65s,54s (32.1%)
7:22+,A2o+,Kto+,A2s+,K4s+,Qts+,J9s+,T8s+,97s+,87s,76s,65s,54s (29.4%)
8:22+,ATo+,KTo+,A2s+,K5s+,QTs+,JTs,T9s,98s

value+bluffs
1:100%
2:100%
3:100%
4:77.6%
5:70.2%
6:64.2%
7:58.8%
8:39.6%

Preflop defense 1 tournament odds 1/2 pot
1)66.67%
2)42.26%
3)30.66%
4)24.02%
5)19.73%
6)16.73%
7)14.53%
8)12.83%

equity needed vs range: 25%



1.2
Opponents fold 2x pot 70.58823% of the time
Opponents fold 1x pot 54.54545% of the time
Opponents fold half pot 37.5% of the time


Preflop defense 1.2 tournament odds 2x pot bet
1)29.41177%
2)15.98%
3)10.96%
4)8.34%
5)6.73%
6)5.64%
7)4.85%
8)4.26%

tournament odds adjusted equity needed:48%
1:55+,A8o+,KJo+,A6s+,KTs+,QJs
2:66+,AJo+,ATs+
3:99+,AQo+,AJs+
4:TT+,AKo+, AQs
5:TT+,AKo+,AKs
6:AKs,JJ+
7:AKs,JJ+
8:JJ+

value+bluffs
1:22+,A2s+,K8s+,Q9s+,J8s+,T7s+,96s+,85s+,75s+,64s+,53s+,42s+,32s,A7o+,KTo+,QTo+,JTo,T9o  (30.9%)
2:33+,A7s+,A5s,K9s+,Q9s+,JTs,T9s,98s,87s,76s,65s,54s,43s,AJo+,KQo (16%)
3:77+,A9s+,KTs+,QTs+,JTs,AJo+,KQo (10.6%)
4:77+,ATs+,KJs+,QJs,AQo+ (7.6%)
5:66+,A9s+,KQs,QJs,AKo (7.1%)
6:99+,AQs+,AKo (4.2%)
7:99+,AQs+,AKo (4.2%)
8:TT+,AQs+,AKo (3.8%)

Preflop defense 1.2 tournament odds 1x pot bet
1)45.454545%
2)26.15%
3)18.30%
4)14.06%
5)11.42%
6)9.61%
7)8.30%
8)7.30%


tournament odds adjusted equity needed:40%
1:22+,A2o+,K2o+,Q7o+,J8o+,t9o,A2s+,K2s+,Q2s+,J6s+,T7s+,97s+,87s,76s (48.4%)
2:22+,A2o+,K9o+,QTo+,A2s+,K3s+,Q9s+,JTs+ (30%)
3:22+,A2o+,KTo+,A2s+,K9s+,QJs (24.6%)
4:22+,A9o+,Kjo+,A2s+,KTs+ (16.7%)
5:22+,ATo+,KQo+,A9s+,KJs+ (12.5%)
6:33+,AJo+,ATs+,KQs (9.7%)
7:66+,AQo+,AJs+,KQs (7.1%)
8:88+,Aqo+,Ajs+ (5.9%)

value+bluffs
1:96.8%
2:60%
3:49.2%
4:33.4%
5:25%
6:19.4%
7:14.2%
8:11.8%


Preflop defense 1.2 tournament odds half pot bet
1)62.5%
2)38.76%
3)27.89%
4)21.75%
5)17.81%
6)15.08%
7)13.07%
8)11.54%
tournament odds adjusted equity needed:30%


Preflop defense 1.4 tournament odds 2x pot
1)26.31579
2)14.00%
3)9.68%
4)7.35%
5)5.92%
6)4.96%
7)4.27%
8)3.75%
tournament odds adjusted equity needed:56%

value
1:99+,AJ+,ATs+ (6.6%)
2:JJ+,AKo,AQs+ (3.3%)
3:JJ+,AKo,AKs (3%
4:QQ+,[AKs] (1.4%/1.7%)
5:QQ+ (1.4%)
6:QQ+ (1.4%)
7:QQ+ (1.4%)
8:QQ+ (1.4%)

value+bluffs
1:13.2%
2:6.6%
3:6%
4:2.8%/3.4%
5:2.8%
6:2.8%
7:2.8%
8:2.8%

Preflop defense 1.4 tournament odds 1x pot
1)41.6666667
2)23.62%
3)16.45%
4)12.61%
5)10.22%
6)8.59%
7)7.41%
8)6.52%

value
1:22+,A2o+,K9o+,QJo,A2s+,K7s+,Q9s+,JTs
2:55+,A9o+,KJo+,A5s,A7s+,KTs
3:77+,ATo+,KQo,A9s+,KQs
4:88+,AJo+,AJs+
5:99+,AQo+,AJs+
6:TTo+,AQo+,AQs+
7:TT+,AK,AQs+
8:TT+,AKo,AKs

value+bluffs
1:55.8%
2:27.2%
3:20%
4:13.6%
5:10.8%
6:9.4%
7:7.6%
8:7%


tournament odds adjusted equity needed:46.67%



Preflop defense 1.4 tournament odds half pot
1)58.82o353
2)35.83%
3)25.60%
4)19.89%
5)16.26%
6)13.75%
7)11.91%
8)10.50%

tournament odds adjusted equity needed:35%

J72 flop

Preflop defense 1.6 tournament odds 2x pot
1)23.80953
2)12.71%
3)8.67%
4)6.57%
5)5.29%
6)4.43%
7)3.81%
8)3.34%

tournament odds adjusted equity needed:64%
-
tournament odds adjusted equity needed:53.3%
Preflop defense 1.6 tournament odds 1x pot
1)38.46154
2)21.55%
3)14.94%
4)11.43%
5)9.25%
6)7.77%
7)6.70%
8)5.89%

tournament odds adjusted equity needed:53.3%

1:77+,A9o+,A8s+,KJs+
2:
3:
4:TT+,AKo+,AQs+
5:
6:
7:
8:JJ+

1:21.2%
2:
3:
4:7.6%
5:
6:
7:
8:3.6%



Preflop defense 1.6 tournament odds half pot
1)55.56%
2)33.33%
3)23.69%
4)18.35%
5)14.97%
6)12.64%
7)10.94%
8)9.64%

tournament odds adjusted equity needed:40%

Equity range for pot bet:

Equity range for half pot bet:



Flop equity vs
15%
with 60%
on J72
half pot bet
Aq+, AT, 22+,
23.7% with value
45% including bluffs


---------
Tournament odds divided by bubble factor equals your tournament odds.
pot odds/bubble factor=tournament odds
Bubble factor of 1.6
pot odds of 1.3125
Tournament odds of 1.3125/1.6=.8203125