How wrong is ICM in Poker Tournaments?

Everyone knows ICM makes certain assumptions that are probably not true.
How wrong is it?

Very.

There's 2 things you need to know about poker tournaments.
1 is how fast you need to earn money to avoid all ins.
2 is how opponents would play if they adjusted a varient of GTO for the tournament odds.

Here is a variant of GTO. It assumes that it isn't worth even defending often enough to force opponent to break even as gaining chips isn't important as avoiding risk according to ICM. It also isn't worth raising very often either
For instance, rather than forcing opponent to break even in chips on bluffs, opponents should choose to force opponent to break even on reward relative to risk. The problem with this logic is risk is not linear and skill advantages can be gained as players adapt to ICM which assumes players have no skill advantage. Survival is important but risking a small percentage of your stack to gain a chip advantage or prevent opponent from getting one is worth a tradeoff. However,, risking a medium or large amount perhaps is not. ICM doesn't account for the fact that the chips you gain are only worth less than the chips you risk if the level of risk threatens your probability of survival proportionally. It does not. Many other assumptions are very far off. This is a modified GTO as described.
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+ (1.4%%)
5:QQ+ (1.4%)
6:QQ+ (1.4%)
7:QQ+ (1.4%)
8:QQ+ (1.4%)

bluff+value:
1:13.2%
2:6.6%
3:6%
4:2.8%
5:2.8%
6:2.8%
7:2.8%
8:2.8%

ICM assumes equal skill, but if everyone according to ICM they would no longer be of equal skill but instead of very different skill. If no one can call an under the gun raise of 2 times whatever is in the middle without the top 3.75% of hands, the raiser will succeed 73.66%. In fact, that is the expected success rate of a steal attempt from any position. A player who raises EVERY time it folds to him will may risk 3 to win 1.5 and that 1.5 may be worth substantially less according to ICM, such that according to ICM his opponents are forcing him to break even, but according to actual chips he wins about 2.84 big blinds per rotation. When the antes get involved if you risk 4.4 to win 2.2 you will win 4.16 big blinds per rotation on average. It may not always fold to you, but given the very tight hand ranges based upon the above, it will a LOT.If we assume a steady skill level equivalent, that is enough to win the WSOP main event without ever dipping below 60 big blinds. In other words, you will win close to 100% of the time if opponent allowed such easy stealing, especially when you add to the fact some ability to continue on good flops in small pots. That's how bad the assumption of "equal skill" and "risk applied evenly regardless of what percentage of chips you risk."

Conversely, even if you have aces and you risk it all again and again and opponents call you, your chances of elimination approach 100% as the field gets infinitely large.



So the ICM is disastrously bad.

Stealing every hand and avoiding big pots altogether isn't realistic, and with faster blind structures you need to gain chips much faster to avoid dipping below say 20 big blinds where stealing becomes increasingly exploitable to resteal shoves and even steal attempts risk chip volatility that can limit you to all in or fold. So some level of risk may have to be taken but if you can avoid it, how aggressive can you be with good hands?
How much equity do you need for 4bets, 3bets, and 4x raises and minraising at various blind levels?

To understand at what point raising actually produces NEGATIVE long term return we must determine kelly criterion breaking points.

That amount is 2x the kelly. In some situations, your kelly % is so high already that 2x kelly would put you at 100%. In those instances, you actually could go broke risking 2x the kelly but you could risk very close to 100% without a negative long term return or risk of (effective) ruin. Unfortunately that assumes chips are infinitely divisible which isn't the case. But given we are only risking a single buy in, we can still say it probably isn't a mistake to risk 2x the kelly or less especially since the action and speed of blinds may force everyone to take risks eventually. At some phase of the tournament you will trade risk of ruin for probability of higher finishes.

You may still call an all in risking more than 2x kelly, but understand ideally you wouldn't ever exceed 1x kelly. If you had 50% chance of a 1.16 to 1 payout, or 50% equity, you could risk up to 14.28% of your chipstack before it turned against you. That means a 9 big blind bet would not be acceptable at under 63 big blinds without more equity or some chance of opponent folding preflop.

http://www.albionresearch.com/kelly/

It's possible to create a more advanced kelly criterion having a full decision tree of possible outcomes and their reward as a percentage of our starting stack with a probability of that occuring but that is more advanced than I care to do at the time.

I want you to notice how limited your options get as you get shorter stacked. That creates a bizarre scenario whereby in a field of players that obey this, someone who takes risk and correctly anticipates everyone tightening up and is able to accumulate a large stack himself or herself, will get such an advantage that it may be worth some risk of ruin to at least some percentage of the time have enough chips to maintain a positive expected return over an extended period of time.

The nature of tournaments is very very unusual in this regard because at the same time, passing up positive EV is correct more so than ICM suggests due to opportunity costs.
However, passing up any positive EV scenario that is also less than 2x the kelly and probably 1x the kelly and definitely some fraction of the kelly is probably a big mistake.

So Tournament poker is both solvable and unsolvable. We can solve ICM (stupid) we can even solve a theoretical risk % in certain situations based upon assumptions on our opponents, but if our opponents react a certain way there is an infinite series of counter strategies and always different incentives for different players that in turn create different strategies and constantly adapting players based upon how others adapt.

Minraising and folding to reraises becomes acceptable down to 5 big blinds as long as you have a 60% chance of about a 1:1 payment, although you ideally want to only risk half that which means 10 big blinds. If you only have a 55% chance of success you can minraise fold at 10 big blinds, although you ideally would seek to do so down to 20 big blinds. If you could limp in and have it checked to the river, you could do so down to 5 big blinds if you were 55% to win vs one other caller but ideally 10 big blinds. With 3 big blinds you could limp in and check it down all the way down to 2.5 big blinds but ideally 5 if you had 60% chance of winning.
Of course there are always other options and different ways to try to play.
It's tricky to suggest a 3bet strategy without reworking a lot of the numbers.
But if we wanted to raise over a few limpers and risk 5.2, we could do it down to 25 big blinds with a 55% chance of success or more and down to 13 big blinds with 60% chance of success. But ideally  we down to 50 big blinds with a 55% chance of success and 25 big blinds with a 60% chance of success.

3bets could be worked out if the goal was to win preflop, but we would need a very high success rate realistically speaking. In most cases 3bets are met with calls, however 3bet plus Cbet works a fairly high percentage of the time but takes a lot more risk, risks potential 4bets and you still will get called or raised on the flop. When you are called on the flop you may still win but a large percentage of the time it will require you to call at least one other bet. This makes looking at risk management strategies very difficult.
But it can be done.

If we look at a 9BB 3bet plus a 9.75 Cbet and we think our opponent will fold preflop 40% of the time, will raise us off our hand 10% of the time, then fold on the flop 20% of the time, raise us on the flop 10% of the time, will call and make one more bet on the river which we win 8% of the time (and lose 2% of the time), and bet on the river forces us to fold 5% of the time whereas 5% of the time we check it down and win and 2% of the time we lose another big bet... we can actually determine that risking 25% of our chipstack on this series of plays (considering 18.75 big blinds as a full bet)
This means we can make this play ideally with 75 big blinds but still probably fairely safely with 37.5 big blinds. If we instead 3bet 7.5 and risk 16.5 total then we can try it down to 66 big blinds and really down to 33 big blinds. In reality the chances of success should go up slightly as our opponents also get shorter stacked and have more to lose but if i change the assumptions about how often anything happens on any street it changes the results.

If you get creative you can probably find ways to accumulate chips without big risks. You may prefer to limp raise 3bet 12 big blinds with a large percentage of your limp in hands when you have a big stack or face opponents who have a small stack to discourage raising over your limp ins so that you can limp in frequently later on. Limping in creates really small multiway pots and few people know how to play multiway correctly because it's too nuanced for most people to really know how strong of hand they need. You may find ways to keep betting really small.

ALthough your bets after the flop are very correlated to bets and hand ranges before the flop, one way to approach postflop is first start preflop with profitable steal attempts and if you are called then you can treat each decision separately. FOr instance, if you have risked 5% of your chip stack preflop, assume those chips are gone and make decisions based upon how much you have in front of you. So if you had 50 big blinds and now raised 2.5 big blinds and got called and you now have 47.5 big blinds left, if you want to place a pot sized bet of say 7 big blinds that represents nearly 15% of your stack so you need a more than 55% and less than 60% chance of success ideally, but 55% and even less than 55% is acceptable, particularly if opponent calls a and may check additional streets rather than raises. If you risk less than the pot you can do so with a lower chance of success and still avoid unnecessary risk of ruin. You may allow more bad beats by betting less or checking but you also invite bluffs and manage risks.

You may choose to play a little bit more like a limit player in tournament in terms of bet sizing. Keep the bet small on every street. The problem is you may get raised and you may have to play a big pot or you may have to take a stand or change your strategy. There is a reason Helmuth and Negreanu have so much tournament success. They one way or another do unconventional things to manage risks. People say minraise folding is horrible and exploitable but as long as they can find weak enough opponents and have strong enough hands it's fine. They say limping under 12 big blinds is silly and yet Negreanu will limp down to 7 big blinds looking for a spot postflop to get his money in or take down the pot on a semibluff. In some environments he may be able to check to the river and get paid or even minbet on the river and get paid off with a small pair or jam when he hits and get paid off as well. THe important thing is he doesn't subscribe to risk his tournament life just because it is plus EV. and even as a short stack they still find a way to preserve and even grow their chipstack. THe blinds may rise faster than they can grow their stack, but if they grow their stack grow their stack and either double up plus a nice premium of antes and blinds or go bust They will have grown their stack to ssuch a larger amount a high percentage of the time that they don't need to double up as often as everyone else. True, some players would prefer doubling up or going home or taking down enough blinds while risking their life multiple times and when they do win they'll have a big stack of chips, but repeated all in risks eventually have an enormous proobability of a bustout and unless they can convert chipstacks into wins a very high percentage of the time it isn't necessarily better. If Negreanu or Helmuth double up they can continue to accumulate chips and if they happen to double up quickly enough twice in a row they will immediately accelerate their rate of chip accumulation.



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Kelly based bets vs 100% calling station or calls vs 100% betting station.
2.2+2.2+2.2=
6.6 flop
13.2 turn
26.4 river
52.8 after river betting.
2.2+3.3+6.6+13.2=25.3 risk
27.5 reward.

Vs 100% calling station or if you call down 100% aggro
Full Kelly
Pot preflop half pot postflop
1.087 to 1
54%
11.68% 216BBs /108
57%
17.4% 145BBs /72.5
60%
23.2% 109BBs/54.5
65%
32.8% 77/38.5
70%
42.4% 60/30
80%
61.6% 41/20.5
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2/3 streets or float plus check to induce bluffs or one stab at the pot with equal mixture value+bluffs.

2.2+3.3+6.6=12.1 risk
14.3 reward
1.1818181 to 1
52%
11.38% 106/53
54%
15.08% 80/40

57%
20.62 58.6/29.3

60%
26.15% 46/23

65%
35.38% 34/17

70%
44.62% 27/13.5

80%
63.08% 19.2/9.6
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1/3 streets check dry flop bet turn check river or bet flop and give up.

2.2+3.3=5.5 risk
7.4 reward
1.4 to 1

48%
10.86% 50.6/25.3

52%
17.71% 31/15.5

54%
21.14% 26/13

57%
26.29% 21/10.5

60%
31.43% 17.5/8.75

65%
40% 13.75/6.875

70%
48.57% 11.3/5.7

80%
65.71% 8.4/4.2
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Repeat for pot sized bets and other decisions. Build tournament strategy that you can test based upon structure va others such as trying to double up to preserve utility vs trying to preserve life maximally vs some balance.
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