The game at the ICM stage is often considered boring and overly mechanical, but this could not be further from the truth! The influence of ICM creates the most interesting strategic situations in poker. At one time, it was they who made such an impression on me that I plunged headlong into working on the theory.

In this article, you will see several not always intuitive situations in which it is optimal to fold aces (or it is prohibited to fold ). They were the first step for me on the path to learning poker.

Fold aces in a satellite

The most famous scenario and not news to most of you. ICM pressure is especially strong in satellites and often results in players having to fold aces preflop. If the prize for advancing in a satellite has nothing to do with your final stack and if you are guaranteed to earn the seat, there is simply no reason to risk chips. The one who finishes the game with 99% of all chips and the one who has only one ante left will receive exactly the same winnings.

Let's run a simulation: five players compete for four exit spots of equal value. Blinds 500/1,000. If the hijack player is all-in, what range would you call with in the cutoff?

Clearly, this is a trick question, because you don’t have a calling range. You should be folding 100% of your hands because you have a comfortable lead over three players, one of whom is likely to bust before you run out of chips, especially as the blinds increase in the future. Aces should also be folded.

Below are GTO ranges: pushing for hijack and calling from the rest:

As you can see, even the player on the button, whose stack is half the size of the cutoff, must also fold everything, since he is ahead of the two players in the blinds.

Bubble factor for all tournament players:

The bubble factor of the cutoff against the hijack is 26.55, that is, the equity for calling should be at least 96%. Even aces aren't that strong! Hijack can show you A6o and fold with aces will still be correct for you.

There's a simple heuristic that can help you roughly determine whether you're guaranteed to pass or not: If there are as many or more players between you and the last place to go than you need to bust to qualify for the money, you can probably fold to the bitter end.

For example, 10 people are fighting for six satellite seats:

Player 3 can fold aces to a deep stack shove since he is four spots above the bubble. Players 10, 9, 8, and 7 are outside the bubble, and players 6, 5, and 4 are inside the bubble but must step up before player 3 has to take a chance.

Player 5 is not in the most comfortable position, since he is only two places inside the bubble, and players 10, 9, 8, 7, and 6, forced to take active action, can bypass him.

Another spot in the satellite

You probably answered correctly in the previous example, let's move on. Three players fight for the two opening spots. The button is the chip leader with 50,000 chips, the blinds have 5,000 chips at 500/1,000.

In the previous example, the chip leader pushed 76.3% of hands. What should the button's pushing range be now?

Pushing 100% is the wrong answer. It is believed that a big stack must be aggressive, but the optimal strategy, according to the solver, would be to fold 100% of hands. The reason lies in the strategy of the players in the blinds after the button folds.

Left one on one, they are obliged to stack very widely due to the low bubble factor:

Calling the chip leader's all-in would be a disaster: with a bubble factor of 2.91, you need 74% equity to call, but against each other, they play almost ChipEV, with a bubble factor of 1.03. Since the chip leader is practically guaranteed to win, the players in the blinds can be said to play heads-up among themselves. All-ins from the chip leader in such a situation only delay the tournament.

Unique re-push range – any Ace

The next example is more entertaining. We're on the bubble, five prizes. Player stacks:

When the action fols to the hijack, according to GTO he must push all hands. What happens if he mixes it up and opens with a min-raise with TT+ AJs+ and AQo+, but shoves everything else? What should the button's re-push range be in response to a min-raise?

I'll just show you the matrix:

This is one of the strangest ranges I've come across, but it's correct, I've checked with different solvers. Re-push – strictly and nothing more. Even kings are no good, but A2o is a small plus. That's the power of blockers!

The solution, as usual, is in the bubble factor:

For a hijack against the button, it is 4.08, meaning 80% is required to call. Only one hand has that much equity – aces. This is why having an ace on the button is so effective – it guarantees that we will get a lot of folds, and fold equity outweighs even naked equity .

Since fold equity under the influence of ICM becomes the most valuable form of equity, in the later stages of satellites it is best to play all-ins so as not to put yourself in the position of calling someone else's all-in.

Fold Aces in mystery bounty

The last example in our article is related to the rapidly growing Mystery Bounty format. From reading about progressive knockouts, you know that the bubble factor in bounty tournaments often drops below one, and calling ranges become very wide.

There is one key difference in Mystery Bounty: you can receive a bounty not from the first hand of the tournament, but only from a certain moment. In live tournaments – from the second day or some time after the end of late registration, in online – usually after entering the money.

Let's imagine the following situation. We are playing a Mystery Bounty tournament, in which bounties are given out only in the money. There is a bubble, one person is left to the money. We have the biggest stack on our table. The player on UTG has 2bb on his stack and is pushing. We are in the BB, we have aces. Everyone folds before us.

However, at the same time, on another table, a player put a 3bb all-in and received a call from all opponents. In this case, the best decision with your aces is to fold! Two blinds will not affect your chip leader stack; you are guaranteed to get into the money in any case. And if the short stack on another table busts, the tournament will go into the money, and the short stack on your table will be in the BB in the next hand. As a chip leader, you can push him all in on a very wide range and have a high probability of getting called, and with it the chance to win a bounty.

I will illustrate this with the following simulation. Let's take a one-dollar tournament for 90 people with the PokerStars structure. 14 left, 13 in the money. UTG pushes 2bb, everyone folds to BB with 60 blinds.

Calling, of course, is positive with any cards. Expectations from a call:

Even calling with 72o earns you 0.11% of the table's chips or \$0.06. Calling with aces pays 0.82% or \$0.41.

But let’s say that we folded the cards, and after the elimination, the bounty stage began on another table. New simulation – \$1.50 Mystery Bounty, where \$0.50 entry goes into the bounty prize pool. Since we don't know the prize for a knockout until we knock out our opponent, EV needs to be averaged out. There are 13 players left in the 90-person tournament, which means the average bounty is \$3.12.

In such tournaments, the game before and after the money is very different. Before the money, an almost normal tournament is played. Yes, there is a slight difference, since Mystery Bounty increases the profit from entering prizes, but it does not compare to how you need to play in the final stage.

The short stack, whose push we folded the aces to, moved to the BB with a stack of 4.2 bb. We are in the small blind with 59bb, and if everyone folds before us, we will shove any hand and will always get called.

Expectations from pushing (as a % of table equity):

72o now brings us more than aces just one hand ago! And aces now give as much as 4.11% of table equity, \$2.92 – almost three buy-ins! So, folding aces on the bubble prepared us for a much more profitable situation. I purposely gave us a chip lead stack to discourage other players from entering the pot, but even if they dare, it will give us additional opportunities to enter a multiway pot or isolate raise.

Modern ICM calculators cannot calculate this situation – they do not know how to take into account format changes. When choosing a strategy in such situations, we still have to rely on our own brains.