Theory: Hands where ICM doesn't work

[SitNGo Wizard]

The actual simulation of each future game is fairly simplified. It only considers the possibility of each player pushing all-in and another player calling the all-in bet. It does not consider pre-flop limps or raises or any post-flop decisions.

The simulation starts with the first player to act. Based on opponent modeling, the Wizard computes the probability that the first player will push all-in. Then the Wizard then computes the probability that each of the remaining players will call the first player's push. Each call creates a showdown and the equity from each showdown is computed. When nobody calls the first player's push, he picks up the blinds.

The simulation repeats the procedure for each player in the hand; each player pushes and each remaining player calls or folds. The equity from all of the outcomes is summed up to produce the total equity of the future game.

The opponent model you choose for each player determines the push/call ranges for each opponent. You cannot adjust a particular hand range in a future game, but the opponent model gives you some control over how loose or tight a player will be.

If the total probability an outcome of a future game is greater than about 1%, another future game simulation is created for that outcome. It is possible to have several levels of nested future games.

The Wizard provides a future game browser so you can see exactly how each future game is constructed. The FGS beta is included in the latest release.

I will try to answer your specific hand questions in the next post. You asked a lot of questions, so if I missed something please ask again.

[SitNGo Wizard]

[ QUOTE ]
From my last two hands, let's back up 4 hands and see how it looked then.

Blinds 200/400
CO 4000, folds
BN 1000, folds
SB 7300, pushes
BB 1200.

Hero is in the BB. What range should hero call with?

[/ QUOTE ]

Without FGS, the Wizard suggest calling with top 35%. With FGS, the call range drops to about 12%. Honestly, I am not if this is correct. I need to look into the details some more.

Adding 1 chip to hero’s stack makes almost no difference. I see where you are going with this, but it takes 8 games into the future before the 1 extra chip makes a difference. By that time the probability of that game happening is so low it is insignificant. The Wizard stopped creating future games way before this.

[marand]

[ QUOTE ]
[ QUOTE ]
From my last two hands, let's back up 4 hands and see how it looked then.

Blinds 200/400
CO 4000, folds
BN 1000, folds
SB 7300, pushes
BB 1200.

Hero is in the BB. What range should hero call with?

[/ QUOTE ]

Without FGS, the Wizard suggest calling with top 35%. With FGS, the call range drops to about 12%. Honestly, I am not if this is correct. I need to look into the details some more.

Adding 1 chip to hero’s stack makes almost no difference. I see where you are going with this, but it takes 8 games into the future before the 1 extra chip makes a difference. By that time the probability of that game happening is so low it is insignificant. The Wizard stopped creating future games way before this.

[/ QUOTE ]

Thanks for your reply.

This hand is just 4 hands away from the scenario where we have:

CO 3400
BN 400
SB 9100
BB 600

Most of the time the big stack will push and steal the blinds. You said that FGS only calculates branches that are 1% likely to happen. I would guess that from:
4000, 1000, 7300, 1200 we will get to 3400, 400, 9100, 600 quite often.

I think 12% calling range must be wrong in the situation where we have 1200 chips. The correct answer should logically be higher than what ICM would suggest.

Perhaps this problem is caused by the opponent modeling not giving the different scenarios realistic probabilities?

For example the big stack will push close to 100% from all positions. The 4000 stack will only call with monsters like JJ+. If the two short stacks would only call 12% of the time in the BB then after 4 hands we would the majority of the time reach the 3400, 400, 9100, 600 hand.

Let's look at a sample hand. The scenario when we fold our BB in the last hand. We reach the following situation:

CO 1000
BTN 7700
SB 800
BB 4000

According to the opponent modeling / FGS.
What range does CO push with?
What range does BTN push with if CO folds?
If BTN pushes, what range does BB call with?

Anyway, sorry to bug you with all these questions. Just think this FGS seems like a promising idea if the bugs can be sorted out. Keep up the good work.

[SitNGo Wizard]

Sorry for the delay in responding, but I am still looking into the previous hand. I think the 12% range is wrong, but I am not sure why yet. I will try to reply when I have an answer.

[marand]

[ QUOTE ]
Sorry for the delay in responding, but I am still looking into the previous hand. I think the 12% range is wrong, but I am not sure why yet. I will try to reply when I have an answer.

[/ QUOTE ]

No worries. Looking forward to the results.