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01-09-2022 , 09:02 AM

eenvis

old hand

Join Date: Jan 2014 Posts: 1,340

Heads up pot betting 1 into pot = 1, opponent will need to defend 50% of the time to reach MDF.
How is the fold equity being split in a 2way or 3way pot vs the same betsize?

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01-09-2022 , 09:14 AM

ZKesic

veteran

Join Date: Jan 2014 Posts: 2,089

When you bet pot size, your bet should "go through" (everyone folds) 50% of the time. Each one of your opponents will therefore fold more than 70% of the time on average.

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01-09-2022 , 10:06 AM

eenvis

old hand

Join Date: Jan 2014 Posts: 1,340

What's the equation?

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01-09-2022 , 10:19 AM

CallMeVernon

COTM Crusher

Join Date: Jun 2010 Posts: 4,086

The answer I think you are looking for is this: ALL the calling (at least with pure bluff catchers) is supposed to be done by the player closing the action.

Awhile ago I solved a toy game that shows what I think you’re asking. Let’s say one player bets pot on the river with a polarized range, into 2 players with the same range as each other. The one who is first to act will fold 100% of the time at equilibrium, and the one last to act will call 50% of the time to reach MDF.

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01-09-2022 , 10:53 AM

tombos21

veteran

Join Date: Sep 2018 Posts: 2,044

A pot-sized bluff needs to work 50% of the time. That means the total folding frequency of all players needs to multiply to 50%.

player1 fold% x player2 fold% = 50%

If both players equally share the burden of defense, then simply take the square root of 50% to find the individual folding frequencies

player1 folds 70.7%.
Player 2 folds 70.7%.

For three players you'd take the cube root, for 4 players you'd take the 4th root and so on.

Now in practice, the burden of defence is not shared equally. Typically the last player to act will defend wider than the first player to act.

Here's an excerpt from modern poker theory that might help:

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01-10-2022 , 02:52 PM

Fast Fold Poker

journeyman

Join Date: Sep 2021 Posts: 235

Quote:

Originally Posted by CallMeVernon

Turning this around somewhat, should the first player bet a slightly stronger range given that he has two players still to act that could call him, as from what you are suggesting he can just bet the same range of value and air if he has one opponent left to act, as he does if he has two opponents left to act. I guess this is also the same if he has 3 players left to act, namely the first two players fold 100% and the third player calls 50% of the time?

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01-10-2022 , 03:20 PM

CallMeVernon

COTM Crusher

Join Date: Jun 2010 Posts: 4,086

So one of the premises of the game I solved is that the two potential callers have identical ranges, and none of that range beats the bettor’s value range.

In real life, I think that we should not expect this to be the case. But the real lessons are:

1. If the bettor expects that their value range beats all of the other players’ ranges, the value/bluff ratio is not supposed to change at equilibrium.

2. If you are thinking of calling a river bet with a bluff catcher, you should not do it when there is someone else behind you (in theory).

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01-10-2022 , 04:09 PM

Fast Fold Poker

journeyman

Join Date: Sep 2021 Posts: 235

Quote:

Originally Posted by CallMeVernon

Number 2 is interesting because sometimes the player before you calls with a bluffcatcher that they shouldn't have done as you were still to act, and this causes you to fold a better bluff catcher than them in the process. Very frustrating when your bluffcatcher would have won the pot on that occasion.

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