Poker Math How-To: Optimal Bluffing Frequency
In a no-limit texas hold'em hand, you are first to act with the river card about to come with $100 behind and the pot after the turn is $200 (our single opponent has us covered). You hold T:c: 8:c: on a board of J:c: 9:c: 5:d: 2:s: and your opponent holds T :d: T:h:. Quite obviously we're value-shoving our $100 when a Q, 7 or club falls on the river, but how often should we bluff the river for optimal play?
First we need to define what we mean by optimal play. When we play optimally in general, there is no way our opponent can exploit our play. In the described scenario above, our opponent will have two choices at his disposal: to call our bet, or to fold. Our goal is to make both of these options have the same EV, in which case he will have no exploitive option. Our lives are made easier by the simple fact that the EV of folding is always 0. So now we have to figure out how often we should be bluffing so that the EV of him calling is also 0.
From our villain's point of view, he will be needing to call $100 in a pot of $300 after we shove the river, getting 3:1 odds. If we are bluffing more often than 25%, he should call since his 3:1 odds will pull a profit on a call. If we are bluffing less often than 25%, he should fold since his 3:1 odds will pull a loss on a call. But what if we bluff exactly 25% of the time? Then a call is breakeven. Zing!
There are 15 cards (nine clubs, 3 more queens and 3 more sevens) that make our hand. If before the river comes we pick out 5 distinct cards (that aren't a club, a queen, or a seven) that we'll bluff on, then we will be bluffing exactly 25% of the time, and our river betting will not be exploitable.
Re: Poker Math How-To: Optimal Bluffing Frequency
Quote:
Originally Posted by spoonitnow
In a no-limit texas hold'em hand, you are first to act with the river card about to come with $100 behind and the pot after the turn is $200 (our single opponent has us covered). You hold T:c: 8:c: on a board of J:c: 9:c: 5:d: 2:s: and your opponent holds T :d: T:h:. Quite obviously we're value-shoving our $100 when a Q, 7 or club falls on the river, but how often should we bluff the river for optimal play?
First we need to define what we mean by optimal play. When we play optimally in general, there is no way our opponent can exploit our play. In the described scenario above, our opponent will have two choices at his disposal: to call our bet, or to fold. Our goal is to make both of these options have the same EV, in which case he will have no exploitive option. Our lives are made easier by the simple fact that the EV of folding is always 0. So now we have to figure out how often we should be bluffing so that the EV of him calling is also 0.
From our villain's point of view, he will be needing to call $100 in a pot of $300 after we shove the river, getting 3:1 odds. If we are bluffing more often than 25%, he should call since his 3:1 odds will pull a profit on a call. If we are bluffing less often than 25%, he should fold since his 3:1 odds will pull a loss on a call. But what if we bluff exactly 25% of the time? Then a call is breakeven. Zing!
There are 15 cards (nine clubs, 3 more queens and 3 more sevens) that make our hand. If before the river comes we pick out 5 distinct cards (that aren't a club, a queen, or a seven) that we'll bluff on, then we will be bluffing exactly 25% of the time, and our river betting will not be exploitable.
Game theory
Sklansky: Theory of poker
calculate odds you give your opponent on call (example 3-1)
use same ratio in bluffing (example 15outs - 5bluffing cards or 3-1)
adjust on the lower for calling stations, on the higher for nits
choose your bluffing cards before they appear so your bluffing is in fact random
Re: Poker Math How-To: Optimal Bluffing Frequency
Quote:
Originally Posted by asdpikas
Game theory
Sklansky: Theory of poker
calculate odds you give your opponent on call (example 3-1)
use same ratio in bluffing (example 15outs - 5bluffing cards or 3-1)
adjust on the lower for calling stations, on the higher for nits
choose your bluffing cards before they appear so your bluffing is in fact random
