## More comments on Pot odds & Bluffing frequency

on March 12th, 2011 at 3:17 pmPosted In: Uncategorized

I’m uploading slides that were used in the Mar 3rd presentation.

I’ll also add some comments to discuss issues in them.

*pdf: poker

Principles of Knowledge Engineering and Reconstruction

In page 6, the odds of making the flush are “4.22 to 1″ (9 of the 47 unseen cards) because when we compute odds, we compare the number of ‘the card does not make the flush’ to ‘the card does make the flush’, not to ‘the total number of cards.’

So, the odds of making the flush are ’38 to 9′, not ’47 to 9′.

In bluffing frequency, I’ll once again define bluffing in our case.

“Bluffing is betting without holding the best hand”.

So for example, let us say that you’re holding the full house. Thus, of course you did not fold this game. But if someone happened to hold the straight flush, then we say you were bluffing.

In page 16, I think we should know about the concepts of semi-bluff and pure-bluff.

Let say there are total 6 players including yourself, and in the final round, you have no hand (you don’t even have a single pair). So you bluffed. In order for you to win this game, all 5 of your opponents should fold which is very unlikely. This is called ‘pure-bluff’. Let say two of your opponents were fooled by your bluff and they folded. Even so, you lose this game.

Now let say you were holding two pairs. But you somehow know that you are not holding the best hand. You have the second-best hand, and you made a bet. This is still a bluff since someone else was holding the best hand. Again, two of your opponents folded, and If one of them had the best hand, you win this game. This is called ‘semi-bluff’. You made a bet even though you knew your hand was not the best (so this is a bluff), but your hand has some value, so you don’t have to fool all of your opponents.

So, in this table, bluffing frequency ‘b’ is increased when the probability ‘p’ increases. ‘p’ is the probability that your hand is the best hand in this game. So you may think this as a ‘value of your hand’. Let say, for example, ‘three of a kind’ has a 60% of a winning chance. According to this table, your bluffing frequency is 75%. If your ‘three of a kind’ is the best hand (60%), then you bet and you win. If your ‘three of a kind’ was not the best hand (40%), you still want to make a bet (75% of in this situation) even if you somehow knew that your hand was not the best since you don’t have to fool all of your opponents, and there’s more chance to win this game by bluffing.

If your hand has 0% of winning chance, yes you still can bluff, but it’s not worth your money spending for the extra betting (it’s a pot sized bet!) since it’s really really hard to fool all five of your opponents.

I think this scenario may not always true when the number of the players is only two. And I do think that the equation should reflect more variables (such as # of players). I think the author was trying to mathematize Sklansky’s words in his book, so it’s not a good idea to directly use this equation, but it explains the value of the semi-bluff and the value of computing the pot and bet size before making decisions.

What you describe isn’t what people usually mean by “semi-bluff”. It is when you bet when you believe you do not have the best hand, but you have a strong draw. The odds of hitting the draw aren’t enough to justify a bet (i.e., if there’s one other player, you have less that even chance of being ahead by the river), but when you factor in the chances the opponent will fold to the bluff, and the implied odds opportunity of making a bigger pot if the opponent calls and you hit the draw, the semi-bluff has positive expected value. (Here’s Wikipedia’s definition, which is more or less consistent with mine.)

The closest name for what you describe is a “squeeze” play. When there are 3 players left, and you are first to act. You have a good enough read to believe player 2 is strongest, player 3 is very weak, but player 2 doesn’t know that. So, you bet. Player 2 folds because he is worried about player 3, and player 3 is too weak to call. Such a bet requires a very good read on both opponents.