Posted by Dr Fro 9:31 PM
The river brought a 7, improving my trips to quads, beating Bear's flush (Queen high).

"You lucky bastard, you caught a 7."

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Sounds like I got pretty lucky. Let's rewind and analyze the hand. I may remember a couple facts incorrectly, but here are the salient points:

This crowd is a typical home game crowd. Two key traits that differentiate this home game (well all home games, really) from tougher games are:

• They are "call happy"
• They are often excited with their flush even when the board is paired. (i.e. they don't fear "scare cards")

In this particular hand, I was dealt Ad7c. The flop came 7d7s2d. I flopped trips, and I feel that someone may be drawing at diamonds. I bet large enough to get a "feel" but I am not quite chasing off drawers yet. I get 2 calls. Barring the 22 or the 72 slowplaying, I feel pretty confident that I have a couple guys that are behind me on the flop.

The turn comes 8d. Aggie leads out with a small bet. I think for a bit. Sure, I may have just been drawn out on by a flush, but no opponent could be convinced that they had the nut flush (I had the Ace). I consider my options:

• I could fold.
• I could raise approximately pot-sized. This would have the benefit of getting fold equity*, but as stated above: the crowd is call-happy and they don't fear "scare cards".
• I could make a ridiculously large bet (e.g. go all-in for about 1.75 times the pot). This has many of the advantages of the pot-sized bet, except that I make it much, much more likely that I get a fold. Even call-happy crowds notice bets this large. I considered the math of this option:

*Fold equity is used to often to justify some really poor poker playing. It similiar to that guy in college (we called him "Hugh") that would drink any time, any day and say "well it's noon somewhere". People will raise anything and say "well I had fold equity." It sounds quite enlightened of them, but they are really just being idiots. In this particulary hand. I hold the Ace of diamonds and I suspect that my opponents are farting around with lower flushes; I think fold equity is quite appropriate to consider.


Assuming nothing about their holdings except that I need to improve to win, I have 19 outs (the case 7, 3 8's, 3 2's, 3 Aces and 9 diamonds) out of 46 cards. If I assume that two diamonds are in one of the opponent's hand (we will call him Bear), I get 17 outs out of 44 cards or 39% chance of winning. I'll also assume Aggie folds, which is reasonable given his small bet and his betting patterns thus far. Finally, I'll assume there is no boat out there, as it is very unlikely I am against 27, 22, 28 (all of which suck) and 88 (which should have left the room after the betting on the flop). If the chance of a fold is X%, then my EV is:

X% * Pot (fold equity) +
(1-X%) * (1 + 1.75) * Pot * 39% (a call and I win) +
(1-X%) * (-1.75) * Pot * 61% (a call and I win)

Run the math and you will see that even with X = 0% (that is, with no chance of getting a fold or "no fold equity") it is almost a break-even proposition. The value comes from "pot equity". Even though I have less than 39% chance on winning the bet & call (even money) on the turn, I have equity in the pot that was already there before I bet. This comes from the bets from other players that have already folded and my sunk costs that are in the pot.

The all-in play I am considering is +EV at X=1.12% and higher. If you assume a high value of X, then it is very profitable. For X = 50%, I have an EV of nearly 28% of my bet. Where can you get a 28% return these days? This return is high enough to compensate for "model risk" (the possibility that my assumptions are not reasonable).

In short, even though it is probably the right move to go all-in even when there is a small chance of getting a fold out Bear, it is a great move when the chance of a fold is high. Given that I have the Ace, I think the chance is high. I want a fold, but I won't cry if he calls.

I go all in

Bear calls.

Aggie folds.

The river brought a 7, improving my trips to quads, beating Bear's flush (Queen high).

"You lucky bastard, you caught a 7."

I don't consider myself lucky at all.

2 Comment(s):

Posted by  Anonymous, at 10:26 PM, February 15, 2006  

That picture really doesn't do him justice. He actually a big scary grizzly bear.

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Posted by  Anonymous, at 1:06 AM, February 17, 2006  

did you check to see if you had a 10 before you commented?

fro - you need a girlfriend

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