Chart - EV of Calling on the River... (is folding as bad as we think?)

[MarkD]

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BTW, I folded two big pots last night that I would have won and think both of my decisions were "good", until about 10 minutes later when my opponents were no longer unknown and were both horrible donks. We always remember those big pots... maybe I'll start calling more.

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The margin of error against unknowns is a lot greater than the chart allows for.

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I didn't fold because of the chart - it was because of the board and betting sequence.

But you are absolutely righ.

[cartman]

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I'm asking because up until now I've been using a heuristic approach that considers the above factors, but is not really precise.

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It will never be precise. Even if you could pause and go run pokerstove and excel for hours, you will still only be as good as your subjective estimates are. The fact that you can't do these indepth calculations at the table make it even more imprecise. When people talk about a player being a good hand reader or being experienced, I think it is situations like this one that we are referring to in large part. Obviously the better you get, the closer your estimates in these spots will be to the "truth".

Cartman

[Moozh]

One question for Cartman about his 'Zero Philosophy' shifting the judgment towards a call. For that to be true, doesn't it assume a flat distribution? I would imagine that even in a situation like that where we need to be good 5% and we're +/- 6%, the distribution may be a bit bottom heavy to make up for the lack of range the zero creates.

[cartman]

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One question for Cartman about his 'Zero Philosophy' shifting the judgment towards a call. For that to be true, doesn't it assume a flat distribution? I would imagine that even in a situation like that where we need to be good 5% and we're +/- 6%, the distribution may be a bit bottom heavy to make up for the lack of range the zero creates.

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Hi Moozh,

Maybe I am misunderstanding your question. My "zero philosophy" assertion did assume that we are equally likely to be off by x% in both directions. Since our estimate of how often we are good is a subjective estimate, unless the player has a natural bias toward folding or calling, it seems that this is a valid assumption. So I would expect a player's true probability of winning to be a normal distribution centered around his estimate.

I don't understand in what you mean by the distribution being bottom-heavy in this context. Can you elaborate?

Thanks,
Cartman

So now it's time for a new book called the "Complete Theory of Limit Hold'em" [img]/images/graemlins/wink.gif[/img]

[Moozh]

Ok, I think I'm being nitty here, but maybe these pictures will help.

I gathered that your agument said lean towards a call in those close decisions because assuming a flat or normal distribution around your estimation of how often you'll win, it's possible that the actual likelyhood of winning is a lot higher than you think, but can only be a little lower because it can't be lower than zero. (That was a mouthful)

What I wanted to consider is that you can't assume an even normal distribution around your guess.

I made these two graphs by freehand in Paint, so be nice.



In graph A, you think need to be good 5% to call profitably. Since the distribution is even, there's more area under the curve to the right since the left side is cut off. Thus, you're more likely to be better off more often than worse off. This would lead towards a call.

In graph B, the distribution isn't normal. Notice that the zero cutoff on the left has caused the bell curve to 'bunch' on that side. Thus, the areas under the curve on each side are fairly close and thus you can't necessarily lean one way or the other. I would think that graph B is a more accurate representation of the way things are when dealing with small percentages.

Did that make any sense and did it have anything at all to do with what you were saying? I think I'm just making things more confusing.