help me understand

[BIGRED]

A discussion came up in another forum about certain cards being more likely to come out on certain streets. Obvioulsy this idea suggests some kind of an on-line conspiracy, which I do not support.

Specifically, the original poster of that thread made a statement that went something like, "... 9 or T comes more on the river..."

Just to disprove this idea with some hard numbers, I suggested an experiment in PokerTracker, where one would do a filter for all hands that saw the river card, where the river card was a T. If you divide this number by all hands that saw the river in general, then I said that the ratio would be 1/13.

What is the flaw in expecting this ratio to be 1/13. Some suggested that this ratio will be higher because certain cards are less likely to hit on the river, such as an Ace, an Ace being a card that's likely to be played, thus eliminating it from the deck. But isn't it just as likely that a less-premium card might have been mucked, and also elminated from the deck, so that evens out the possibility of any card hitting the river?

[Bez]

It would definitely even out if every hand was played to the river, regardless of what cards people are playing. It might be slightly different considering that certain boards may be more likely to induce folds, but I think this factor would be miniscule.

[uuDevil]

I saw Lori's replies in the Zoo and I'm pretty sure she's right (she knows this stuff).

I think the effect is similar to what people call "bunching," where if the first several people fold, it indicates that the remaining hands are slightly more likely to be good ones. You can do a search for this or see this thread for example: bunching. (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1140570&page=&view=&s b=5&o=&vc=1)

In this case, the fact that people haven't folded means they hold better than average hands. Those better than average hands are more likely to contain aces, so the aces don't show up as often on the river as they would if people were sticking around with random hands. This effect is too small to put to practical use (so don't discount your outs) but noticeable in a large sample of hands.

[BIGRED]

Ok, thanks for the search help. I will read about this effect called "bunching".

However, I just want to make my point. You said, as well as others,

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In this case, the fact that people haven't folded means they hold better than average hands. Those better than average hands are more likely to contain aces,...

[/ QUOTE ]
Ok, I understand this.


But what I don't understand is this.

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... so the aces don't show up as often on the river as they would if people were sticking around with random hands.

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Well, if you are saying Aces are more likely to be held by someone if the hand goes to the river (which I agree), then isn't it just as likely that that less-valued cards were mucked by the hands that folded before the river?

I haven't read about bunching yet, as I just read this reply. Perhaps this question will be answered in the thread you pointed to.

[uuDevil]

[ QUOTE ]
Well, if you are saying Aces are more likely to be held by someone if the hand goes to the river (which I agree), then isn't it just as likely that that less-valued cards were mucked by the hands that folded before the river?


[/ QUOTE ]

Well if you agree that more aces are in player's hands, and therefore fewer show up on the river, don't you also have to agree that there must be more low-value cards on the river? Decreasing the number of one kind of card must be counterbalanced by increasing another, right?

If we follow what happens to low value cards, we should be able to arrive at the same conclusions. Here is a rough argument:

/images/graemlins/diamond.gifPeople tend to fold low value cards.
/images/graemlins/diamond.gifThe river was dealt, so people did not fold.
/images/graemlins/diamond.gifIf people did not fold, low value cards were not folded.
/images/graemlins/diamond.gifIf low value cards were not folded, there are more left in the deck.
/images/graemlins/diamond.gifIf there are more left in the deck, more will show up on the river.
/images/graemlins/diamond.gifIf more low-value cards show up, fewer high-value cards will show up.

This is the same situation as before.

[lorinda]

Also posted in the zoo.

If you agree with me my outs are still 8 and my probability of hitting my open ender on the river is still 8/48, I'll settle for that. Beyond that, I guess I'm too thick to see your point.

You are correct.

You will however read posts in some situations where you work out your maximum outs and then subtract some for possible overlap, for instance when you have KQ on a J93 board. The kings, queens and tens come to 10 outs, but If you posted this in Small Stakes, I'm sure people would tell you to count your outs as less than ten (depending on how betting went of course) because of the possibility of being up against AA, or AQ and so on.

This is the hidden 'tax' on your outs that is represented in the chart and is only applicable in certain scenarios.

Lori