River card syndrom (cross-posted in psychology)

[PrayingMantis]

After the short discussion with Gonzoman (above), I would like to restate what I said in the original post, and clarify it. This has to do with psychology and probability alike.

The situation is: Player A holds AA, Player B holds 22, they are both all-in PF. (I'm discounting redraws and other draws).

Player B has 2/48 (0.04166) prob. to hit his set on the first card.

If he *did not* hit it, he will have now a 2/47 (0.04255) probablity to hit on the 2nd card. *In his view*, and rightly so, this is a greater probablity than he had to hit it on the first card, *alone*.

If he does not hit it on th 2nd, he *now* has 2/46 (0.0435) prob. to do it on the 3rd card and so on.

When he'll be facing the river card (if he didn't make he's set until then), he'll have a specific 2/44 (0.04545) probability of hitting the set NOW. This is a greater *specific* probability to hit his set than on any other specific street.


We are very used to see these problems, in a way, from an "objective" point of view. In this view, as Gonzoman stated, the chances to hit the set are getting *smaller* as more cards fall. But this is an "external" view of probability. It is improtant to notice, IMO, that from an "internal" view, things can look quite different (if not opposite).

I find this concept of "internal probabilty" (that's the best name I can think of it now), very intriguing, since it has much to do with how we deal with chance in general. It is obviously very relevant to poker.

I believe that behaviours like the "river card syndrom" (I apologize for this fancy title, but can't think of any better option), can be explained very thoroughly with such a tool.

Any more thoughts will be greatly appriciated.

[PrayingMantis]

More discussion and clarification of this idea, in the psychology forum:

internal probability

[Lexander]

The results you posted in my mind are pretty trivial in general (but useful to keep in mind). The chances that the river cards will hit the opponent are higher at that point if we assume that none of the previous cards have done so (which is required for your calculation).

I think the more interesting thing is that the river has three properties that make losing at the river more frustrating:

#1) You can't catch to win if you are behind at the river.
#2) You have generally put a lot of money in the pot that you have now lost.
#3) Many times your opponent made a poor call on the turn and got lucky.

[PrayingMantis]

[ QUOTE ]
The results you posted in my mind are pretty trivial in general (but useful to keep in mind). The chances that the river cards will hit the opponent are higher at that point if we assume that none of the previous cards have done so (which is required for your calculation).

I think the more interesting thing is that the river has three properties that make losing at the river more frustrating:

#1) You can't catch to win if you are behind at the river.
#2) You have generally put a lot of money in the pot that you have now lost.
#3) Many times your opponent made a poor call on the turn and got lucky.


[/ QUOTE ]


I do agree my calculaions and results are trivial. However, these by themselves were not the point of this thread, here and in the psychology forum. I wanted to show how we can solve a seemingly conflict between the mathematical ("chances are equal for any card to bring the suckout, or even: chances are smallest for the river to bring it"), and the very common psychological point of view, which many posts here, on various forums, are an evidence for its existance ("river suckouts are more frequent than they sould be on XYZ poker site").


I believe the 3 points you give do not really solve it.

1. The fact that you can't catch to improve after you're behind on the river is correct, but I think that the "river syndrom" will appear regardless, even if you are not able to improve (redraw) at all, no matter on what street, i.e., any situation where you'll have 0 outs for a redraw. Conditional probability calculations ("internal prob.") will be much more helpful in explaining the river suckout feeling, IMO.

2. The fact that you have put lots of money and you've now lost, is a variation on your first point. You have now lost, i.e, you cannot catch and improve any more.

3. That's true, but is not really relevant to most aspects of the syndrom, as I described it. I'm refering basically to a scenario where both opponents are all-in PF (or at least on the flop) and are dealt few community cards for them to make hands with. In the case where a bad call was made on the turn, there's no difference between conditional and non-conditional probabilities (interior vs. exterior), because no matter how you look at it, there's only one more card to come.