Don't look for an Ace on the River

[AaronBrown]

I was browsing the url=http://www.pokerroom.com/main/page/games/cardStats]stats[/url] at Poker Room and noticed that small cards are more common on the board than big ones. Maybe everyone knows this, but it struck me as interesting.

It's nothing you'd notice in a round or two, but over 332,894 hands that got dealt to the river, the river card was a 2 25,965 times and an Ace 25,209 times. I give this only as the most extreme example, you see the same pattern for all board cards and all small versus large cards.

The nonstatisticians will yawn, but a quick calculation shows that the odds of this happening by random chance are almost exactly the odds of dealing a spade royal flush in one try from a well-shuffled deck.

Obviously you're more likely to go to showdown if players holding Aces than 2's. But I don't think this should be true in theory. Aces make you more likely to bet, of course, but they also increase the strength of your opponents hands. You should go to showdown in situations where two (or more) players have good pot odds, not just when one or more players have strong hands. It's the uncertainty about hand valuation that makes a showdown (as the old saying goes, "it's differences of opinion that make a horserace") not strong hands. Whether horses were fast or slow, people would race them.

I'm not sure of this, I've been thinking it over, but I wonder if this doesn't indicate that the players in this sample overvalued Aces.

I don't expect to get rich exploiting this tendency, even if it turns out to be real. But it's interesting to think about.

[PairTheBoard]

Hands that include good Aces tend to generate more preflop action thus building pots that induce people to stay through the river. You might not even see the Aces at the river even though they played a major role in steering the pot to a river showdown.

I think Ace-rag hands are commonly overvalued by poor players so that would magnify this phenomenon even more.

PairTheBoard

[Siegmund]

Doesn't seem overly surprising to me.

When everyone at the table (or all but one person at the table) is dealt a bad hand, board cards don't get dealt at all from "enriched" stubs. When many people are dealt high cards it's more likely that at least two of them will want to fight over a pot, and force a board to be dealt from "depleted" stubs.

The effect is probably much stronger for aces than any other rank, since between 1/3 and 1/2 of ace-high hands are worth seeing a flop for one bet while less than 1/4 of K- and Q-high hands are.

This is part of why it's so hard to directly address the "poker is rigged" complaints since a simplistic experimental design will falsely accuse a fair game of dealing too many 'bad' rivers. (And broadways on the river will tend to help the person who was already ahead with his TPTK, while small cards will either be blanks or complete straight and flush suckouts.)

[PairTheBoard]

Given all that, the suprising thing might be how small the effect actually seems to be according to Aaron's Stats. While you'd expect the Ace to hit 7.69% of the time, his stats have it hitting 7.57% about 1.5% less than normal. Doesn't seem enough to change your pot odds calculations.

I wonder if the so called bunching effect is of this kind of order of magnitude. Maybe less.

PairTheBoard