Jacks are better than 10’s, but just a little better. I suspect jacks are generally overvalued because they are face cards. I’m not sure how I’d use this knowledge (supposing for a moment that my conjecture is actually true), it’s just a thought I had after reading a couple of books about poker.
so expound (and don't butcher my trackback words as you did the last and only time I responded). I and I'm sure many others would be interested.
The probability of having the best hand may be roughly continuous, though the difference in expected payoffs may be much sharper because not only are you more likely to win, the hands you beat will be more willing to bet, so you win more. So as hands get better, the expected value of a hand would be convex in the probability that the hand is the best hand, so the premium on jacks over tens will be higher than the premium on fours over threes.
Though, to test whether pretty-looking hands are overvalued, I wonder if you could get data on whether people bet ace-high spade flushes harder than they bet other ace-high flushes.
Fkeane,
I don't understand your comment–perhaps it's some sort of spam, but since it has no links, it's hard for me to say.
Brad,
Yes, I certainly agree about the convexity, nonetheless I suspect J's are overvalued compared to 10's even accounting for this. That is, I'd expect a graph of valuations vs. cards to look smooth (but convex) but with a jump from 10 to J. But how to measure this, I'm not sure.
The spades conjecture is amusing: indeed, the ace of spades looks pretty impressive. This should be an easy one to test (and a publishable paper, at that). Are there any large poker databases out there?
When I was an undergarduate – I designed a novel card game in my Psy course as an attempt to experimentally induce a type of gamblers' fallacy. Just a thought.
Keith
p.s. no record of what I did
Poker is pretty complicated. For example, one thing that I've heard from experienced players is that a pair of aces is not as good as it seems, because you'll either win a small pot or lose a big one. If you bet early to prevent people from "drawing out" a flush or straight, you'll chase everyone out and win only a small amount of money. If you "slow play" by not showing your strength, you risk losing a large amount of money if someone does hit a straight, two-pair, or three-of-a-kind later on. A related point is that players play "connectors" (e.g. 9-10) frequently, even though they very rarely complete the straight. The reasoning is that if they do make their hand, they stand to win a large pot because other players will be unlikely to notice the possible straight, or will not believe they have it. The point is that because of the decision-making involved, the expected value of a poker hand is only tangentially related to its likelihood of being the best hand at the table.