Is Q6 really the "average" hand in holdem?

[PE101]

I've read that Q6 is the "average" hand dealt in holdem.

I can't really figure out if this is correct. Is this correct, and how do you figure it out?

Thanks,

[dogmeat]

Think of the numbers 1-1326. What is the average number?

Dogmeat [img]/images/graemlins/spade.gif[/img]

[PE101]

Okay, maybe I’m kind of dense…

I understand that there are 1326 possibilities of starting hands.
Okay, on a scale of 1 being the best hand and 1326 being the worst, I guess the 1st 6 hands are “a pair of aces”. The last 6 (1321, 1322, 1323, 1324, 1325, 1326) would be “2 7 offsuit”.

How do we sequence the rest? There seems like there could be some ambiguity in the mid ranges. (Is 2 7 suited better than 3 8 offsuit?)

In other words: Why is Q6 number 663?

[Siegmund]

You have correctly suspected that the answer depends on your defintion of "average."

One such definition is "a hand that wins an all-in heads-up match 50% of the time": according to that definition, Jazbo's calculations say Q5o wins 50.12% of the time while J5s wins 49.986% of the time.

Another such definition is "a hand that wins 10% of the time in a 10-way all-in matchup", in which case 63s is in the middle, while hands as weak as 43s are better and hands as strong 98o and A6o are worse than average.

Another is to look at actual play: according to PokerRoom's records people have won money overall at their site with A2s and 98s, and better, lost with T8s, K7s, and worse (but because their site is raked, an "average hand" might be expected to lose money, 0.03 to 0.05 big bets per deal, and you might move a few lines lower on their chart.)

The value of hands falls off very steeply at the top, and then flattens out very quickly, whatever method you use. There is a huge range of hands that are 'close to average', and you can make a case for any one of them, for some definition of average.

[PE101]

Wow, great answer.
Thanks for the thoughtful response.

[dan123]

motown

[scottgiese]

Siegmund covered the heart of the issue extremely well, but just to add in a bit of trivia:

Q7o is sometimes called the "computer hand", because it happens to fall right around the middle of the pack if you analyze all the starting hands against one another heads-up. This sort of analysis requires a computer, so the average-ness of this hand comes out with computer analysis, hence the name.

If you played heads-up with no blinds against someone who always pushed all-in before the flop with any two cards, a call with Q6o is about a break-even proposition.

But how that information is going to make you a profit, I don't know, since that scenario is ludicrous. I did say this was trivia, after all.

But Sieg's right -- a true average hand depends on the situation and what you mean by "average".