average high hole card

[brassnuts]

Can anyone tell me what the average high card is in the hole?

[Henke]

Assuming that we are talking about hold'em, and there are 10 players seated, then 20 cards will be dealt out preflop. The probability that no ace is among those 20 cards is only about 13%, meaning that about 87% of the time, the high card will be an ace.

[brassnuts]

I'm sorry, I didn't make myself very clear. This question really has no purpose other than to satisfy my own curiousity. Yes, in holdem, but what is the average high card in the hole of a single players hand. In other words, average high card of 2 cards randomly drawn from a full deck.

[Henke]

Hmm...

The most likely high card is an A, since there are then 48 other cards that can complete the hand. (The probability of two cards containing at least one ace is about 15%.)

However, about 52.5% of the time, the highest card will be an A, K, Q or J.

Another way to look at it is to normalize the high-card by their probability of appearance. if we then sum these weighted values, we'll get an "average high card" of 10.2 /images/graemlins/cool.gif

[brassnuts]

Thanks! I need to catch up on probabilities and statistics. At one time, I was actually fairly good at math. It's funny too, how your subconscious makes calculations. My intuition was that it would be just above 10.

[DJStarr]

I am not sure what your agenda was with this question and forgive me if I am overstepping my boundaries but in VERY general terms, I will raise preflop heads up with Q-7 or better.

[brassnuts]

Didn't have much of an agenda. It was really just random curiousity. But, yes, this information would really only be useful in heads up play.