Sample size question...

[R_Ellender]

I don't even know why this question is relevant to me, I guess I just feel like gaining some knowledge.

Let's say I wanted to find the expectation for A [img]/images/graemlins/heart.gif[/img]Q [img]/images/graemlins/heart.gif[/img], and a friend of mine wanted to do the same. However, I wanted to find the expectation of AQ against random hands while he would like to find the expectation of AQ against J [img]/images/graemlins/spade.gif[/img]T [img]/images/graemlins/spade.gif[/img].

Since my friend is testing the expectation of AQ against only one hand, would I need a larger sample size than him since I am comparing my AQ against 1225 different hands?

[AaronBrown]

It depends how you plan to do the research. Also, I'm not sure what you mean about the expectation of A[img]/images/graemlins/heart.gif[/img] Q[img]/images/graemlins/heart.gif[/img] against J[img]/images/graemlins/spade.gif[/img] T[img]/images/graemlins/spade.gif[/img]. Do you mean the probability of each hand winning if the full board is dealt? Expectation usually refers to the average amount of money won or lost in actual play. In this case, that would suggest having two people play a lot of Poker hands, then looking at the results when they had the indicated hands. But you'd need an average of 270,725 hands dealt per observation. You could just deal these two hands, or they would play differently. The only practical way to estimate this would be by computer simulation.

If you mean the probability of the hands winning if played to showdown, that figure is easy to compute for either case. No need to sample when you can count every case.