Working out probabilities...

Just looking at something and it got me thinking.

How often should you get the following hole cards if u only played

AA, AK, KK, QQ, JJ

1:20 hands, 1:30, ???

Hope that question is simple enough?

The odds of getting any of those five sets of pocket cards is 1 in 33.15.

There are two ways to arrive at this number:

1) The odds of getting a specific pocket pair are 1 in 221 or (4/52)*3(51). You have four pocket pair in this example so the odds of getting any of the four pocket pairs is 4/221. The odds of getting AK is 1 out of 82.875 or (8/52)*(4/51). Calculate (4/221)+(1/82.875) and you get .030166 or 1 in 33.15

2) There are 12 ways to get a pocket pair by drawing two cards out of the deck. For this example, AcAh counts as one way and AhAc counts as another. This means that there are4x12 or 48 ways to get your four pocket pairs. There are also 32 ways to get AK (4x4x2). There are 52*51 or 2652 combinations of two cards in a deck. The odds of getting any of those sets of pocket cards is 2652/(48+32) or the same 33.15.

It's the same basic math. If you want to understand it, just pick the method that makes the most sense.

Thanks Joe - both ways make sense if I understand that u wil g one of those hand for every 33 delt?

It just came to me when readg a website that suggested beginners only play those hands.

Sounds a boring way to play, but I guess if you factor in you will play about 50% of your blinds regardless of cards it drops it down to playing one hand in aout 30?

that should explain it