STARTING HANDS

[storman99]

my starting hands
with 233.334 thousand hands how many times should i get

pocket pair.


suited connectors.. 4-5, 5-6, 6-7, 7-8, 8-9, 9-10, 10-J



all connectors suited and unsuited. 4-5, 5-6, 6-7, 7-8, 8-9, 9-10, 10-J



single A.


suited cards


thanks

[BaseMetal]

I'll have a go at answering some parts - with the working out, I may get this wrong because I'm not an expert and probability problems are often very subtle.

I think the bast way to calculate probabilites for these type hands is to work out how many different starting hands there are (allPossH), how many ways you can get the target type hands (tarCntH), and then the probability of the target occuring is:
P = tarCntH/allPossH

How many possible starting hands are there is the combination of any 2 from 52, which is: 52!/(52-2)! 2!
or as most of this stuff cancels out becomes:
52 * 51 / 2 = 1326.
allPossH = 1326.

So how many of these 1326 are pocket pairs. For a particular pair say 55, there are 4 fives in the deck and we need two of these at a time which is comb. 2 from 4
= 4!/(4-2)!2! = 12/2 = 6
So out of the 1326 possible hands 6 are 55. Similarly there are also 6 pairs of twos, 6 .. threes etc
Total pairs hands is 13 * 6 = 78
So the probability of your next hand being a pocket pair is:
78/1326 = 0.0589 (about 1 in 16) [edit: sry, meant about 16 to 1]

You can do the similar type calcs for the other problems.
For 4-5 suited, there are 4 of these hands so the probability for these if
4/1326
and similarly for the other suited connectors mentioned.
[ QUOTE ]
suited connectors.. 4-5, 5-6, 6-7, 7-8, 8-9, 9-10, 10-J

[/ QUOTE ]
7 * 4 / 1326 = 0.0211 (approx. 1 in 46) [edit: 46 to 1]

You state you have [ QUOTE ]
233.334 thousand hands

[/ QUOTE ]
This seems to imply that you have these already stored in a db or something, if this is the case using probability after the event may be misleading for instance earlier I was dealt 3 AA hands in 5 deals [img]/images/graemlins/smile.gif[/img] the chances of me getting 3 pairs of aces in the next 5 hands I'm dealt is extremely low but that unlooked for event happened in those hands. I can't say that that event was a 1 in a squillion because it had already happened and so occured 100% in those hands.

(If you want to know if the frequencies of the hands you have is in some way statistically significant then you may want to use something like a chi-squared test)

Hope this helps in some way.
BaseMetal