For this example, you shove in the SB
You have AK, what are the odds your opponent has AA or KK?
There are 1225 possible combinations of hands your opponent could have
There are 3 possible combinations of AA and 3 of KK (6\1225x100)=.48%
For this example, you raise in the Cutoff
You have A10, what are the odds your opponent has, Pocket Pairs AA1010 and AKAJ?
There are 6 combos of AA and 1010, and 18 combos of KKJJ, There are 36 combos of AKAJ
 That gives us a total of 60 combos out of 1225 (60/1225x100)=4.9% FOR A SINGLE OPPONENT, since we're in the Cutoff, there are 3 opponents to act after us. We'll round 4.9% to 5%, multiply by 3=15% chance your in bad shape.
You have 1010 in Middle Position
What are the odds your opponent has JJAA?
6 combos for each, so 6x4=24 out of 1225=About 2%. There are 5 opponents to act after you. So 10% chance.
Remember, There are 16 unpaired combination of any starting hand, 12 unsuited amd 4 suited
There are 6 combinations per paired hand.
If you have a "blocker" or a card such as an ace in YOUR hand, that drops the combinations of your opponent down. 12 unpaired Combinations and 3 paired.
Try and memorize as much as you can.
quick note on drawing hands.
example 1: the flop is 78A Rainbow, you have AK, and are HU after the flop, what are the odds your opponent has an openended Straight draw?Gutshot?
16 combos of 56
16 combos of 910
16 combos of 69
16 combos of 610
16 combos of 10J
16 combos of 59
Now, things are a little different than before, we've already seen 5 out of the 52 cards. Thus, our oppponent has now a possible 1081 combinations total.
So, 48/1081=4.44% for an openender
If we include 48 more draws for gutoshot. . . 96\1081=About 9%
Now, we included some hands like 59 for mathematical purposes, however, we could assume a player would not play this hand.
So in conclusion, to use rounded numbers, on a 2 runner flop, there is about a 5% chance your opponent has an OESD, and 10% for gutshot and OE.
If you were interested in finding out the odds of you being beat on the last example, you'd figure out the # of combos for Trips, and Two pair.
i'll do more examples in a future thread. HAVE A GODO DAY EVERYONE!
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Thread: Combinatorics expanded

05292012, 10:35 AM #1
Combinatorics expanded
Last edited by GottImHimmel; 05292012 at 10:39 AM.
"Power is my mistress. I have worked too hard at her conquest to allow anyone to take her away from me."  Napoléon Bonaparte

05292012, 11:04 AM #2
Cool, thanks for posting. Looking forward to the next one.
"When a man with money meets a man with experience, the man with experience leaves with money and the man with money leaves with experience." anonymous quote

05292012, 04:09 PM #3
 Join Date
 May 2012
 Posts
 16
good post thank you very much, I hope that I may have something to play poker at PokerStars! gl

05292012, 11:51 PM #4
This is important stuff people! don't just throw it under the bus, please!
"Power is my mistress. I have worked too hard at her conquest to allow anyone to take her away from me."  Napoléon Bonaparte

05302012, 12:05 AM #5
 Join Date
 May 2012
 Posts
 42
This is good stuff. and its all fore free!! lol