Combinatorics expanded

**GottImHimmel** · 05-29-2012, 10:35 AM

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 A-10, what are the odds your opponent has, Pocket Pairs AA-10-10 and AK-AJ?

There are 6 combos of AA and 10-10, and 18 combos of KK-JJ, There are 36 combos of AK-AJ

- 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 10-10 in Middle Position

What are the odds your opponent has JJ-AA?

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 7-8-A Rainbow, you have AK, and are HU after the flop, what are the odds your opponent has an open-ended Straight draw?Gutshot?

16 combos of 5-6
16 combos of 9-10
16 combos of 6-9
16 combos of 6-10
16 combos of 10-J
16 combos of 5-9

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 open-ender

If we include 48 more draws for gutoshot. . . 96\1081=About 9%

Now, we included some hands like 5-9 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!