Combinatorics expanded

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!

Cool, thanks for posting. Looking forward to the next one.

good post thank you very much, I hope that I may have something to play poker at PokerStars! gl

This is important stuff people! don't just throw it under the bus, please!

This is good stuff. and its all fore free!! lol