Combinatorics

[GottImHimmel]

POKER MATH (NOT ALL POKER MATH IS MENTIONED, OBVIOUSLY.

This first section has to do with a Combinatorics , and has a great amount to do with Pre-flop starting hands.

Combinatorics is removing one card from the deck, and multiplying it by the number of cards left, but since A-7 is the same as 7-A, we must divide by 2.

There are 52 cards in a deck, remove on, and pair it with one of the other 51.
---52x51=2652/2= 1326 combinations of starting hands.

6 Different Combinations for each Paired hand, 16 for Any Unpaire

---Now that we have that, we can get our % chances of starting hands.

A Specific card Pocket pair (e.g A-A) .47%
A Pocket pair (5.8%)
Any Specific Unpaired (1.2%)
A Suited Hand (23.5%)

Once you get your Two Cards, Your Opponent only has 1225 Combinations available, and obviously this changes the %s of probability, Especially if you have what's known as a Blocker, or a card that you think they have or are trying to rep. E.G) You have an Ace, the odds of your opponent having an ace is obviously decreased.

Probability is Very useful In determining what kind of range you think your opponent is on, for example, you can assume a loose player is playing a wider range, thus you can make more plays and have greater fold equity, and you can avoid the tight range of a tight player.

It also is what drives some of the smartest LAG players in the world to play some oddball hands, but they know that if for example they are playing a tight player, the odds of them having any A-x hand is higher, making a hand like 4-5s easier to play, while playing a looser opponent is trickier, as they know more flops hit their wider ranges more often.


Probability also shows us yet again why position is such a massive advantage.
For a great example, lets look at the hand J-J.

There are 3 ranks of cards, which when paired, crush J-J (A-A,K-K,Q-Q.)
There are 6 paired combinations of each, 6x3= 18. 18/1255=1.4% chance a single opponent has one of these hands.

If you open on the button, there's only a 2.8% chance of this happening, however, UTG at a 10 handed table (1.4x9=12.8% or 1/8 approx) Meaning that 1 out of 8 times, your absolutely crushed.

CONCLUSION NOTES

Without going into great detail, I at least want you to go away with the math behind pre-flop play.

So Remember:
---There are 6 combinations of any SPECIFIC paired hand, meaning by odds you will get any SPECIFIC pocket pair 1 out of 208 (approx) times. Or .47%

---There are 16 combinations of any SPECIFIC unpaired hand (A-K for example)
4 are Suited, 12 Unsuited

----1326 Combos before you see your cards, 1255 combos for your opponent.
----Remember to find the odds of a single opponent having a hand or range of hands (for example, hands that have you Crushed, Dominated, Or hands that you dominated), then Multiply that % by the # of opponents you have to act behind you.

---REMEMBER THE GAP CONCEPT! ( It takes a better hand to raise after an opening raiser than to open raise, remember to widen or shrink that "Gap" according to the style of the opening raiser, the # of callers, the Pot Odds your being offered, etc. . .)

----You can in general only slightly tighten that gap if the opener just limps, this is because of the improved pot odds, the weakness the limp might've shown, and to try and Isolate that limper if you have position.


That's Combinatorics, I know that Many of you just like to play by feel and intuition, so the odds might not be for you, but remember that even the greatest feel players know the math behind they're actions.


----If you have any suggestions or topics that you want to discuss in a later thread, please respond with it. (For example---Express and Implied Odds---Continuation Betting, Probe Betting, Floating, Flop Texture, Blind Stealing, Squeeze and Reverse Squeeze plays, Post-Flop Math, and much more.


Your Friend and Community Member,



GottImHimmel

[IamStuUnger]

I hate it when you are in a conflict hand and you have a scond best hand thinking theirs no way the could have the best hand(especially when you have one of their cards) and they wind up having it

[MIGO14]

Thanks for this, very usefull I think. Have to learn more about this...

[pokerpiglet]

have to take a look at this when i can comprehend it too early lol

[nazgardeq]

sure

[bmeelneg]

Also might want to mention that the 1326 possible staring hands can be further narrowed down to 169 hands.

You can get dealt AA 6 different ways but none of those six combos is strong than the others (preflop). The 169 number is more manageable than the 1326 number.

[GottImHimmel]

Bmeelneg. The Point of combinatorics is not to point out how many starting "hands" there are, rather, It is to find the percentage of probability that your OPPONENT can have a hand. You cannot use the 169 number for this.

[IamStuUnger]

yea I see what your saying its more just an extra thing to take in consideration with position, like position its not always needed but something you should try to always account for and largely depends on the hand you have first

[bmeelneg]

Bmeelneg. The Point of combinatorics is not to point out how many starting "hands" there are, rather, It is to find the percentage of probability that your OPPONENT can have a hand. You cannot use the 169 number for this.

ok no problem ... I was responding more to your first few sentences where you show the math of how the 1326 number was achieved.

Any chance you want to tackle PLO/O8 with combinatorics? Joking ... your head would probably explode.

[scottieb668]

wow that's interesting. i will have to check it out.....