Shuffle Up and Deal!

This site is devoted to the mathematics of the Cadillac of Poker, Texas Hold'em. I will be adding my theories, the basic strategies, chip tricks etc. as my schedule allows.


So, what is this game everybody's playing? Its called Texas Hold'em and its full of great mathematics.

How to play -- Everybody is dealt two cards face down. The the two people left of the dealer have forced bets called blinds to ensure money is in the pot. There is a round of betting, each person having the option to call (or meet) the current bet, raise the bet (make the bet higher), or fold (give the dealer your cards and wait for next turn).

Once the pot is right the dealer flips up the first three of five community cards, called 'the flop' to come that everyone can use. Next comes another round of betting. The dealer turns up the fourth community card, 'the turn'. Another round of betting. The dealer turns up the fifth community card, 'the river'. One last round of betting, then everyone sees who can make the best 5-card hand between the seven cards (your two plus the community five).

So Where's the Math?

Hold'em is a game of imperfect information. So, the more information you can extract from the game, the better off your chances of winning. Now, there are supposed ways of 'reading your opponents' and things like that, which may be true, but that will not be the focus of this site as it is not a well defined concept.

The single handedly most important information we can extract from a particular hand is your number of 'outs'. Outs are the number of cards left in the deck that will make your hand win. Without seeing anothers cards it is a bit abstract to guess at your number of outs but usually this isn't too hard.

Example:
Say you have a 10s-Jd and 9s-Ks-Ah comes up on the flop. You should (whether true or not) probably assume your opponent has an A or K putting him ahead of you. Assuming this, you have 4 outs, all 4 Queens in the deck. Sure 2 spades would make you a winner as would 2 Jacks or 10's but never count on these.

Check out some Chip Tricks


I can do: Twirl

I'm working on:Shuffle

Impossible:3-Stack Shuffle

Some poker hand nicknames.

Hand Number
Royal Flush 4
Straight Flush 36
4-of-a-kind 624
Full House 3,744
Flush 5,108
Straight 10,200
3-of-a-kind 54,912
Two Pair 123,552
Pair 1,098,240
High Card 1,302,540
Total 2,598,960

To see where these numbers come from go here.