Do The Math

1 Nov 2005 PokerPlayer Cash Games Strategy

We explain why your times tables will come in handy round the baize tables

On the face of it Texas Hold’em seems to be a pretty straightforward game played with up to ten players and 52 cards. But the mathematics underlying it is extremely complex. Players are generally split into four groups when it comes to this topic: the bleary-eyed amateurs who chase inside straights and flush draws even when the odds don’t compute; the old-timers who’ve learnt everything by rote but can’t tell you that 2-2 vs 9-10 suited is a dog whereas 10-10 vs A-K is a 4-3 favourite; the maths literate who can calculate odds and conceptualise poker situations with the help of a calculator or notepad; and the crackpot geniuses with degrees in game theory and computer science who can bang on for hours about stuff no one else understands.

Now, while fitting a degree course into two pages is beyond even our talents, we want to start out this series of articles by getting your poker brain to the third stage, where you can calculate odds, think about the game for yourself and analyse various situations – then we’ll start branching out into more advanced areas. So, what are the magic numbers you need to start drilling into your head?

Counting cards

Well, 52 cards means you can be dealt 1,326 possible two-card starting hands (assuming you count A♥-K♦ as different from A♥-K♣ ), of which 78 will be pairs (1 in 17), 312 will be suited and the other 936 will be unsuited. Each pair can occur six ways and each unpaired hand 16 ways, of which it will be suited a quarter of the time (to learn how to calculate these numbers see School daze below). Of course, all this might seem as interesting as watching a game of Crown Green bowls, but these numbers define everything that can happen to you in a poker hand – they are the terrain you’re going to war on, so it’s a good idea to get a feel for them.

Dog or dominant

For example, if you find yourself sitting to the right of a maniac drinking double VATs and raising every second hand before looking at his cards, you can figure out where your pair of Jacks stands when you raise and he inevitably re-raises all-in. There are six ways he can have A-A, K-K or Q-Q, which are the only hands that dominate you, and 16 ways he can have A-K, A-Q or K-Q, against which you’re a marginal favourite anyway. So, assuming you’re happy to risk the coin-flip, the 18 in 1,225 chance that you’re losing is a fantastic proposition.

But what if the same thing happened close to the bubble and the drunk had busted out and been replaced by a solid player you know would only re-raise with a bigger pair or A-K? Well now you might not be so happy, as of the 34 possible hands you put him on, 18 have you dominated and 16 are virtual coin-flips, meaning you’re actually a favourite to be the dog. This is a time to think very carefully about pot odds and relative chip standings.

Making a hand

Moving on to the flop, you’re now confronted by a plethora of possibilities (19,600 to be precise!). But aside from the numbers, the key factor to remember is pretty obvious – that the proportion of the hand that you’ve seen just increased from 2/7 to 5/7 (you’ve now got five of the seven cards that will make up your potential best hand). This makes the flop the defining moment in every hand of Texas Hold’em and around which everything else revolves. And if you’re playing no-limit or potlimit Hold’em, this is where it’s going to start getting expensive.

So what are the possibilities? Well, the good news (assuming you’re an aggressive player) is that most hands miss most flops. In fact, two-thirds of the time an unpaired hand will fail to make a pair on the flop and a pair will only turn into trips one in eight or so times.

So, assuming you raised preflop and therefore have the momentum on the flop, a routine bet of around half the pot can be a very profitable venture. Even if your opponent only folds 50 percent of the time because he’s holding a pair, a draw or the inkling that you’re ‘at it’, you’re still playing winning poker. And of course, some of the time you’ll actually have a hand as well!

This then is part of the beauty of poker – you can bend the rules in as many directions as you want, as nothing is concrete except the numbers behind the cards. Learn them well and winning and losing will eventually pale into insignificance, as playing poker becomes more like running a business – some days you sell a showroom full of Ferraris and others you’re just paying bills, but at the end of the month the sums still add up and you’re left smiling all the way to the bank.