Poker players – the smart ones, at least – love to talk about The Art of War. Sun Tzu's ancient Chinese book of military tactics can be traced back to the 5th Century BCE, but it contains much wisdom that still holds true today, including this passage:

“The general who wins the battle makes many calculations in his temple before the battle is fought. The general who loses makes but few calculations beforehand.”

There's no getting around it: If you want to win at poker, and you're not counting on blind luck to make it happen, you'll need to know some math. It doesn't have to be difficult math, but at the very least, you should be aware of the probabilities that certain events will occur. That way, there will be fewer surprises at the table, and you'll be able to make smarter decisions.
 

Waiting is the Hardest Part

Let's say you've been sitting at a live table for three hours, playing no-limit Hold'em, and you still haven't been dealt pocket Aces. Have the poker gods turned a blind eye to you? Not necessarily. In a live setting, you might get dealt about 30 hands an hour. How many times can you expect to see pocket rockets when you look down at your cards? Just once in 221 hands, on average. That's once every seven hours or so.

What about any pocket pair? There are 13 of them, one for every rank in the deck, so you can expect to see them once in every 17 hands, or about 6% of the time. The chances of getting dealt any two suited cards: 13/4, or 23.5%. Suited connectors? That probability shrinks to almost 93/2, or 2.1%. There are 1,326 different possible starting hands in Hold'em, and most of them will be junk that you'll have to fold.
 

Floppy Bird

Now let's say you finally get those pocket Aces and you're ready for some postflop play. There are 19,600 possible flops, so things get a little more tricky with those three community cards on the board. Your chances of making trip Aces on the flop: a shade worse than 10/1 (8.98%). And that's not counting the fact that people tend to play hands with Aces in them rather than folding. If you're in a multi-way pot, there might not be any more Aces in the deck.

The more powerful the hands become, the less likely you are to hit them. Flopping a boat (a full house) with three Aces in it will happen only 0.73% of the time, and the elusive quads (four of a kind) will arrive on the flop in just 0.24% of your hands. There are two more cards to come, though. If you've got AA and you didn't improve on the flop, never fear: You still have almost a 6% chance of getting trip Aces by the river. Now all you need is a plan for what to do when it happens.