By John Vorhaus

When you’re just coming up in poker, it’s easy to feel self-conscious about the game if you don’t have a solid grounding in its math. That self-consciousness can kill your self-confidence, and a player without self-confidence has just no chance of winning in almost any game she plays. With that in mind, I’d like to introduce — or reintroduce — to you some numbers of note. Once you have these memorized (and I do recommend that you memorize them) you’ll be on much firmer footing every time you go to play.

ODDS AGAINST STARTING WITH A PAIR: 16-1. In a normal ring game, you can go almost two laps without seeing a pair, on average. Maybe all those crummy unpaired hands aren’t so unusual after all.

ODDS AGAINST STARTING WITH A PAIR OF ACES: 220-1. 220 hands! That’s about ten hours of play at common card room dealing rates. People always think they’re “overdue” for aces, but really they’re not.

ODDS AGAINST STARTING WITH A PAIR OR AN ACE: 4-1. This is an interesting number. It means that in a nine-handed game, if you don’t have a pair or an ace, an average of two of your opponents will. This makes a very good argument for folding crap hands, since you know going in that you’re probably beaten in two places.

ODDS AGAINST FLOPPING A SET: 7.5-1. Your pocket pair will turn into trips only about 13% of the time. What does this mean? In simplest terms, if you’re not calling into a big pot, or confident that the pot will become big, you don’t have adequate odds to draw to a set.

ODDS AGAINST FLOPPING A FOUR-FLUSH: 8-1. If you start with two suited cards, you’ll pick up another two suited cards about 1 time in 9. From that point, you’ll complete the flush about 1 time in 3. So, again, a flush draw likes lots of company and lots of money in the pot.

ODDS AGAINST HITTING A RUNNER-RUNNER FLUSH DRAW: 23-1. People always complain about the fricka-fracking slackjaws who hit runner runner flush cards to beat them. Sure it’s rare, but not unheard of. After all, you’re about ten times more likely to make a runner-runner flush than to pick up pocket aces.

ODDS AGAINST COMPLETING AN OPEN-ENDED STRAIGHT DRAW: 2-1. If you flop an open-ender, you’ll complete that straight about 1 time in 3. Again, make sure that the pot odds — the amount of money you stand to win — justifies drawing to this hand. If you’ll only get a dollar back for every dollar you bet, the pot isn’t “laying you the right price” for your draw.

ODDS AGAINST COMPLETING A GUTSHOT STRAIGHT DRAW. 10-1. This is why mama always said, “Don’t draw to inside straights.” With the odds against you at ten to one, you rarely find enough money in the pot to pay you off adequately when you hit.

ODDS AGAINST STARTING WITH A-K UNSUITED: 110-1. We think that pocket aces are rare while Big Slick is quite common. But is it true? Yes, you’ll get A-K twice as often as A-A, but you’ll still go more than 100 hands, on average, between Slicks.

ODDS AGAINST STARTING WITH A-K SUITED: 330-1. You’ll actually have A-K suited a third less often than A-A. Why? Because there are six different ways to make A-A, but only four ways to make A-K suited. This doesn’t make A-K suited more powerful than A-A, just more rare.

ODDS AGAINST FLOPPING AN ACE OR KING AFTER STARTING WITH A-K: 2-1. Here’s some good news. One time in three, your Big Slick will improve to top pair, top kicker or better on the flop. Considering all five board cards, your A-K will actually bump up about 60% of the time.

I know these are a lot of numbers to swallow at once, so let’s make it easier for two ways. First, here’s a handy little odds chart you can print out and keep with you to work on your memorization.

Next, here’s a quick and dirty way to calculate your chances of improving. Just count the number of “outs” — outstanding cards that can help your hand — then multiply that number by the number of cards yet to be seen, and multiply again by two per cent.

For instance, if you have four to a flush on the turn, you know that there are 9 cards on the river that can complete the flush. Multiply 9 by 1 (the number of cards to come) by 2%, and you get 18%, which is very close to the true odds of 4-1 against.

To take another example, suppose you have just A-Q and you’re looking at a flop of 9-6-3. You figure that if the turn or the river is an ace or a queen, you’ll probably win… but what are the chances of that? Well, there are 3 aces and 3 queens left in the deck, so you have six outs times two cards to come, times 2%. 6 times 2 times 2% = 24%. About ¼ of the time, you’ll hit the overcard you’re looking for. If the pot is offering you at least a 4 to 1 return on your betting investment, then you can go ahead and profitably take that draw.

Folks, I’m no numbers wonk. Back in school when they said, “math,” I thought they said, “bath” and went off to take one. But I’ve discovered that the math of poker is really very easy, if you just take a little time to memorize a few numbers and learn a few tricks. Try it! You’ll be surprised how much confidence it adds to your game.

John Vorhaus is author of the KILLER POKER book series and News Ambassador for UltimateBet.com. You can find him online at vorza.com.

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