The Texas Hold'em Coin Flip

How likely is it, mathematically speaking, that you will draw to a flush?

How likely is it, mathematically speaking, that you will hit the straight you're hoping for?

Common Hold'em questions like these cannot be answered without the use of math. Without math, you're just flying blind and relying on luck--which is bad poker.

Let's look at the absolute simplest example:

Think of flipping a standard two-sided coin. What is the possibility of the coin landing on tails? It’s the same possibility as heads, right? If I were to offer you $1 for heads and you were to offer me $1 for tails, what would you think of that proposition?

Have you recognized that it is an even-money proposition and a tremendous waste of time for both of us? The ratio is 1-to-1 and in that case, no one wins.

But, what if I were to offer you $2 for heads, while you still only had to give me $1 for tails? Then, the ratio would be 2-to-1 in your favor and I am sure that you'd be willing to flip a coin with me until I lost all my money and went home with my tail between my legs. You would be getting a 2-to-1 payment for 1-to-1 odds.

Can you think of how this fundamental principle might work to your advantage in a game of Texas Hold'em? Having the odds mathematically in your favor is called Z"getting the best of it," and it's what Hold'em players hope to achieve every single hand.

As you play the game of Texas Hold'em, you must constantly be evaluating whether or not you are mathematically getting the best of it at any given moment.

back to top of page

Low Limit Texas Hold'em: Where Math Really Pays Off

When you're first starting out playing poker, you'll likely be playing Low Limit Texas Hold'em. Fortunately, Limit Hold'em is an excellent forum to get familiar with poker math, because these games will show you the profit potential of Hold'em math.

Math calculations are especially important (and profitable) in Low Limit Hold'em because there are typically more players in each hand and the bets are small compared to the size of the pot, so you can usually play deeper into the hand relatively cheaply.

However, if you are consistently getting the worst of it, if you're consistently the person giving your opponents 2-1 odds, you can go broke at even the lowest limit tables. In fact, it's a mathematical fact that if you play long enough, you will go broke!

Or, if you prefer, you can protect and grow your bankroll by knowing basic Texas Hold'em math.

back to top of page

Hold'em Math for Drawing Hands

The best use of Hold'em math pertains to "drawing" hands, in other words hands where you don't already have a hand that's likely to win the pot. Drawing hands are obviously extremely important because you don't always get Pocket Aces or Pocket Kings.

We all know that there are 52 cards in a deck.

We also know that in Hold'em we get two of cards to ourselves.

So, the remaining cards equal 50.

Since the possibility of anything happening is based on 100 percent, we have ourselves a very nice ratio of 100/50, or 2-to-1. What this actually means, in real life, is that every card that is not currently ours has a 2 percent chance of showing up on the board.

Even after the flop, that ratio barely changes, becoming 100/47, or 2.13-to-1, still close enough to 2 percent to be accurate for these purposes.

So, if you flop a club flush draw, meaning that you need only one more card after the flop to get a flush, what are your odds that you will in fact make your flush?

Well, there are 13 clubs in the deck, minus the two in your hand, and minus the two on the board, that leaves nine clubs. Nine times two is 18, giving you an 18 percent likelihood of hitting your flush on the next card dealt.

18 percent is essentially 5.5/1.

That means that you can put in $1 for every $5.50 in the pot. Those are your even-money odds. In this case, any time you are getting more than $5.50 for your $1, you are getting the best of it and you should be betting that you'll hit your flush.

Anytime you are drawing to your hand, and aren't sure that your opponent will fold to a raise, let the math be your guide. Ask yourself, what cards do I want to come? Add them up and multiply that number by 2 to get your success percentage.

Converting that percentage to a ratio will tell you exactly how much you can put into the pot and continue to expect a positive result over the long term with math on your side.

back to top of page