The question How do I win at Texas Hold’em poker? is one that we get posed a lot working in this industry, but unfortunately there is no simple answer to this question. Winning strategy in Texas Hold’em poker will always take some element of luck, but this format of poker definitely favours prepared and knowledgeable players. Basically, hours spent refining the skills of Texas Hold’em poker is how you will put yourself in contention to win games.

Understanding Texas Hold’em poker mathematics and probability

If you want to win at hold’em, at any limit and in any format, you must first understand the concept of mathematical expectation. You will then know how to bet, when to bet, and most importantly why you should or should not bet in any given hand of poker.

Now, I don’t want to lose any of you by getting overly complicated, or veering off into a long, tangled lecture on statistics. Instead, I am going to keep it simple and all my examples will be based on poker hands. But, there is one scary term that needs to be understood before we can proceed and that term of course is “mathematical expectation”. Mathematical expectation is the amount, expressed as an average, that you will win or lose for a given bet. Huh? We need an example, immediately!

You are playing heads-up hold’em and you hold AA. Your opponent is holding KK, the poor bastard. He puts $1000 into the pot. Should you match this bet? This is the easiest poker decision you will ever make, and of course you match the bet, but why did you do this? The answer, which you intuitively know, is that you have the “best of it” – you will win this bet a lot more times than you will lose it.

Mathematically speaking, however, we can be a lot more precise. Your Texas Hold’em hand will win against your opponent’s hand 4 out of 5 times. So every time you put up $1000 to win $1000 you are actually making $800 each time. Even that 1 time when you lose the bet you have a positive mathematical expectation. Basically you would like to repeat this situation an infinite number of times, beause in the long-run you are guaranteed to make $800 multiplied by the number of times you bet $1000.

Why does the House always win in poker?

This is the concept behind casino games, and it explains why casinos are multi-billion dollar empires while the people who bet on the games are just having fun. Poker rooms want to deal out an infinite number of hands because they have a positive mathematical expectation for every hand that they deal. They will make a certain amount, the rake, on every hand. Poker players have to think in the same terms when they place a bet. The issue, however, is that in the short term these results can swing against you with disastrous outcomes.

Back to our example. You know that you are a huge favorite to win with AA over KK. You know that if you played the hand 1 million times you would win 800,000 times and end up with enough money to lure a playmate to your mansion while wearing only a greasy robe. Fair enough. The problem for poker players is that many of them only have enough money to test out the maths this one time. You have $1000 now, but the chances of raising the cash for another 999,999 instances of this hand may be remote. Here is the gambling aspect of poker. Technically it isn’t a gamble because you have a positive expectation, but try telling that to your parents when they ask you what happened to their $1000 that they sent you to pay for your textbooks, but you dropped it at the local online casino, playing poker.

When does mathematical expectation fail Texas Hold’em players?

There are several other issues that the math geniuses, who write about poker, like to skirt around and pretend like they do not exist: namely, a lot of positive mathematical expectations are slight, and all of them shift in a volatile manner as the cards continue to be dealt. So, in a hand of Texas hold’em you might be an 80% favorite before the flop, but if our flop comes K-x-x you are suddenly no longer the favorite at all. Which leads me to the biggest problem with mathematical expectation – many times in poker you do not know your mathematical expectation with any certainty! You might still continue to believe that you are a big favorite in our example, because you hold those magical bullets. The cruel reality of the situation is that you are now reduced to a 12-1 underdog in the same hand where you were once a 4-1 odds-on favorite. This calamitous fall from grace can be extremely costly, and the main factor is that a lot of online poker players make an initial judgement regarding expectation but then fail to adjust that expectation as the hand progresses. Every time another card is dealt in hold’em you must start afresh and make a new calculation. It doesn’t matter that you started out ahead. They only award the pot after the last card is dealt, but you’d be surprised how many players don’t seem to realize this point.

The more you play poker, the more you understand the nuances

Our example was lovely. It was black and white simple. Any fool knows enough to get his money in with AA, and if you knew for certain that you faced KK you would do it at warp speed. But there are thousands of hands where you cannot know if you are the favorite to win, or if you do have “the best of it”. You can make an informed guess, and as you improve your poker strategy and gain more experience there will be many times when you are almost positive that your hand will end up being best. However, every poker player makes mistakes, some of which end up making a ton of money. That’s still not gambling; that’s more like life, but we will deal with these grey situations later.

Texas Hold’em mathematical probability summary

For now you need to know that if you play heads and tails and pay out $1 for every $1 wagered you have a mathematical expectation of $0. Similarly if you insist on going all-in every time you have AK and your opponent has 22 you will end up with a similar mathematical expectation of $0, but your stress levels will go straight through the roof. You’ll also lose all your chips around 50% of the time, which is a big problem if you don’t have the resources to play as many hands as abstract mathematics would like you to play.