Know your odds
If someone asked you to define what it took to be a consistent winner in poker or in online poker, what would you tell him? On my part, I’d say the following: playing in accordance with the fundamental theorem of poker, knowing exactly when to call, when to raise and when to fold.
The fundamental theorem of poker says, that you need to play as if you could see all your opponents’ cards, all the time. Every time you succeed in doing this, you gain value, every time you don’t, you give value up. Since you cannot ever play 100% correctly according to this theorem, you must settle for the next best thing: attempt to play as close to what the theorem says, as possible.
In order to achieve that, you must make sure you consistently bet positive expected value hands. The theory behind mathematical expectation is simple to understand: if you were to play a given hand against your opponent’s given hand over and over, how many times would you win on average? If the percentage is above 50%, you have positive mathematical expectation on the bet itself. Expected value also depends on the bet-sizes involved too, though. If you won 51% of bets on average but you posted double the bet that your opponent did, you’d still be stuck in negative EV-land.
Therefore, in order to recognize positive EV, you need to have a thorough understanding of pot odds, (including the effective and the implied odds), the odds you get for your hand (which is largely dependant on the number of outs), and the inter-dependency that exists between the two.
If you understand all that, and the mathematics behind them, you’ll have a solid basis for your decision-making. I say it’s a basis only, because this whole theory only gives you mathematical guidance as to what the right thing to do is, from a mathematical perspective. Poker is not just about mathematics, a whole lot of it is about playing one’s opponents and not the actual cards involved, so with that in mind, based on the reads that you make and the table image that you manage to sell, sometimes the decision that the math-model gives you is not the right one.
Let’s see now what it’s all about though.
Calling a bet based on the pot odds when all the cards are out on the table is not really a mathematical decision. In this case, all you need to do is compare your pot odds with the likeliness of you beating your opponent’s hand, or better yet, think about all the hands he could have that you could possibly beat. If a bluff is all you can beat, then the decision is easy, but mind you, if you know your opponent is just probing you with a bet and that he’ll fold when faced with a raise, you should raise. Calls like this are based on gut-feelings, reads and experience, but they are part of poker, even though they are not anchored in anything even remotely scientific.
Calls based on pot odds when there are several cards still to come are more complicated. Lets look at a Texas Holdem situation which comes up rather frequently, and is therefore of increased significance: the chasing of a flush after the flop, when one has a four-card one. (we’ll assume that two of the suited cards are in your pocket, because if you only have one of them in the hole, you shouldn’t chase the flush unless it is a card above 8. Anything under 8 will give you a more than 50% chance of losing to another flush, even if you do make yours).
Let’s consider that the pot is $50 big, and that you’re faced with a $10 bet. Should you call or should you fold (again, only considered from a strictly mathematical perspective). In this situation, you’d have to risk $10 to win $50, which means your pot odds are 5-1.
The odds of you making your flush are as follows: there are 9 cards in the deck that will help you. That means you have nine outs. Since there are 38 cards in the 47-card unseen deck (52 – the 5 cards you already see: 2 in your pocket and 3 on the board) that will not help you, the odds against making your hand are 38 to 9, which is 4.22 – 1. Those odds are obviously better than the 5 – 1 pot odds you get, so you should indeed make the call.
The funny thing about this is, that the odds presented are only valid for the turn-card. You may miss your flush on the turn, yet make it on the river. This means, you’ll have to take into account the amount your opponent raises on the turn, that you’ll be forced to call to see the river, and re-calculate the odds based on that. These are called effective odds. You can just add the odds on the turn and the river up, to get your final odds, but this is already an estimated value (you never know how much your opponent decides to bet after the turn).
The most important thing you have to pay attention to when calculating your odds according to the above example, is that you do indeed take ALL your outs into account. While you’re chasing a flush, there is a possibility that you’ll make a straight (if the board texture is right). Under those circumstances, it may even be right to raise, just make sure you don’t ruin the pot odds you get, or you’ll turn the whole equation upside down.
Implied odds are even more abstract. Calling in short-handed games with a low pair in the pocket is often a good idea, because the amount of money you spend calling and not making your trips, is more than compensated for the times when you do make them, because a set with two of the cards in the pocket is a hand that is bound to take down a huge pot.
Your mathematical odds are always good advisors. Just remember not to make your decisions based solely on them. There are plenty of other factors that a good poker player needs to consider.
Top class poker professionals care less about the mathematical odds than they do about the reads they exchange with their opponents. It’s called "playing the player”.
