Updated on 09/17/2011 11:28PM

Payoff-to-probability ratio is crucial math


One of the key differences between horse race handicapping and hold'em poker is the way players approach the concept of betting favorites.

In horse racing you always look for playable longshots, hoping to avoid taking 6-5, even on a seemingly well-placed betting favorite. By contrast, in poker you are glad to be the favorite - the shorter the price the better - and when you bet on your solid holdings with gusto, you just hope no one draws out on you with improbable longshots to take the pot away. Yet, in both games it is impossible to know who should be the favorite unless you know the odds of the situation, or have a way of figuring that out.

In horse racing you might rate a front-running stakes horse as the logical favorite - perhaps even-money - when he has no competition for the early lead. But, realistically, you are only guesstimating this horse's true winning odds based on your experience and some elusive statistical trends. In poker, however, you can figure your odds much closer to exact reality through basic mathematics, but that is not the only thing you must know.

Consider this everyday example:

You open your hand and find a pair of kings, a great starting hand in hold'em poker. But, as soon as you bet a bunch of chips, the diabolical nature of poker presents itself: An ace falls on the flop.

Do you call the bet, believing that your kings are still good?

Do you put in a raise to represent aces yourself or flush out a possible bluff?

Or should you fold in the belief that you are no longer a heavy favorite, because you probably will need a third king to restore the power of your starting hand?

It depends.

It depends on who you are playing against and how large the bet was against you. It depends on whether you believe the bet was made to drive you out of the hand, or whether you believe your opponent actually has made a higher pair.

You cannot know for sure, but folding would be the conservative way out of the dilemma considering the cold mathematical realities.

Other than your two kings and the three cards on the board, there are 47 cards left in the deck (including your opponent's two). With the turn card coming you will have two kings still out - two good "outs" - against 45 potentially bad outcomes. That translates to 22.5-1 odds, (4.4 percent) to catch one of the kings on fourth street, and the same two outs from the remaining 46 cards (22-1) to catch the king on the river.

That is slightly less than a 9 percent combined chance to catch a set of kings. In other words, you will draw your set of kings once in every 11 similar situations. (Please note that your opponent will have the same chance of catching a third ace on the turn or river.)

Logically, you should go forward with your kings only if you have a great deal of insight about your opponent's tendencies.

If he or she is a relatively tight player who rarely bullies the table, one who seldom relies on scare cards to win pots, you cannot justify playing unless the bet was small or you have a major chip advantage and would be willing to lose more chips to get a read on your opponent.

If however, your opponent has a history of trying to overrun the table, you certainly should consider a raise to flush him away from a possible bluff. Calling is probably the weakest choice because it will invite the raiser to make it more expensive for you to go to the river.

Merely knowing the odds will not give you all the answers, but it is an essential starting point. Fortunately, there is no need to memorize complicated mathematical formulas to get a good grip. Try this shortcut approach:

If you have two outs and one card to come you have roughly a 4 percent chance to catch lightning in a bottle. Therefore, each out can be presumed to be worth about 2 percent for each card yet to be exposed. So, when you have three outs and two cards to come you have 3 (outs) x 2 (percent) x 2 (cards to come), which roughly equals 12 percent to get lucky, or 7-1 odds.

Because this is a shortcut to the actual math, you will find it necessary to reduce your percentages by about 10 percent whenever you have eight or more outs and by 15 percent when you have 15 or more outs. This is not rocket science.

Let's say you have J-10 unsuited in your hand and the flop contains 3-9-Q rainbow. That gives you an open-ended straight draw with eight outs (four 8's and four kings), with two cards to come. That translates to 8 (outs) x 2 (percent) x 2 (cards to come) = about 32 percent, before you reduce that by almost four points or about 2 .5-1 odds.

Without considering the concept of "implied odds," which takes into account the likelihood that the pot may swell significantly if you do catch a winning card, you should be willing to chase your straight on the turn so long as the pot is offering a payoff greater than $2.50 for every $1 you have to bet. On the river, however, the odds against you will approach 6-1.

By deciding to make a wager when the payoff is greater than the odds, you are following the single most important practice in poker and handicapping: Getting good value for your money.

* More information on odds and poker probabilities is available at www.cardplayer.com or www.twodimes.net, or the book Holdem's Odd(s) Book, by Mike Petriv.

Steve Davidowitz plays as "StevenLD" on various Internet poker sites and is the author of the handicapping book "Betting Thoroughbreds."