05/24/2006 12:00AM

Keep percentages handy - and in your favor


With the Triple Crown in progress, I haven't played much poker in recent weeks, so it feels like a good time to brush up on some fundamentals.

Here's a pop quiz I created for myself that you might also wish to take.

Question A: It is the first hand of a tournament and you are holding A-A at a table of 10 players in which four people go all-in before it comes around to you. Should you go all-in with glee? What are your odds that this high-grade holding will stand up?

Answer: 3-2 against you, if none of the other players holds an ace; 2-1 against if one of the other players has one of the other aces in the hole. Either way, you will bow out of this tournament 60 to 66 percent of the time with A-A facing four opponents who have committed all their chips before the flop. Of course, 33 to 40 percent of the time your aces will stand up and you will grab a significant chip advantage by taking down all four players. The choice you make will help identify how aggressive you are after you've just bought into this tournament. In the case of the World Series of Poker, the cost would be $10,000. In the case of a rebuy tournament, you would have no reason to hesitate. Go all-in. Should your aces get cracked, you can get a fresh stack of chips with the rebuy.

Question B: In the same situation as above, how many all-ins against you would keep the odds of survival in your favor?

Answer: Ideally, A-A works best head-to-head or against two opponents. Against three players you still would have a 50 to 53 average win percentage with a potential threefold chip win. Logically, getting 3-1 on an even-money proposition would be worth the gamble, but you can expect to be pitched out of the tournament half the time.

Question C: Which two card holding gives you a better chance to beat 2-2: K-Q suited or J-10 suited?

Answer: K-Q suited has a marginal 2 percent advantage over 2-2. J-10 suited has a 6 percentage edge over 2-2. The reason is the greater number of straights you can form with J-10.

Question D: The game is no-limit hold'em and you have K-Q suited in hearts and the four cards to the turn are: 10-h, J-h, 4-c, 4-s. There is $405 in the pot; you are on the button playing against one remaining player - the big blind - who called your $60 pre-flop bet, called your $120 bet after the flop, and now has made a $200 bet of his own coming out of the turn. What is the most likely holding for the player in the big blind?

Answer D: A-4. The reason we can deduce this comes from playing the hand out in our mind through reverse logic. The big blind's initial call could have been anything, but the raise coming out of the turn signifies trips (three of a kind). If so, and it does seems likely, he really could not have had something like 10-4 or J-4, or Q-4, or K-4, because those are folding hands in the face of a pre-flop bet and now we know that one of his cards probably is a 4. Having a 4 eliminates other acceptable starting hands, including a range of suited connectors and/or a small pair. A large pair would have given the big blind motive for a raise pre-flop and/or after the flop.

Question E: You are in a $50 single table no-limit hold'em tourney and you hold A-2 suited in spades. There were three other players in the hand before the flop and you are sure one of them just made trips, while the others may have straight or flush draws. You have a nut flush draw and a small pair. The board shows J-s, 2-h, 10-s, there is $600 in the pot, and the bet is $300 to you, with two players to follow. You have $1,200 in remaining chips. What is your best play: Fold? Call? Raise? Raise all-in?

Answer: Call. Reason: If you raise you might drive out the remaining players and you would like their money in the pot if possible. If you fold you will be giving away good pot odds to make your nut flush. You have nine cards out there to hit it, which means you have about a 25 percent chance to catch it on the next card and a total of 30 to 35 percent chance to catch it with two cards to come, pending the actual holdings of the other two players. Your call will represent one-fourth of the existing pot and more money may be added to it on this round when the remaining player acts. Should he fold, you still will be getting a 3-1 payoff on a 2-1 proposition and you have other possibilities that increase slightly your odds for success should two more aces fall on the turn and river, and/or an ace and a deuce, which would give you a winning full house.

Question F: What's the best method to get the odds for any of the above situations as well as a wide variety of additional two-card holdings and flops?

Answer: You can use basic math, such as was applied in Question E, where nine "winning" flush cards still were in the deck vs. 38 unexposed "losing" cards, which translated to about one chance in four or 3-1 odds to make the flush on the turn and a slightly higher percentage overall when the river card is added to the equation. Or, you can do what many other poker players do to save time: Go to www.twodimes.com; or www.cardplayer.com/poker_odds, where you can plug in any two-card combination vs. any projected flop to get the precise percentages you are facing.

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