by Todd Gross

About a year ago, I decided I wanted to try playing poker. Live. In a casino. Like many of you (all of you?), I'd seen the World Poker Tour on the Travel Channel, the World Series of Poker on ESPN, and other poker on television. I used to play poker many years ago, when I lived in Las Vegas. I felt ready to try my luck. But not so fast…

I knew from my experience in Las Vegas that many of the people I'd be playing against would have played for years. They would know when to call (or check), when to raise, and when to fold. They would also know how to keep their hand a secret, by not giving away any clues (or tells) during the hand. Furthermore, when I played years ago in Las Vegas, I played Seven Card Stud. This time, I wanted to play Texas Hold'Em. I knew I needed help if I didn't want to spend hundreds of dollars making mistakes, playing hands I shouldn't have played, or throwing away hands that I could win with. But what help could I get that would keep me from wasting money?

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I decided the best help I could get would be knowing which starting hands were worth spending money on, the ones that would give me the best odds of winning if I stayed in the hand. A starting hand is the two cards each player is dealt at the start of the game. You use these two cards, along with five community cards that are dealt in the center of the table and used by all players, to make the best five card poker hand you can. For example, if your starting hand was 10♣ 10♦ and the community cards were as follows:

the best hand you can create uses both of your starting cards and the 10♥ community card to make three of a kind. That's a good hand. But if you're unlucky enough to be against a player who started with 9♥ 2♦ , they can use their 2♦ and the 6♠ 3♥ 4♣ 5♥ cards from the center to make a straight, which beats your three of a kind. But most of the time, you with the pair of tens would end up with a better hand than the player with the nine and deuce.

I decided to write a program that would tell me which starting hands were worth betting money on, and which weren't. Fortunately, you only get two cards in your starting hand, so there aren't many possible outcomes. Furthermore, because a deck of cards has the same 13 cards in each of the four suits, the starting suits don't matter. For example, you have the same odds of winning with 2♠ 2♦ as you do with 2♥ 2♣ .

However, because of flushes, it does matter if both cards are the same suit or different suits. If both cards are the same suit (these are called suited starting hands), they have a higher chance of winning versus cards of different suits (called unsuited starting hands), because you can make flushes using your suited hand that you could not make with an unsuited hand. For example, given the five community cards we used in our previous example,

you would have a flush if your starting hand was the suited A♥ K♥ but not with the unsuited starting hand A♥ K♠ . Therefore, I need to keep separate results for A K suited versus A K unsuited, but I don't need to keep track of specific suits.

The program was fairly simple in concept: deal out thousands of Hold'Em games, for each game, look at each player and see

1. if the player won or lost the game
2. what their starting hand was

In this way, I would end up with two values for each possible starting hand: the number of games won and the number lost. Actually, I had to modify this a bit, because it's possible for more than one player (with different starting hands) to have a winning hand, and therefore split the pot. So I gave each starting hand half the points for winning a game if two players split the pot, a third if three players split the pot, and so on.

Furthermore, you want to give more points for a win than for a loss, because when you lose you only lose the money you bet…but when you win, you win all the money everyone bet, including you. Ideally, you would make the points for winning versus losing match the amount you would actually win versus what you would actually bet. I chose a much simpler method: 6 points for a win, and 1 for a loss. This is really too high, the average win is closer to 3 times the amount you bet. These numbers made the math easier, though.

Now all you need to do is subtract the number of points for losing from the points for winning, and you have the expected result from playing all those games with a given starting hand. If the result is positive, that means you got more from winning pots than you spent on losing pots. In other words, you made money. Similarly, if the result is negative, you spent more than you won, you lost money.

Now I know which starting hands I should play: the ones with positive results. But before I tell you the results of running the program, I made one more calculation so I could compare hands to each other. Starting hands can be divided into three categories:

• Pairs
• Suited cards
• Unsuited nonpairing cards

Hands in the third category (unsuited unpaired) will, on average, appear twice as often as pairs, and three times as often as suited hands. Therefore, if I want to see if A K suited is better than A K unsuited, I need to multiply my result for the suited hand by 3 before I compare values.

Now I can give you some of the results from my program. When I first ran the program, I had the program play 1 million hands with 8 players. The top 10 starting hands were as follows:

1. Aces
2. Kings
3. Queens
4. Ace King suited
5. Jacks
6. Ace Queen suited
7. King Queen suited
8. Ace King unsuited
9. Tens
10. Ace Jack suited

All of these hands had high positive result values, meaning you would want to play them in almost any case. In fact, most experts would recommend raising with these hands in most cases. You are very likely to have the best starting hand, which means you have the best chance of winning the pot.

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Of course, I was most interested in what hands I should start with. I am a fairly conservative player, so I didn't want to play hands where the expected result was too close to zero. The simulations gave me a surprisingly simple starting hand strategy, which I used myself when playing in the casino. I don't claim this is the optimal set of starting hands, which hands you play will depend on many factors, including how many other players are at the table, how tight or loose they are in betting, how good or bad they are (do they play hands with a low chance of winning), and how tight or loose you are. Still, if you want to know what hands I considered good enough to start with, I give you the formula below:

• Pairs: play sevens or better
• Suited cards:
  • play A x (an ace with any other card of the same suit)
  • play K x (a king with any other suited card)
  • play 7 low or better
• Unsuited unpaired: play 10 low or better

When I say "7 low or better," I mean that the lowest of the two cards in your starting hand must be a 7 or higher. For example, a 8♣ J♣ starting hand meets the 7 low or better criterion, but a K♥ 5♥ does not. 10 low or better for unsuited cards works similarly.

I want to reiterate that which starting hands you choose to play should depend on several factors that change over time. In fact, one of the most important factors is whether you're playing the big or small blind, which changes from hand to hand. But this article should give you a good starting point for deciding which hands to play, and as you gain experience and confidence, you can make adjustments to your starting hands to match your playing style and who you're playing against. Good luck!