# No Limit Hold’em Poker Bot Profits by Effective Stack Size

This is post #8 in an ongoing series of articles about my work as a poker bot developer.

Two weeks ago I posted a chart of the poker bot’s net income for its last full month of play, September 2008. As a poker player, your net income is a crucial figure because it determines what you can actually buy with your hard earned profits. That’s the number you would tell your non-poker playing friends if they asked how you were doing. However, net income only paints part of the picture. To truly measure your results and your progress, you have to break down net income and analyze exactly where your profits and losses are coming from.

As a bot developer, identifying and eliminating weaknesses in the bot’s play were crucial to making it profitable. One way I did this was to break down its results into groups based on its effective stack size.

Effective stack size is best explained by example: Say you’re playing No Limit Hold’em with one opponent and you have \$25 and he has \$10. The important thing to realize is that your opponent cannot risk more than \$10 in a single hand because that’s all he has in front of him. If he can’t risk more than \$10, you can’t win or lose more than \$10 either. Your effective stacks, therefore, are \$10. It’s what you’re effectively playing with.

Put another way, your extra \$15 does you no good playing against an opponent that can only risk \$10. Because that extra \$15 is not in play, you should devise your strategy based on the effective stack size; not your actual stack size (stack size should play a central role in your poker strategy).

Furthermore, you shouldn’t measure the size of your stack in chips or in dollars; you should measure it in terms of big blinds.

Consider this: you’re playing \$1/\$2 Heads Up No Limit Hold’em with a \$200 stack. You’re the small blind and dealt pocket tens. All other things considered equal, you should make the same move as if you were playing \$100/\$200 with a \$20,000 stack because in both cases, you’re playing with a 100 big blind stack (\$200/\$2 = 100, \$20,000/\$200 = 100). You could also measure your stack in terms of how many small blinds you have, but the standard is usually big blinds.

Q. You’re playing a Heads Up No Limit Hold’em Sit-n-Go (HUSNG) and the blinds are 25/50. You have 2,000 chips and your opponent has 1,000. What’s your effective stack size in big blinds?

A. You can’t risk more than 1,000 chips in a hand, so your effective stack is 1,000 chips, or 1,000/50 = 20 big blinds (bb).

When you start a HUSNG you’re given 1,500 chips and the blinds are 10/20, so you have a 75bb effective stack, meaning that in a HUSNG, you can never have more than a 75bb effective stack. If the blinds jump to 15/30 and you still have 1500 chips, you have a 1500/30 = 50bb stack.

The bot’s strategy changed depending on the effective stack size, which is why I broke down the net income into the different groups. The groups might seem strange (ie: why “22-35 bb’s?”) but there’s a method to the madness. Some of it is based on postflop stack to pot ratios and some of it simply based on preflop stack size.

Finally, “5 bb/100” means that the bot won, on average, 5 big blinds every 100 hands. Measuring bb/100 is the standard way to gauge a player’s ability and what is a good number will vary based on the stakes and type of game.

This is all a long way of saying here are the results of my poker bot for its last three months of play broken down by effective stack size.

# 50 – 75 Big Blinds

21,479 hands @ 31 bb/100

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# 35 – 50 Big Blinds

12,279 hands @ 14 bb/100

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# 22 – 35 Big Blinds

11,615 hands @ 4 bb/100

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# 15 – 22 Big Blinds

5,688 hands @ 5 bb/100

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# 10 – 15 Big Blinds

6,609 hands @ 5 bb/100

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# 0 – 10 Big Blinds

5,076 hands @ 3 bb/100