When to take action

[thestuman]

When to take action

By Phil Gordon
ESPN.com poker columnist
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At the no-limit table, I've found that there are certain actions that should be matched at very specific ratios. When performed at the appropriate ratios, a player's strategy becomes unbeatable. Game theory, the branch of mathematics that deals with these types of ratios, is of great service in determining the correct proportions for these actions. When I mention game theory to most people, they cringe in fear and uncertainty. But fear not: This is not rocket science and you don't have to have Chris Ferguson's Ph.D. to be able to figure this stuff out.Let's start with an example: Poker DVD by Expert Insight with Phil GordonWe're in the cut-off position with a hyper-aggressive, great player on our left on the button and two very weak players in the small and big blinds. Everyone folds to us and we're enticed to play this hand in order to play against the weak players in the blinds. We decide we're going to raise three times the big blind.Our aggressive, observant opponent on our left knows what we're up to -- he knows that we're "on a steal" more often than not and decides that every single time we raise from the cut-off he's going to reraise from the button and make it about nine times the big blind (three times our initial raise). Now, the question is this: If we know the button is going to employ this strategy, what is our "break even" ratio of hands we're going to play, where we're going to fold to the reraise vs. we're going to re-reraise and hope to take down the pot?Let's set up a mathematical formula:"F" equals the percentage of hands we'll raise on, and then fold to a reraise, losing three blinds."R" equals the percentage of hands we'll raise and then re-reraise, winning 10.5 blinds (the opponent's nine blinds of his reraise, the small blind, and the big blind).So, our formula looks something like this:F multiplied by 3 equals R multiplied by 10.5 (lose three blinds when we fold, win 10.5 when we re-reraise)F divided by R equals 10.5 divided by 3F divided by R equals 3.5Translated, this means that to "break even" over the long term, we should fold 3.5 times for every time we come over the top. First, I pick the hands that I'm going to make the big re-reraise with and be confident that I've made the right play:A-A: 6 possible hands (AcAd, AcAh, AcAs, AdAh, AdAs, AhAs)K-K: 6 possible handsQ-Q: 6 possible handsJ-J: 6 possible handsA-K 16 possible hands (AcKc, AcKd, AcKh, AcKs, etc.)A-Q 16 possible hands-------------------------------
There are 56 total hands I'm going to re-reraise with.Next, I use the action ratio to figure out how many hands I'll raise with and then fold to the reraise:56 multiplied by 3.5 equals 196 handsWhat this tells me is that I should be willing to raise with 196 plus 56, or 252 of the hands I'm dealt in the cut-off.How many two-card combinations are possible?52 multipled by 51 divided by 2, equals 2,652 divided by 2, equals 1,326Thus, I should be willing to risk that preflop raise with 252 divided by 1,326, or about 20 percent of the hands I'm dealt.Think through some of these situations at the table and come up with your own action ratios. I think you'll find it very instructive and it will definitely improve your game. Next time you raise from the cut-off and fold to the button's reraise at your home game, tell all your friends you're using game theory. They'll roll their eyes, but you'll win their money in the long run..