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Poker Strategy With Ed Miller: Test The Edge Cases

A Simple Tool To See If You Are Making The Correct Play


Ed MillerI was a physics major in college. Physics is very hard — too hard for me it turned out, and I haven’t cracked a physics book since the day I got my degree.

One reason it’s so hard is that much of it is abstract. You’re learning about how the world works, but a lot of what you study in physics are things you can’t see. You write wave functions for the tiny things that make up atoms. These are long equations with multiple variables that purport to describe the behavior of matter. Many times I finished a problem in school by producing a complex equation, and I would think, “I think that’s right. But it could be wrong, and there’s no real way for me to tell. I don’t have any idea what this equation even means!”

I learned a trick to deal with this problem, and it’s a trick I think everyone should learn. It doesn’t apply just to third year physics problem sets. It applies to darn near everything in life that’s more complicated than tic-tac-toe. It’s called testing the edge cases.

Let’s go back to physics for just a moment. (Don’t worry, I’ll spare you a discussion of infinite dimensional Hilbert spaces.)

Say I have written an equation for how far a ball will travel when I throw it on the moon. I know the ball will go further than on the Earth, but how much further? Twice as far? Ten times as far? I don’t have any intuition for the answer, likely because I’ve never thrown a ball on the moon. I want to know if my equation is correct, but I can’t just look at it and tell, because I don’t know what the right answer looks like.

So I test the edge cases. First, I’m going to set the gravity on the moon to zero. If there’s zero gravity, how far does my ball travel? With nothing pulling on it, the ball will go out to infinity. That’s an edge case. I don’t know how far a ball is supposed to travel on the moon, but I do know that if I set the gravity equal to zero, my equation should say the ball goes forever.

If it doesn’t say that, I know I’ve made a mistake and I need to go back and look for it. If it passes this edge case test, however, that’s evidence I did things right.
Now I test another edge case. What happens if I set gravity to infinity? In that case, the ball shouldn’t travel at all. It should just fall immediately to the floor. So if gravity is infinity, my equation should say the distance is zero. I can check that edge case.

I could even check one more edge case. What if I set the gravity the same as it is on earth? Does my equation reduce to one that I know is correct on our planet?

If my equation can pass all three of these edge case tests, then it’s likely (though not guaranteed) that it is correct for all cases — including for gravity on the moon.
So what does this have to do with poker?

It’s simple. Most people play no-limit hold’em with a strategy that they’ve honed over the years. Is their strategy the right strategy? Is it close?

It’s very hard to tell! The game is so complex — even relatively basic no-limit strategies are complex — that it’s nearly impossible just to look at a strategy and say, “Yup, that’s right.” So you should test the edge cases.

What’s an edge case in poker look like? Well, here’s one. “What if my opponent bets every time I check?”

If your strategy is any good, you should win a ton of money against a player who plays like that. That’s a given. If anyone is so crazy, yet so predictable, that they will bet every single time you check, you should be able to crush them.

Here’s the thing. When I sit in a $2-$5 game, I see most of the regular players playing a strategy that, in my opinion, would actually lose to someone who simply bet when checked to.

Why? Because these players tend to keep betting until they are ready to give up on a pot. Then they check and fold. In many cases, these experienced no-limit players will fold after they check 70 percent of the time or more. So if they played against someone who called along and then bet whenever checked to, the regulars would end up giving up on way too many pots.

How about this one. “What if my opponent raises every time I bet?” How does your strategy do against that player?

Really think about it. What would happen to you if every time you made a bet, you got raised? Would you clean up? You should, of course, since any strong strategy would destroy a maniac like this.

But again, many regular $2-$5 no-limit players are quite timid against raises. They fold a lot. They call once and then fold to the next bet. I see it again and again. I would say that many regular players out there would lose to someone who played the couldn’t-be-any-simpler strategy of simply raising every bet.

“Now, wait a second, Ed,” you say, “Maybe my strategy would lose to someone who raised every time I bet — for two hands. Then I would adjust and start calling that guy down.”

No doubt, you would. But what if your opponents didn’t make it so obvious. What if they didn’t raise you every time, but just half the time? What about a third of the time? There’s a point where your opponents are taking advantage of your strategy, and you’re not adjusting either. That’s the point where you lose at poker, and you can’t figure out why.

So test the edge cases. You shouldn’t play a strategy that’s vulnerable to someone who just bets every time you check. After every session, write down hands where you fold on the turn or river. Then test the edge case. “What happens if my opponent bets 100 percent of his hands in this situation? Do I usually get him? Or does he usually get me?”

Write down every hand you can hold. Think about what you would do with each one — if you would fold it or not. If you are folding most of them, then your edge case test has failed. Your strategy doesn’t even beat someone who just bets 100 percent of the time. This indicates that you are doing something wrong, and you need to go back and figure it out. What can you change about the way you play that prevents such a simple strategy from beating you?

It’s very hard to look at a complex physics equation and know that it’s right. It’s much easier to check if it’s wrong — by testing edge cases. Poker is the same. You can find the flaws in a strategy by checking edge cases. Use this simple tool to test your play and see what you can find. ♠

Ed’s brand new book, Poker’s 1%: The One Big Secret That Keeps Elite Players On Top, is on sale now at Find Ed on Facebook at and on Twitter @EdMillerPoker.