Thursday, June 4, 2009

"The Right Play" Early in a Game

It makes me chuckle when I read books, like DeLynn Colvert's "Play Winning Cribbage" (great book btw), because they state emphatically that a defensive play is best to start when you are the dealer, because on average that's the right play.

In golf, if the odds of hitting a ball in the water are 80%, do you putt the entire hole? (probably a bad analogy) But what I'm trying to say is that each game individually isn't "the average play". How many times have you played the first hand defensively and then gotten to the end of the game and lost by 2 points? Probably as many times as you've gotten to the end of a game and thought, wow, glad I played that first hand defensively.

The problem with the logic is that a defensive play in the first hand is optimal assuming the rest of the game is average, but the odds of that happening are very low. You can't state in the first hand of the game what an optimal strategy is for winning the game. You can however, say which strategy gets you a bigger lead, which I think is more important to winning.

The classic example here is the 5-6 as the dealer. Do you play the 5 or the 6 on a 10 lead? I always play the 5. Why? Two reasons. First, you never know if the game is to be an average game or not on the first hand, so it's too early to think about that. And then second, my odds are better of being farther in the lead playing the 5. What do I mean? I play the 5, that gives me 2 points, then let's say it's 50/50 if my opponent plays a 5 back, in which case I likely play a 10-card for a 3-2 edge. If it's 50-50 he plays another 10-card, then I'm up 4-0 with my 6. So I figure there's a 50-50 change I'm up 1 or 4, which means on average I'm up 2.5 points by playing the 5. Doing the 5-6 way would give me a 2 point lead. So because I don't know if it's an average game or not, I pair the 5. There's probably some real odds of having a 5 and a face card, but I'm lazy, I assumed it's 50/50. But lazy is ok here, because it's the right play until the expected value drops below 2, which is what you get the other way. 1*.67 + 4*.33 = 2, so unless the odds of my opponent having a 5 are more than 67% I'm making the right play.

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