re: Poker & Should good players run below EV?
Originally Posted by TheWall
I'm not sure if this is nonsensical or pointless but its something that has gotten me thinking. Isn't it logical that good players should run below EV. I say this because they are less likely to get into situations where they pull off bad beats. Where a bad player might whimsically push it all in with 99 only to crack a hero's AA, a good player would make the lay down. Discuss, Set me straight, Do something.
I, too, used to think along these lines. But over a long enough period of time everyone should run at expectation. I think you're making the same error in thinking as I did. I'll try and explain:
Imagine (the unlikely scenario) that a particular player only ever gets himself all-in with AA. He was so tight he wouldn't even consider it with any other cards. My thought process, and presumably yours, was that he could only either win, which was 'expected', or get sucked-out on, which was -ev. There was no hand that he would ever be behind against for him to suck out and create any +ev.
But this isn't actually the case. Imagine AA versus 55. For ease of argument, let's say that AA is 80% favourite to win. If we play this hand 1 time, head-up and AA wins we are actually running ABOVE expectation for that hand. We have 100% value when, over a long enough sample of games, we should only actually be at 80%. In a slightly strange, counter-intuitive sense, you could say we are getting lucky every time our aces hold up as we are running at 20% over expected.
Now imagine AA versus 55 a 'typical' 10 times. The first 8 times we run it we win every time. That's 8 times we've run at 20% +ev That's 8X20 = 160% +ev. When lose the final 2 in a row we're running 80% below ev. 80X2 = 160% -ev. Thus cancelling each other out and we're running as expected. It's also worth noting that, obviously, we're not going to reach expected value
after 10 hands, or after 10000 hands or even after 1000000 hands. But...the longer we play, the more likely we are to converge at this true point.
So the general conclusion is that it doesn't matter how strong a pre-all-in holding is - you should always expect to run at expected value after la ong enough sample.
I'm not sure that's a great explanation - my use of poker terminology isn't always spot-on so if anyone cares to correct me then fire away. I think the general theory is right though...