Aggression in Card Games

The other night, I couldn't sleep. So, at 3 or 4 AM, I was watching the final table from the Main Event at last year's World Series of Poker. For those of you who don't know, the Main Event is a $10,000 buy-in No Limit Texas Hold Em event. So, on any hand, you can bet as much as you like including the infamous 'all in' where you put all your chips in the pot. If somebody calls your bet and they have as many chips as you and you win, you double your stack, but if you lose your out of the event.

So, as I looked at the final table, most of the players were amateurs and of the poker pros there, they were almost all in their 20s and not among the best known players. Why is that?

I think it has to do with a combination of youthful exuberance and the fact that once you are playing with chips as compared to real money, the players with experience in big cash games are actually at a disadvantage. Consider this. At any table, the player with the biggest chip stack has a big advantage. He can be the table bully. So, on the first hand of the tournament, if you get dealt a good hand, why not go all in? If you lose, well so be it. Most people don't stick around long enough to 'cash' in the Main Event. If you happen to double up, you are now the bully, the boss, the head honcho.

Top players don't play this way. It's not a percentage bet. But the internet players who have gotten used to playing hand after hand after hand, usually in lower stakes games aren't bothered. Online, if you lose, you just find another tournament. It happens so fast.

Consider the effect of doubling up early though. When you start the event as a random player, you have about an 11% chance of cashing. That is, roughly 89% of players will lose their $10,000. The remainder will turn a profit, albeit small for most of those who cash. I don't know this, but I would hazard a guess that someone who rolls the dice, so to speak, gets lucky early on, and doubles up a few times significantly increases their chances of cashing. So, for example, if by being ultra-aggressive (some might say ultra-risky) early on, you might double your chances of cashing, or even more. Now, here's where the math gets funny.

Suppose the result of over-aggression is that at the end of the first day of play, either you have doubled your chances of cashing or been eliminated. Let's also defined 2 possible outcomes, either you cash, "C", or you lose, "L". Initially, your chances of C were 11% and that has doubled to 22%. Initially, your chances of L were 89% and that has increased by only about 1/8 to 100%. Frankly, I like that play, but the top pros are too conditioned to make the same play they would make in a cash game. I would never play against them for real money, but in tournament conditions, I think their edge is diminished significantly.

I could take this analysis to duplicate bridge as well, especially head-to-head team games. Suppose my partner and I are playing against two of the best players in the world, and similarly at the other table, our poor teammates are playing against another top pair. If we play things straight, we may rate to lose 95% of the time and win 5% of the time. Suppose we go wild instead. We interfere in their auctions ultra-aggressively and take lots of chances.

Frankly, we will probably now lose by an extremely large margin most of the time. But, if we lose, we don't care what the margin is. If you lose in a knockout, you are out. So, suppose when we played things straight, in our 19 losses out of 20, we lost on average by perhaps 50 IMPs. Now, by taking a walk on the wild side, when we are losing, it is by 125 IMPs on average. But, we are now winning 2 matches out of 20. Then we have increased our winning percentage by 100% (2 divided by 1 minus 100%), and the way we got there was by losing by more when we lose.

Bottom line: in the right circumstances, stupid looking aggression can pay off. If the worst downside is humiliation, but the upside makes sense, go for it.