I am first in a small HORSE tournament at the moment. Eighty players remain of 240 who started.

If we stopped the tournament now and paid everyone equally then all of us would triple our buy-ins (240 / 80 = 3 buy-ins per player remaining). But that doesn’t take into account stack size or player skill. I’ve thinned the field more than other players — it seems fair that I should get more. Still, an equal payout seems like the happiness-maximizing distribution — it pays more than 75% of the remaining field will end up getting.

The equal distribution is also not Pareto-efficient because there is another distribution which doesn’t make anyone relatively worse off while enriching others. You could, for example, take $1 from all remaining entrants and give it to the chip leader. It seems that setting a tournament structure is an exercise in balancing overall happiness using Pareto efficiency. More efficient tournaments make better players happier at a cost to everyone else.

At least in theory.

This week I’ve enjoyed a few hundred smaller tournaments that pay the top half of the field twice the starting buy-in and then call it quits. Their pay structure is highly perfectly Pareto-inefficient and that affects the strategy for playing them. First, it drives variance way down — it’s harder to lose “accidentally”.

Second, essentially the top half of the field all have the same chip count so there’s almost no point in two people above that cutoff getting involved in a hand — it’s not likely that doing so will get you closer to winning. This brings Sklansky’s theorem into play in interesting ways, especially the bit about implicit collusion, and can give rise to the almost-mythical “folding Aces preflop” situation (I’ve been mucking AK like crazy). Morton’s theorem is wrong in certain situations as well — perhaps counter-intuitively it makes sense for you to help your neighbors stack the 50% – 1st player by playing sub-optimally. Cooperative poker!

Anyway: Pareto efficiency doesn’t consider fairness, equality, or happiness. Maybe we should be balancing our big economy differently? Pareto inefficiency seems to make small poker economies more fun