The more I think about it, the more I think that there should be a better way to distribute prize money at the end of a tournament if the remaining participants agree on a chop. Typically, the remaining players simply divide the remaining prize money; sometimes, it will be arranged that the chip leader gets a bit more.
Up until last weekend, I’d not done chops. On the rare occasions I’ve made it to the point where someone proposed a chop, I was of the mind of playing it out, practicing my live shorthanded play, and letting the cards and chips fall as they may, accepting wherever I finished. And I think there’s nothing wrong with that.
Last weekend, I played in a tournament where a nine-way chop was proposed. And it was an interesting proposal. The initial proposal was that the two short stacks get $700, with the remaining 7 players splitting the rest. As I was one of the short stacks, with just one big blind, and because 9th place paid out $280, I was amenable.
The tournament director pointed out that the chip leader was significant ahead of the rest of the table and suggested that a chop might want to recognize this. The table essentially agreed, the rest saying they’d take a bit less and pass the difference to the chip leader, who got something in the vicinity of $2000. The player in second place got about $100 more than the rest of the table, which all got about $1500.
But I think there’s a better way, even if it means a bit more math.
Put in semi-math terms, I think in a chop between X players, each player remaining should get the payout for Xth place, and then split up the remaining amount in the prize pool proportionally to their chip stack.
Let’s show a simple example.
Say there are two players remaining. First place pays $20,000, second place pays $10,000. There are 100,000 chips in play. Player A has 60,000 in chips and Player B has $40,000 in chips.
In this chop scenario, both players would get $10,000, the second place prize. Remaining in the prize pool is $10,000. Player A has 60% of the remaining chips, so Player A would get 60% of the remaining prize pool, or $6000, for $16,000 total. Player B has 40% of the remaining chips, so Player B would get 40% of the remaining prize pool, or $4000, for $14,000 total.
Basically, this rewards players for the effort they have expended to put themselves in a position to win. Most poker pundits will say that a player that has X percent of the chips in play will, in the long run, have the same X percent change of winning. So in the long run, this chop formula will give them their long-term money expectation.
Let’s look at another, more complicated example.
Say 4 players remain in a tournament that pays $4600, $2300, $1500, and $600 for 1st, 2nd, 3rd, and 4th places, respectively. The 4 players have played for 5 hours and have beaten out a pool of 126 players. They have chip totals of $58,000 (Player A), $6000 (Player B), $33,000 (Player C), and $29,000 (Player D), for a total of $126,000 in chips.
The total remaining prize pool is $9000. Each player gets $600, for $2400 total, to the prize pool available to divide is $6600. Now we calculate.
Player A gets 58,000 / 126,000 = 0.46 x $6600 = $3038 + $600 = $3638
Player B gets 6000 / 126,000 = 0.05 x $6600 = $314 + $600 = $914
Player C gets 33,000 / 126,000 = 0.26 x $6600 = $1729 + $600 = $2329
Player D gets 29,000 / 126,000 = 0.23 x $6600 = $1519 + $600 = $2119
Pragmatically, unless the chip leader has amassed a stack more than double the size of any other, that player will give back from the first place money. But it will be better than an even split, and even better than most splits that give the chip leader some extra.
The calculations are easy to do. The methodology awards each player’s tournament effort. And so I can’t see it as anything but fair.