The ways of chopping a prize pool

By Mark Lasser

Last week I played in one of the tournaments at the Golden Gates. I hadn’t played a tourney in awhile and it was starting right when I got there, so I took a shot. I think their breakdown for a $90 buy in is $10 for the dealers, $17 for the house and $63 for the prize pool. We had 40 players so the event paid four spots. With 20-minute rounds, things move pretty fast and I figured it would be four to five hours.

I’ve really been in the zone lately and have booked seven consecutive winning sessions. This day was no different and I managed to lay down pocket queens twice to pocket kings. I pulled off some dynamite bluffs and induced all in bets twice. The first one was with a nut flush on the turn against an aggressive player. I “Hollywooded” the turn pretty hard and threw about three solid fake tells at her. I won’t say what they were, but she was completely sure I didn’t have the goods. On the next hand the guy to my left made a comment about the acting job and said it took a lot of skill to pull that off convincingly. Hey, who doesn’t like compliments?

As we got to the final table, all the stacks were pretty short. There are two ways to evaluate how deep one’s chips stack is. The easiest way is to divide a stack by the amount of the big blind and think in terms of big blinds, i.e., I might have five big blinds left and my opponent has 12 big blinds left. The weakness in this is that it doesn’t count the small blind, which might be substantial, and it won’t take antes into account when they’re at play as well. It also doesn’t figure that your stack is in more trouble when a table is short handed.

The alternative is to divide your stack by the cost of playing around the table once. So divide your stack by the sum of the small and big blinds and all antes. That tells you how many times you can go around before being blinded off at the current levels. Dan Harrington calls this the “M” number. There are other names but it’s generally considered an important figure to be aware of.

Once play gets to the point where everyone’s “M” number is below 3, there’s not much strategy left to the game and it really becomes about luck. In this tournament, when we got down to seven players, the chip stacks for most of the table was 50K with blinds at 9/18, so most players couldn’t make the blinds more than one more time. I had 100K and the chip lead had 150K, so we could go around three times and five times respectively. Anytime two of the 50K stacks played a hand, a double up was going to be likely. So, I floated a chop option to the table. I’ve done this before at the Gates and had problems, but today’s crowd was a little more relaxed.

There are three ways one can chop a prize pool. The first is simply to chop evenly, which only makes sense when everyone is close to even. The second option is to split the pool proportionately. In this case it would mean we could divide the prize pool so that I got twice the average share and the chip lead would get 3X the average share. The problem with this system is that it doesn’t take into account the volatility and luck that now dominates with these massive blinds.

The third option is the most complicated and requires a calculator and some software that on Sunday no one had. It’s called the ICM model and it stands for Independent Chip Model. The idea here is that the largest stacks are not likely to finish as the largest stacks and some of the short stacks are likely to increase their stacks and improve as play continues into the luck rounds. So the ICM model softens the chasm between the top and the bottom.

If we chopped the pot proportionally, the chip lead would make $756, I’d make $504 and everyone else would get $252. But knowing that the chance of finishing with nothing is significant, even for me and the chip lead, there’s some value in giving up a few dollars for the certainty of cash in hand. The ICM model calculates this.

The formulas are complicated but come down to a calculation of probability and expected value like in many other games. Sure, I’m in second place now, but what is the probability I’ll finish in second place and get the second place money, which in this case was $750?

There’s actually a greater chance I won’t finish in second place and a decent probability I’ll finish in fourth or even on the bubble with nothing. The old bird-in-the-hand issue, right? It’s a question of equity.

There are phone apps and software to calculate the ICM payouts based on prize pools, distributions, starting and remaining chips stacks, etc. but I didn’t have one on me on Sunday. So we did come to an approximation and settled the game then and there.

When I got home I popped the numbers into an ICM calculator and found I shorted myself by about $100 and the chip lead by maybe $150, so I’ll be sure to bring an ICM to future games. In truth this is something the card rooms should offer to do for you but there are tools out there.

Mark B. Lasser is Denver writer and international poker player. He regularly plays in Colorado, Arizona, California, Missouri and Nevada. You can hear him talk about gambling and casinos every Friday at 5 PM on KEZW AM 1430. Readers can send questions and comments to him at ColoradoPokerMark@comcast.net.