Final-Table Dealmaking

You've used all of your skill to get down to the final three or four players in a tournament or supersatellite (or even home-game tourney), and the subject of making a deal arises. You are open to the suggestion, but how do you figure out what a fair deal is for four players (or more), each with different stack sizes? This is where some players believe that another skill comes into play - negotiation. Those who know - or are able to figure out - what the best division of the spoils is try to wangle more of a share than they deserve, and those who don't know often agree to terrible deals because they thought, "That seems fair," when it was anything but.

The dealmaking method is of less importance online because poker sites usually offer to mediate when players are talking deals. One major poker site withdraws a certain amount, usually 10 percent of the prize money in contention, and then offers a "by-the-chips" split. The money left on the table is then played for and awarded to the eventual winner. This method may seem fair, but actually is biased toward the large stacks and against the short stacks.

Here's an example that shows how the by-the-chips method (also known as "chip chop figures") works:

All players involved in the deal are initially assigned a payout equal to that of the smallest regular payout yet to be awarded. The remaining prize money is then distributed in direct proportion to the players' fraction of chips in the tournament.

So, if three players remained in a tournament with scheduled prize money of:

First - $100
Second - $50
Third - $25

And the players had these chip stacks:

A - 1,200
B - 800
C - 500

Each player would receive $25 (third-place prize money), leaving $100 in the prize pool; so, the chip chop figures would be:

A - $25 + (1,200 ÷ 2,500) x $100 = $73
B - $25 + (800 ÷ 2,500) x $100 = $57
C - $25 + (500 ÷ 2,500) x $100 = $45

In addition to this, in any deal, it is possible to put any amount aside for the eventual winner. This amount also is deducted from the prize pool before any calculations are made. So, in the example above, if $25 was left on the table for the winner, the division would be:

A - $25 + (1,200 ÷ 2,500) x $75 = $61
B - $25 + (800 ÷ 2,500) x $75 = $49
C - $25 + (500 ÷ 2,500) x $75 = $40

In such a deal, either B or C could potentially earn more than A by going on, after the deal was made, to win the tournament.
In addition to online, this method is used in many Southern California cardrooms. You can see another example and more detailed description in my column "Tournament Deals" in Vol. 19/No. 20, with a cover date of Oct. 11, 2006.

A more equitable split can be accomplished by using the "Burns-Landrum estimate," described in detail in my column "Let's Make a (Fair) Deal" in Vol. 19/No. 19, with a cover date of Sept. 27, 2006. The method is not strictly accurate, allotting more to small stacks and less to large stacks than perhaps is warranted, but it fits into a convenient formula. In the preceding example (without any prize money being left on the table for the winner), the division would be: A, $67.50; B, $57.50; C, $50.

Many people argue that the best way to make a deal is by using the Independent Chip Model (ICM), a mathematical method of calculating tournament chip equity - that is, a method of estimating each player's winning chances based on the percentage that each holds of the overall amount of chips. To calculate your expected value in a tournament based on your present amount of chips, find the probability for finishing in each one of the paid places, multiply that by the corresponding prize money, and add up all of these pieces of equity. The details of the calculations, which are beyond the scope of this column, can be found in an online search of this phrase: "Explaining the Independent Chip Model."

An application exists for the iPhone or iPod Touch that uses the ICM method. Developer and tournament player Ed Fernandez wrote Poker DealMaker ICM to enable him to ascertain in seconds his own best final-table deals. Essentially, the math behind the application is this: Assume that your stack size relative to the total chips in play represents your chance of taking first place. If you don't take first, assign equal probabilities to finishing in all other places. Do this for all remaining players, take a weighted average, and then reassign results for each player. This is not a calculation that can be represented in a simple mathematical formula. It must be done programmatically, something a computer can do in seconds.



Users like how fast and easy it is to use the application during live "heat-of-the-moment" discussions for making a deal. Under the pressure of time - particularly since you are usually given only a few minutes to talk a deal - it's a huge advantage for the iPhone application to crank out a deal in seconds. Also, the ability to enter partial data when you are not in a hand, suspend entry, and return later to finish data entry makes the application even more attractive. Most top tournaments have a no cellphone or iPod rule at the final table (or even when you are in the money, which is usually the top 10 percent of the field), so you have to step away from the table to enter data. Thus, not needing to enter the figures all at once is useful.

Players who use this application in the heat of the battle never have to worry about incorrect calculations or making mistakes figuring out the deal. That gives them a huge edge over opponents, particularly at a final table that usually comes after many grueling hours when everyone is mentally drained.

This application should quickly find a home. An informal survey at the last World Series of Poker indicated that more than 30 percent of the players had iPhones or iPod Touch devices. (The application runs on both.) The application costs $1.99 from the iPhone App Store. To use it, you enter values into two screens, prize pool payouts and player chip amounts. The application then calculates a fair deal in less than five seconds. You can enter other amounts, such as those proposed by your opponents, to see who would be getting more than he should, and who less. You then negotiate from that point.

Do you even want to make a deal? I followed up the two methodology columns mentioned previously with "Why Make a Deal?" in Vol. 19/No. 24, cover date of Dec. 6, 2006. That column explained why you may not want to make a deal.

All columns referred to here are archived on the CardPlayer.com website.

Michael Wiesenberg has been a columnist for Card Player since the first issue in 1988. He has written or edited many books about poker, and has also written extensively about computers. The Official Dictionary of Poker should see a new incarnation as part of a more extensive work within a year. Send critique, censure, and coaxing to [email protected].