Thursday, February 01, 2007
Let's chop one last time
On some early posts I talked about the prize chop that frequently happens at the end of poker tournaments. This whole topic seems like more of theoretical problem than a practical problem. But, I find the topic sort of interesting, so I really dug into it.
Straight Distribution. Most players probably have a decent understanding of the "straight distribution" method for chopping money. This method is intuitive and works pretty well when the remaining players in a tournament have fairly close stack sizes (all within 30% to 60% of the total chips in play). This method can be calculated easily. The drawback is that it gives too much equity to the chip leader and the calculations start to break down when the chip leader has 70% or more of the chips in play.
Burns-Landrum. An alternate method for determining chop amount is the Burns-Landrum model. This model fixes the some of the problems of the straight distribution method, but it's too difficult to calculate and it has an unfair bias toward the short stack.
Prize Probability. I was directed to a model (by Brandon) that adequately solves the problem (no errors for short stacks or large stacks). This model determines, based on the chips that you have, the probability of you winning each prize. Your chop amount is the combined probabilities of winning each prize amount. The shortcoming of this model is that you need a computer to figure it out.
JJ Method What if you had a model that had no bias, and was easy to use? Check out the chart below (patent pending). Imagine that you print this chart and stick it in your wallet. Then, if you end up in a chop situation, you can use to determine where you should start your negotiations with the other players.
Here's how it works. I'm looking for feedback here!
First, you need to determine your proportion of the total chips in play. This should be no big deal. Almost all chop deals begin with a count of chips. To do this, just add up all of the remaining players chips (including yours). Then, divide your chip count by the total.
Next you need to determine which prize "line" on the attached chart most closely matches the prize structure of the tournament. For example, if there are three prizes left (675, 425, 275), simply add them up and divide each prize by the total. In this example the total prize pool is 1375. Top prize is 675/1375 or around 50%. 2nd prize is 425/1375 or around 30%. 3rd prize is 275/1375 or around 20%. So the prize structure is pretty close to 50/30/20.
To determine your chop amount simply follow a line straight up from your chip proportion to the line that most closely matches the prize structure of the tournament. Then, follow that line straight across. Bingo, that is the proportion of the overall prize pool that you are due.
An example. After a chip count, you find that you have 65% of the chips in play. You and 2 other players are chopping the top 3 prizes ($1375 in total) that looks alot like a 50/30/20 split. Draw a line straight up from 65% until it hits the dark blue line. Then draw a line horizontally. It looks like you should be "due" about 45% of the total prize pool or about $620 ($1375 x .45).
Another example. Let's say that after a chip count you have about 300K out of the 1 million chips in play (30%). You and the other 4 players decided to chop the top 5 prizes. Draw a line up from 30% until it intersects with the curve that represents 5 prizes. Then, draw a line horizontally to determine how much of the remaining prize pool you should "claim". In this case, you have a claim to around 25% of the total prize pool.
So, what do you think? Is this any good? If you want the excel file, just let me know.
Comments:
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I can get you the number to gamblers anonymous. You may already have it...No wonder OnStar is losing $$$ these days. You're creating these graphs all day.
# posted by 
: 9:15 PM
: 9:15 PM
Use the "independant chip model" for chops. http://www.poker-tools-online.com/icm.html
It hasn't done me wrong for SNGs.
It hasn't done me wrong for SNGs.
# posted by : 9:56 AM
: 9:56 AM
I enjoy these problem solvers. I am currently taking a calculus-based statistics class and find this interesting. Please keep up the good work!
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# posted by : 11:08 PM
: 11:08 PM<< Home
