Friday, January 26, 2007
Let's Chop It Some More
THE CHOP
So as the tournament got down to 3 handed, players started negotiating a chop. After an agreement was reached, Ryno was overheard getting scolded by his entourage for making a bad deal. He defended himself, “hey man, I’ve never really been in this situation before”.
That’s understandable. I’m not sure any of us really have enough experience at working out these types of deals to be considered “skilled”. The last thing you want to have happen, after you plow through 95% of the field, is to make a bad deal and give up more prize equity than you should. This isn’t one of those situations where you just try to figure it out “in the moment” – to “wing it” I think you’d be much better served to give this complex topic a little thought before hand….you know, be prepared!
As I started doing a little research on this topic (gambling forums and web sites), I found this is a pretty complex topic. I’ve not really found anyone that solves this problem accurately or effectively. An accurate solution is one that produces a mathematically precise answer. An effective solution is one that anyone can use, in the moment, while sitting around a pile of chips after a long poker tournament – and one that you can convince others is “fair”.
THE SET UP:
At the end of the NLHE tournament, we had this situations:
Chip leader, Dave S., has 71K in chips. Short stack, Dangeruss, has 17K in chips. In the middle, Ryno has 34K in chips. Prizes (1rst $675, 2nd $425, 3rd 250).
Approaches to the Chop:
There are probably 2 main ways (with a few derivatives each) that people make chop deals.
Approach 1: Get What You Can
The first way is a strict “get what you can” approach. In this approach, someone just suggests that they should get a certain amount. Everyone follows this same approach until a deal is reached. In the scenario laid out above, Dave may just pick a number, say $600 and propose, “since I have most of the chips, I’ll settle for $600”. This approach is not all that scientific, but it sure is easy to administer. Of course the problem with this approach is that you can quite easily end up giving away more equity than you should. The advantage of this approach goes to the master negotiator who can take advantage of lesser skilled negotiators.
Approach 2: The Straight Line Distribution
Another, slightly more methodical approach is called a “straight distribution”. To determine how much you are “due”, you follow these 4 simple steps. Most of this math can be done in your head, but you should probably ask the tournament director/host for a calculator or pen/paper.
1. Add all of the prize money up. From the example above, you have $675 + 425 + 250 = $1350.
2. Since all players are guaranteed at least the last place prize money, take that amount times the number of players and subtract from step #1. This amount is known as the “remainder”. Using the example above, the last place pays $250 multiplied by 3 players = $750 subtracted from $1350 from step #1 above will leave $600 that is the “remainder”. This is the amount that the remaining player will be negotiating for.
3. Determine your chip proportion. To do this, have everyone count their chips and then total them. Then, divide your chip count by the total. From the example above, there were 121,600 chips in play, Dave had 59%, Ryno had 28%, and Russ had 14%. This amount represents your “claim” to the remaining prize money. The more chips you have, the larger your claim.
4. Finally, multiply your claim (Step #3) to the remainder (step #2) and add your guarantee amount (last prize). This is your ‘targeted’ payout that you negotiate for.
The following table shows how this deal would look for our example. It looks like these guys worked out a deal that was real close to ‘straight distribution’ deal. Not too bad…right?
Here’s the problem. This methodology doesn’t really work for more than 2 players and is biased unfairly to the short stack (sorry Russ) and overly generous to the big stack (Nice work Dave). The methodology really starts to break down when there are big difference in chip stack sizes. You can even find situations where this method would calculate a payout target for the chip leader that is higher than the top prize…this makes no sense. You should read the article in Card Player on this subject. http://www.cardplayer.com/author/article/all/14/3986
Below is a graph of the payout targets when only 2 people are chopping using a Straight Distribution method. In this example, if you had 70% of the chips and there was 2 prizes left ($1000, $400), you would expect to chop for a little over $800.
Below is a graph of the payout targets when 3 people are chopping. As you move up the scale for the chip leader towards 80%, your targeted payout actually exceeds the “ceiling” amount that you can claim (the top prize). This is clearly an indication that the slope of the line is too sharp.
A new approach: Burns Landrum
This approach attempts to correct for the errors using the straight distribution method. The Burn Landrum model though has the disadvantage of being too complex for most players to conceptualize in their head. There is no way to do a sort of 'sense check'. You almost need the tournament host to offer a spreadsheet calculator using this formula to determine your targeted payout. Too complex! In addition, this model give too much equity to the short stacks. In extreme cases (when the short stack has only a couple of chips left), this model would still suggest that that player is due substantially more than the bottom prize. Using the data from our actual tournament, the Burns Landrum model would have allocated only $537 to the chip leader (Dave) as opposed to the $600 he actually recieved. Conversely, it would allocate $385 to Russ instead of the $350 that he actually took.
So as the tournament got down to 3 handed, players started negotiating a chop. After an agreement was reached, Ryno was overheard getting scolded by his entourage for making a bad deal. He defended himself, “hey man, I’ve never really been in this situation before”.
That’s understandable. I’m not sure any of us really have enough experience at working out these types of deals to be considered “skilled”. The last thing you want to have happen, after you plow through 95% of the field, is to make a bad deal and give up more prize equity than you should. This isn’t one of those situations where you just try to figure it out “in the moment” – to “wing it” I think you’d be much better served to give this complex topic a little thought before hand….you know, be prepared!
As I started doing a little research on this topic (gambling forums and web sites), I found this is a pretty complex topic. I’ve not really found anyone that solves this problem accurately or effectively. An accurate solution is one that produces a mathematically precise answer. An effective solution is one that anyone can use, in the moment, while sitting around a pile of chips after a long poker tournament – and one that you can convince others is “fair”.
THE SET UP:
At the end of the NLHE tournament, we had this situations:
Chip leader, Dave S., has 71K in chips. Short stack, Dangeruss, has 17K in chips. In the middle, Ryno has 34K in chips. Prizes (1rst $675, 2nd $425, 3rd 250).
Approaches to the Chop:
There are probably 2 main ways (with a few derivatives each) that people make chop deals.
Approach 1: Get What You Can
The first way is a strict “get what you can” approach. In this approach, someone just suggests that they should get a certain amount. Everyone follows this same approach until a deal is reached. In the scenario laid out above, Dave may just pick a number, say $600 and propose, “since I have most of the chips, I’ll settle for $600”. This approach is not all that scientific, but it sure is easy to administer. Of course the problem with this approach is that you can quite easily end up giving away more equity than you should. The advantage of this approach goes to the master negotiator who can take advantage of lesser skilled negotiators.
Approach 2: The Straight Line Distribution
Another, slightly more methodical approach is called a “straight distribution”. To determine how much you are “due”, you follow these 4 simple steps. Most of this math can be done in your head, but you should probably ask the tournament director/host for a calculator or pen/paper.
1. Add all of the prize money up. From the example above, you have $675 + 425 + 250 = $1350.
2. Since all players are guaranteed at least the last place prize money, take that amount times the number of players and subtract from step #1. This amount is known as the “remainder”. Using the example above, the last place pays $250 multiplied by 3 players = $750 subtracted from $1350 from step #1 above will leave $600 that is the “remainder”. This is the amount that the remaining player will be negotiating for.
3. Determine your chip proportion. To do this, have everyone count their chips and then total them. Then, divide your chip count by the total. From the example above, there were 121,600 chips in play, Dave had 59%, Ryno had 28%, and Russ had 14%. This amount represents your “claim” to the remaining prize money. The more chips you have, the larger your claim.
4. Finally, multiply your claim (Step #3) to the remainder (step #2) and add your guarantee amount (last prize). This is your ‘targeted’ payout that you negotiate for.
The following table shows how this deal would look for our example. It looks like these guys worked out a deal that was real close to ‘straight distribution’ deal. Not too bad…right?
Here’s the problem. This methodology doesn’t really work for more than 2 players and is biased unfairly to the short stack (sorry Russ) and overly generous to the big stack (Nice work Dave). The methodology really starts to break down when there are big difference in chip stack sizes. You can even find situations where this method would calculate a payout target for the chip leader that is higher than the top prize…this makes no sense. You should read the article in Card Player on this subject. http://www.cardplayer.com/author/article/all/14/3986
Below is a graph of the payout targets when only 2 people are chopping using a Straight Distribution method. In this example, if you had 70% of the chips and there was 2 prizes left ($1000, $400), you would expect to chop for a little over $800.
Below is a graph of the payout targets when 3 people are chopping. As you move up the scale for the chip leader towards 80%, your targeted payout actually exceeds the “ceiling” amount that you can claim (the top prize). This is clearly an indication that the slope of the line is too sharp.
A new approach: Burns Landrum
This approach attempts to correct for the errors using the straight distribution method. The Burn Landrum model though has the disadvantage of being too complex for most players to conceptualize in their head. There is no way to do a sort of 'sense check'. You almost need the tournament host to offer a spreadsheet calculator using this formula to determine your targeted payout. Too complex! In addition, this model give too much equity to the short stacks. In extreme cases (when the short stack has only a couple of chips left), this model would still suggest that that player is due substantially more than the bottom prize. Using the data from our actual tournament, the Burns Landrum model would have allocated only $537 to the chip leader (Dave) as opposed to the $600 he actually recieved. Conversely, it would allocate $385 to Russ instead of the $350 that he actually took.
So this model doesn't really work either since it is too complex and is too biased towards the short stack.
So Now What?
I think we might actually be able to come up with a solution. If we combine the best features of the straightline method with the best features of the Burns Landrum and then turn it into a very simple graphical model, it might just provide players an accurate and effective way to determine their "chop equity" at then end of a long tournament.
Next post....
Comments:
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I trust in the "idependant chip model" for converting T$ into EV$.
http://www.poker-tools-online.com/icm.html
It ends up saying a 'fair' chop would be 553/444/352
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http://www.poker-tools-online.com/icm.html
It ends up saying a 'fair' chop would be 553/444/352
# posted by 
: 10:56 AM
: 10:56 AM<< Home
