This week we want to talk about the value of surviving once you reach the stage in the tournament where each prize is unique. This usually happens at the final table. At this point in the tournament, whenever a player goes broke, you make more money. If you subscribe to the idea that the percentage of chips you have are equal to the chances of you winning the tournament ( and almost all the poker math geeks do), then you realize that allowing other players to go broke without changing your chances of winning the tournament is a great thing for you. Each place you survive adds a real amount of guaranteed cash to your pocket. This all happens without lessening your chances to win.
So that very last chip in your stack has a tremendous amount of value. The second to last chip is almost as valuable, and the third to last chip helps protect those last two, so it is pretty valuable as well. Each chip in your stack is slightly less valuable than the one that came before it. If you want to look at how this works, grab an ICM calculator link online (http://www.icmpoker.com/icmcalculator/) and play around with some numbers. We can take a quick look at this from an intuitive level. Suppose there are 10 people left in the hypothetical 1000 person field we discussed in last week’s article. If everyone has equal stacks, in theory, they all have the same value in the tournament, 10% of the unawarded money. Using the WSOP 1000 person field payout schedule:
|Place||Percentage of prize pool||Percentage of unawarded money|
What we need to look at is what happens when some stacks are combined. Now let’s suppose that one player busts 4 other players. This can happen slowly or quickly, but let’s suppose 5 players all go all-in on the same hand. One of those players wins. That player has 50% of the chips, and the other 5 surviving players have 10% each. Now how do we decide what these new stacks are worth? For the 4 players that went broke, this is easy. They were paid 11.3% of the unawarded prize pool. Now for the player with the big stack, let’s start with the assumption that he is 100% to win the tournament. We know this is not possible, but it is the best case scenario and creates a boundary for maximum value that those 5 players’ chips can have when they all end up in one stack. If this player wins, he gets 33.5% of the unawarded money. Now if we add that to the 11.3% that the players who lost got for coming in 7th through 10th, we get a total of 44.8%. This is the most value that these 5 players can collectively get. If this player comes in 2nd, they only get ~32% of the money and less if he comes in 3rd or 4th. So before that hand, those 5 players were worth 50% of the unawarded money, and now they are capped at just under 45% of the money.
This is great for the five people who weren’t involved; they still have 10% of the chips each and worth a minimum of 11% (1/5th of the remaining 55%) of the unawarded money. All they did is just sit there and watch the carnage. And we know that the player with 50% of the chips is only 50% to win. An ICM calculation shows that each of the remaining 5 players is worth a little more than 12.74% of the prize pool. That is up quite a bit from the 10% they were worth before this hand took place. By surviving just 4 more players at this point, without winning any chips, they gained equity equal to 2.74% of the prize pool.
What does all this mean? It means that the chips you win are worth significantly LESS than the chips you lose at this stage in a tournament. This means when you call a bet, you need to have significant edge. The chips you are risking are worth more than the chips you are winning. Surviving has reached its maximum value. The idea that you have to turn down bets that would be slightly positive expectancy because of the difference in chip value might be disturbing to some. This is one of the major ways in which tournaments differ from cash games.
Two quick takeaways are: You would rather bet than call at this point in a tournament, and play tight and be patient late in tournaments.