The following article was orginally published by BlindStraddle online poker e-magazine in October ’08. Unfortunately, Blindstraddle.com has discontinued its publication.
When I am thinking about poker, I am often finding myself more consumed with game theory situations. One theory I have often heard and read in the past is that as one’s stack grows in a tournament, each individual chip is worth less.
Because of this thinking, it is said that one shouldn’t be taking big risks to gather chips since the chips won won’t be worth as much as the chips lost. So I decided to look into it for myself and hopefully I could figure out a proper strategy to take in a tournament.
Browsing through the lobbies on Pokerstars, I first stumbled across a $6.50 six person Sit-N-Go where the starting stack is 1500. So it is only obvious that the starting stack of 1500 is worth six dollars (minus the 50 cents fee). Each person paid for that stack. It is theirs and everyone is playing to not only keep that stack, but increase it. At the beginning of the tournament each chip is worth six dollars divided by 1500, or 0.004 cents.
To win, one would need to gather all the chips in play. With six players starting with 1500 chips, there are a total of 9000 chips in play. If someone is lucky enough to get all 9000 chips, they will be rewarded first place money. In this case, with the standard two person pay out schedule, first place rewards $23.40. This means that each chip in a 9000 stack is worth 0.0026 cents ($23.40 divided by 9000).
So to recap, the chips in a 1500 stack are worth 0.004 cents while the chips in a 9000 stack are worth 0.0026 cents. That is a 35 percent decrease in chip value!
Growing more intrigued I next looked at a $5.50 Heads-Up Sit-N-Go. The five dollars buys 1500 chips, and a 3000 stack wins you ten dollars. Five dollars divided by 1500 is equal to ten dollars divided by 3000. So plainly the value of chips didn’t change. So I guess it can’t always be true.
So what is the difference? How come the first example showed this theory to be true, but the second did not? The only thing I could think of is the number of spots being paid.
So I went back to the six person sit-n-go, but changed it to a winner-take-all format. In this case, the value of the chips didn’t change either because the same 9000 chips it takes to win it all would win the whole prize pool.
“When does this “change” actually take place then?” I asked myself.
Looking at the six person sit-n-go, if there are two players playing for the final two spots, one person will get paid first place money and the other will get second place money. It doesn’t matter how big their stacks are, each chip is still worth the same. So this change of each chip’s value doesn’t actually occur until there is money taken out of the prize pool.
So I decided to test this theory further by looking at a multi-table tournament, specifically a $4 180 man tournament where the top 18 places are paid and the average starting stack is again 1500. With 180 people putting up 4 dollars, there is 720 dollars in the prize pool. If we are down to 18 people the average stack will be 15000. If everyone has the same size stack, then everyone’s stack will be worth 1/18th of the prize pool. In this case that would be 40 dollars.
If I still have this same 15000 stack, how would changing the other chip stack sizes change the value of my chip stack? To go with extremes, as I often do to figure out problems, I looked at a situation where I have 15000, 16 players each have a one-chip stack, and the last player has the rest of the chips in play (254984).
Well it would be a pretty good estimate that my 15000 chip stack really shouldn’t be worth 40 dollars any more, instead it should be closer to second place money, since I should be able fold my way to second place. Second place in this instance is worth 144 dollars, making each chip in my stack worth more than otherwise noted. In this case, it would not be warranted to put my chip stack at risk against the chip leader.
To look at it deeper, with the same situation, if I have AA dealt to me. I would be inclined to fold to a shove from the chip leader. Crazy huh? Well what would doubling up really do at this point? It would give me a stack of 30000, which is still not even near the stack I would need to take down the whole tournament, 270000. Is it worth risking 144 dollars to fade a bad beat? First place money is only worth 72 dollars more ($216), in which I would still have plenty of work to do to take it all down.
After thinking about it, I felt that this was starting to sound similar to independent chip modeling, or ICM. ICM is an extremely powerful mathematical model that is essential for any sit-n-go player’s success. I guess I could just stop with this research I am doing and be content with looking over SNG Wizard or SNG Power Tools, both programs address ICM and I highly recommend them for any sit-n-go competitor.
ICM really takes into effect the other chip stacks at the table to determine the best course of action for a player in a sit-n-go. This is also what I would need to do in the aforementioned 180-man tournament. OK good, I determined that I need to pay more attention to the other stack sizes, move on.
“Ahh, but wait” I said to myself. “How can one possibly take into effect every player’s chip stack in a big tournament that still has over 100 tables left though? How can I use this information to help me?”
I did already see that a form of ICM is still relevant to multi-table tournaments with the experiment I did with the 180-man tournament. But realistically, when is that exact type of situation ever going to come up? I needed something that was more relevant to an everyday situation.
I have often wondered when approaching a bubble of a multi-table tournament if I should just sit back and try to cash, or still play for first. I always hear that in a multi-table tournament I have to play for first. After all that is where all the money is.
Still determined, I thought about three major situations that I am always plagued or fortunate with when approaching the bubble of a big tournament:
- I have a tiny stack, at which point I am just hoping to cash.
- I have a huge stack, where I feel I should keep the pressure on the shorter stacks.
- I have a medium stack, where it’s not concrete on what strategy I should employ.
Let me address each situation so that I can be better prepared when it does come up in the future. I have a tiny stack, what should I do? This is when it starts to become pertinent to use a free resource that every player is blessed with, the tournament lobby.
Well, the critics will say I should still play for first. But what if I have just one chip? Again, looking at an extreme situation to try and get an answer. I can then make that 1 chip worth what last place pays compared to 1/1500 of my buy in or whatever the starting stack was. If I know folding what could be a winner will net me money because someone else will likely bust in this hand, then it would become the best play to fold in the long run.
The first situation was probably the easiest. When I have a huge stack though, it starts to get a little tougher. Should I continue to try and chip up or sit back and preserve my stack? Outside of the table dynamics, and what the table is letting me get away with, I should also be paying attention to the stacks at the other tables. Again looking at the tournament lobby, I need to determine a couple things.
Do I need to continue to apply pressure to keep up with the other chip leaders? In this case, I might want to continue to bully the table if it means I can separate myself from the middle of the pack and inch closer to the other chip leaders. Am I part of a group of players that is way ahead of the pack or personally just way ahead of everyone else? In which case I can sit back and not risk too many chips since there is still a ton of poker to be played. Both questions should be asked and can be answered fairly quickly just by glancing over the stacks in the tournament lobby. By finding out these answers, it will let me know of what degree of risks I should be taking at a given point in the tournament.
Where it really gets tricky is when I start to get closer to my third situation, I have a medium stack. There has to be a break-even point from the first situation and the last. What stack size correlates to what strategy? Should I try and cash first or continue to have the goal of playing for first? This is when the other chip stacks play the biggest part and become most important to look at it from both the big stack and tiny stack perspectives.
If there is a surplus of short stacks and I could conceivably move up quite a few pay scales I might be more inclined to pass on some risky plays to a certain degree. If there really are not that many short stacks, and I am stuck in the middle, I might be leaning to taking some risks to try and chip up. What about the chip leaders? Will a double-up get me that much closer to a stack that will allow me to move into the big stack’s frame of mind, or will it keep me in the middle pack? Depending on the answer, I can also make a determination on how much I should be willing gamble.
What if I might be multi-tabling online and don’t have the time to study every stack by looking over the tournament lobby? Well, I have read the Harrington on Hold’em series, which I highly recommend, where he introduces a couple of concepts to help determine what frame of mind one should have in a specific situation according to their chip stack. One is Magriel’s “M” which to quote from the book is “the ratio of your stack to the current total of blinds and antes.” The other is a ratio of one’s stack to the average stack, or Harrington’s “Q”.
Well, I would also like to introduce a new online-friendly concept. I guess I will call it NoMeNot’s “N”. This is basically just the median stack and how one’s stack compares to it. It should be a good gauge as to where one’s stack compares to the smaller stacks and the bigger stacks. Let me see how this can be applied.
If my stack is 1000 and the median stack is 3000, then my N is .33. With a stack like this I might be more inclined to try and cash first before the bubble and after the bubble, I would be inclined to try and double up unless there is a significant pay jump in the near future.
If my stack is 3000 and the median stack is 3000, then my N is 1. With a similar type stack, I would be caught right in the middle with my thought process just as before in my third situation where I had a middle stack.
Lastly, if my stack is at 9000 and the median stack is 3000, then my N will be 3. In this case, I will not feel too much pressure to gamble. But I will still keep the pressure on high as long as the table is letting me get away with it.
So now what have I learned from just inquiring about the true value of chips in a tournament?
- ICM is not just for sit-n-go’s as it can be applied to multi-table tournaments as well.
- It is important to know where my chip stack compares to the others chips stacks, and not just at my table.
- A good way to gauge my chip stacks worth is by finding the median stack, if there are 100 people left, the median stack would be the player in 50th place.
Whew, done with that theory. On to the next one I guess. That is the outlook I have when I am trying to learn about the game. I definitely suggest others try and do the same. If I can’t think of an answer right off the bat, I like to look at the extremes and see if I can’t find a middle ground. I did just that a couple of times here. It is a great way to come up with a new thought process while learning about what might be the best play to make in a certain situation.
Until next time, what’s your N?
