Once there are a few remaining players in a tournament, you may be proposed a deal by your opponent(s) or you may wish to propose a deal yourself. Tournament deals may involve ending the tournament immediately and splitting the prize pool in a certain way, or perhaps guaranteeing each remaining player a certain amount of the prize pool and playing for the rest.
A truly fair deal would involve splitting the prize pool, according to the exact equities each player has in the tournament. The problem is working out the exact equity each player has in a tournament is difficult.
Chip chop tournament deals
This involves dividing up the remaining prize pool, according to the percentage of chips each player has. Imagine there are three remaining players in a tournament, and one holds 55% of the chips, another 35% of the chips, and the other 10% of the chips. The remaining three prizes are $5000 for 1st, $3000 for 2nd, and $2000 for 3rd. This means the prize pool remaining is $10,000. The prizes would be allocated as $5,500, $3,500, and $1,000. You should already be able to see the massive problem with the chip chop model. In this example, the chip leader ends up getting more than the 1st prize (which is the maximum he can win if the game continues without a deal), and the player with the lowest stack ends up getting less than the 3rd placed prize (which he is guaranteed if he doesn’t accept a deal). We made up the numbers in the example above, to best make our point. However, regardless of this a chip chop deal will usually favor big stacks over small stacks – it will allocate too much equity to the big stacks, and too little equity to the small stacks. The reason for this, is that it does not take into account the diminishing marginal utility of chips in a tournament – your last chip is the most valuable (as it keeps you in the tournament), and every chip you add on is less valuable than any chip you already have.
A chip chop deal becomes fair (assuming no skill edges) when there are just 2 players left in a tournament. Allocate each player the amount of the 2nd place prize, and divide up the remaining amount in the prize pool (which is the difference between 2nd and 1st place prize) according to the chip chop method. This is because there are no ICM structure, as you are only playing for one prize – the difference between first and second. A chip chop deal is also fair, if it’s a winner takes all tournament, as again there are no ICM concerns in this structure – as getting all the chips wins you all the prize pool (i.e. similar to a cash game).
Equal save tournament deals
An equal save involves locking up an equal share of the prize pool for the remaining players, and playing for the rest. The reason some players decide on this is that when the money gets significant to them, they would rather lock up a certain amount than endure the effects of variance. The problem with this is that the more any players have others out-chipped at the time of the equal save, the worse the deal it is for them.
Exact ICM chop
An exact ICM chop involves applying a mathematical model to decide on how the remaining prize pool should be allocated. ICM considers the payout structure of the tournament, and the current stacks. ICM chops will usually produce fairer outcomes than the chip chop method – as it takes into account the diminishing marginal utility of chips in a tournament. An ICM chop is the most common method of deal making today, as most players understand why they ICM chops are fairer than chip chops.
ICM chops, whilst fairer than chip chops, are not without their problems. This is due to the fact ICM is a mathematical model, which takes many important things into account, but not necessarily everything. One of the key things it does not take into account, is future skill edge. If you have more strategy knowledge than your opponents, and will be able to apply that knowledge, an ICM chop will underestimate your equity (and overestimate their equity). Note, it’s not enough to have greater knowledge of strategy if you can’t take advantage of it. For example, shallow stacks, fast blind increases, if the players on your left have bigger stacks than you and are loose aggressive, will make it difficult to use your superior knowledge of strategy. On the other hand deep stacks, slow blind increases, players on your left with smaller stacks than you that are tight/pasive, will mean you can use your superior strategy knowledge. Also, if you are the chip leader (and have a good chance of maintaining this), you may have great ways to carry on building your stack that ICM will not take account of. We have a full explanation about ICM here at betzoo.uk.
Modified ICM chop
If you truly have a future skill edge in the tournament, you can suggest a modified ICM chop, where you get more than the ICM numbers suggest. This will of course come at the expense of players with less future skill edge who will get less than the ICM numbers suggest.
What to do
If you are offered a deal in a tournament, or are considering proposing a deal, you need to first work out your share according to ICM. Free ICM calculators are available online, so if you have a device that can access the internet that you carry with on the table, you should have one bookmarked ready to use. Deals are usually only proposed if there are just a few players left, so it takes less than a minute to type in the remaining chip stacks and payout structures into the calculator, to get the results. If there is no skill differences between the remaining players, or if any skill difference is unlikely to have too much effect (this will be the case if the stacks are shallow, or the blinds are increasing fast), then the ICM numbers are the fair way to proceed for everyone. Of course, if you can then get your less knowledgeable opponents to accept a deal that is better for you than them (such as a chip-chop deal when you are the big stack), from a purely monetary standpoint that is great for you, and bad for them. However, you may have moral objections to offering a deal you know is not fair. If there are skill differences between the players, and these skill differences can be used in the remaining tournament (e.g. stacks are still shallow, and blinds will not go up fast), then if you are the more skilled player you should not accept the ICM deal, unless it is modified to take account of your future skill edge. If you are out-skilled, and your opponents will be able to use their better skills on you, you should bite their hand off if you are offered an ICM deal.
A reason not to accept a fair deal, would be to get tournament experience. You will not always have the opportunity to play in the last few spots of a tournament – this could be a great learning experience.
A reason to accept a slightly bad deal, is if there is opportunity costs associated with carrying on playing in the tournament. For example if you are playing a live tournament, and your opponents will only accept a deal that will cost you a certain amount of dollars in equity, but this tournament might take a long time to finish. However, there is a great live cash game you want to play that is currently running, and you have spotted some whales, so you want to join asap. Alternatively, in a live tournament series, let us imagine it is late at night, and you have an important tournament the following day. It might be better to sacrifice a few dollars of equity, to be more refreshed for the following day.
If there is a non-monetary prize, added to the prize pool, such as a seat to another tournament, and your opponent values the seat at the exact amount it costs, but you would rather have real money, a fair deal might be great for you if you can get him to take the seat and money as part of his payoff, whilst your payoff is all money – it might even behoove you to take an ever so slightly unfair deal for you, to get all money without being committed to playing another future tournament (or having to sell the seat, if you are unlikely to be able to sell it for its for value). You may be able to get a good deal, if one of the players values something non-monetary (e.g. the title of being crowned the winner, or an actual trophy) – they may be prepared to offer you a better deal than ICM suggests in order to be crowned the winner or get the trophy.
