Adjusting to payout structures in MT-SNGs

Introduction

In this article

• When to use ICM, why and how
  
• Why play Chip-EV
• How to adjust your game to different payout structures in multi-table SnGs

Articles you should read first:

Independent Chip Model (ICM)

The Bubble Factor in different SnG formats

When to use ICM, why and how

”Always aim for the first place” - this is a recommendation you will often hear from an experienced MTT player, while an SnG regular will be more likely to tell you to aim for the money ranks first. Neither of these suggestions is wrong, but both of them have their limitations. In theory, the only game where you can truly play for the ”first place” is a cash game, where if you win all the chips in the world, you will also get all the money in the world.

This applies to winner-takes-all tournaments as well. However, as soon as a payout structure is involved, you will only get a portion of the prize pool even if you do win all the chips in the tournament, while the rest of the money goes to the other finishers.

As a result, the value of the tournament chips is not equal and the relation between your stack size and what it is actually worth in dollars is not linear. In general you can say that the (x+1)th chip in your stack is worth less than the xth - how much less depends on the payout structure and your relative stack size.

The goal of the Independent Chip Model is to simulate this very phenomenon.

Non-linearity of chip stack values in different tournament formats

In this example we are dealing with a scenario in which you have x% of the chips in the tournament, while the rest is equally divided among the other players. Remember that these graphs can significantly change if the chip distribution is different.

However, this is a good average case which is suitable for comparing the different tournament formats. The X-axis represents the amount of chips you have (as a percentage of all the chips) and the Y-axis represents the amount of money it is worth (given as a percentage of the prize pool).

9-man game:

45-man final table:

WCOOP final table* :

DoN STT:

*In the following, ”WCOOP” is used to designate an MTT that we picked for comparison purposes in order to demonstrate an MTT payout structure. The WCOOP 1M Guaranteed $1,050 NLHE event had 1,612 entrants in 2010. 180 players got paid off, the final table payouts were as follows:

Application of ICM: The bubble factor

”Definition: The bubble factor illustrates the difference between your odds in chips and your odds in dollars.”

The more concave the above graphs are, the higher your bubble factor will be. You should also be aware of the fact that the larger your stack is, the less you can win in relation to how much can you lose, so in general bigger stacks have a higher bubble factor.

While it might not be the most convenient method, the great thing about using the bubble factor for your analysis is that it can isolate the ICM effect into a single number and as such makes situations objectively comparable.

Far away from the money: The Chip-EV game

As discussed above, in a winner-takes-all tournament you can play exactly the same way as you would in a cash game regarding the mathematical basis for your decisions. It’s not difficult to see why. The ICM model estimates the $EV of your stack based on the probability that you will finish in one of the paid places and multiplies it by the prize for that place.

If all the other prizes are 0, each variable will be excluded from the equation except for your probability of finishing first and winning the entire prize pool. This reduces the ICM analysis to one step only: determining the probability for each player to finish first. The formula for that is quite simple:

Hero’s stack / Total chips.

Note that the value of the total number of chips is constant, therefore every chip you gain or lose will equally increase or decrease your probability of winning. If all the chips have the same value, there is no ICM effect, so you can simply always use the chip EV for your calculations.

There is one more case where you can do that - the heads-up. When there are only two players left, each player is guaranteed at least the second prize, which as such is irrelevant. Therefore, the actual payout will be 100%-0%.

If you are in the early stage of a big multi-table tournament, the payouts will generally be so far away that you can theoretically treat the situation as if there was only one remote payout. Don’t get nervous as you are approaching the bubble – all the finishers who do not reach the final table generally only get a very negligible portion of the prize pool.

The ICM effect is not significant until the bigger payouts are reached and the bubble factors will be so low that you can safely ignore them. Generally, ICM is a final table tool and you will have to play according to cEV earlier in the game.

If you play an STT, you will start the game at the final table, so the ICM effect is already at work because the payouts are close as soon as you start the game. Your bubble factor in the first hand of a regular 9-man STT will be 1.2, and 1.8 if you play a DoN format.

As you approach the final table, the significance of ICM effects starts to increase, the difference between cEV and $EV will grow and the tournament will gradually morph into a more ICM and $EV based game.

The effects however will not be overly significant, and also they are very hard to compute. You should keep them in mind however, and as soon as you enter the short-handed stage at the final two tables in pretty much any tournament that started with more than 3 tables, you should have a minimum edge before you enter any game situations, especially if you have a fairly good chip stack. This means you shouldn’t get involved in situations in which your expected gain is less than a certain amount.

Bubble factors before the final table:

To give you an idea of how much these bubble factors influence the game, we’ll compare the equities you need with different bubble factors to take a flip (50% equity) when getting odds of 1:1.

The final table: The ICM game

Several aspects have an effect on your bubble factor, such as your stack size, your opponent’s stack size and the presence of a short-stack at the table. But in an identical situation (meaning the same chip distribution), the payout ratios will determine the difference between bubble factors in differently structured tournaments. This is what we refer to as top-heaviness. The mathematical relation between the payout structure and the bubble factor is very complex, but in general you can say two things about it:

• The more money is given to the top finishers, the top-heavier a tournament is and the more valuable the chips you gain will be. Therefore, your bubble factor will be lower.
• The higher the payout jump is to the next place (or the closer you are to a big jump), the higher your bubble factor will be. The biggest jump in STTs and MTSnGs will be in the actual bubble, and the bubble factor will exponentially increase as you get closer to it.

A graphic overview of the payout distributions at the final table in different tournaments:

You might find it interesting that our selected MTT (WCOOP) is not as top heavy as most people would assume, and you would actually have to play quite tight at the beginning of the final table.

As soon as the bubble bursts in a tournament, another bubble appears. When you reach a payout position, the prize for that place is guaranteed for all the players and therefore becomes irrelevant for your decisions. In order to make it easier to compare bubble situations, you have to exclude the irrelevant payouts and only deal with those prizes that are still to be won. To do this, we will assume that the player who busts will make zero profit, subtract all the money that is guaranteed for every player from the prize pool and distribute the rest among the remaining places, based on the original payout structure. This way you will create a new artifical bubble.

The method for this is as follows:

Relevant prize pool = Total prize pool - (Number of players * Current payout%)
Adjusted payout% = Current prizes – Current payout%
Relevant payout% = Adjusted payout%/Adjusted prize pool

Repeat for Xi players with Yj prizes.

Full Tilt Poker 27-man tournament 5-handed.

Adjusted payouts in popular tournaments:

Note that as you progress in a tournament, the ”top-heaviness” is not constant and your bubble factors will change accordingly.

Some bubble factors in popular tournaments:

You are in a 4-handed tournament, and each player has a 10BB stack. You are sitting in the BB and it is folded to the SB, who shoves on you. For the sake of simplicity we will asume that the SB goes all-in with any two cards.

Blinds: 50/100

Stacks
UTG: 1,000
BU: 1,000
SB: 1,000
BB (Hero): 1,000

Preflop: Hero is BB with
2 folds, SB goes all-in 1,000.

You now have to call 900 for a pot of 1,100, giving you pot odds of 1.22:1. If we assume this is a cash game or a winner-takes-all tournament, you will need 45% equity, and against a random hand you have 57%, which is a clear call.

Now let’s assume this is a 9-man SnG. In this situation you will have a bubble factor of 1.88, giving you odds of 1.22/1.88:1. In this case you will need roughly 61% equity, and the 44 is an easy laydown. The bubble factor varies for different payout formats and will greatly influence your decision.

Let’s have a look at this*:

*These bubble factors are only valid for this specific situation (even stack distribution). They change greatly as the stack sizes change.

You are at the final table of a 45-man SnG at PokerStars. It’s the bubble. The chip distribution is as follows:

Blinds 200/400 (/25)*

Stacks
UTG: 925
UTG+1: 1,200
MP1: 2,000
MP2: 2,500
CO: 2,500
BU: 4,500
SB: 3,500
BB: 4,000

Preflop:Hero is BB with
5 folds, BU raises 4.500 (All-In)

Your pot odds are 1.34:1.

Let’s have a look at the bubble factors:

Your bubble factor against BU is 2.79, his bubble factor against you is 2.64. This difference grows bigger as the stack sizes start to diverge.

If he pushes, you need an equity of 68% to call. This means you have to fold your AKo even if he pushes with a random hand.

Let’s analyse the situation in other tournaments*:

*At the 200/400 blind level, some structures have antes, some don’t. This is taken into consideration in the above table)

You will notice that the bubble factors can grow pretty big in the early final table game, especially when a short-stack is around. However, there are considerations you have to make that are not included in the ICM model. The chips you can gain in certain situations might be worth less than the chips you can lose, however a bigger stack has additional advantages. You will have the option to get into more profitable situations with a larger stack.

You will probably be able to get into low-risk high-profit stealing situations if you exploit your opponent’s unwillingness to re-steal, which they will naturally display due to the high bubble factors. Therefore, if the spot is right, you will sometimes have to take a leap and get into risky situations to enlarge your stack.

For more details on this topic, please read:

The Gigabet Dilemma

Another common practice that you might know from STTs is the -$EV push, where you shove in order to prevent any further reduction of your stack, which would decrease your fold equity. This should however be applied less often and with extreme care in MTSnGs, since it is usually more likely that you get called here.

Conclusion

Different tournaments require different strategies. The bubble factor is a useful tool to examine the differences between them, although it doesn’t cover every aspect of a given tournament, no matter if it’s an STT, an MTSnG or a bigger MTT. Understanding the effects of payout structures and ICM however is essential to becoming a better player in these games.

Even small differences in the structure can make an identical spot profitable in one tournament and a money burner in the other. With this in mind, you can see how difficult it can be to become a universal winning player in all of these games, but hopefully our recommendations will bring you a bit closer to it.

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Related articles: Independent Chip Model (ICM) The Bubble Factor in different SnG formats The Gigabet Dilemma Discussion Forum: Discuss the article in the forum