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One of the main differences between the MTT discipline and other poker disciplines is the availability of tournament life and a large gradation in the size of prize money, depending on the place occupied in the tournament. All MTT players know that truly valuable prizes are only on the final table, and even more valuable in the top 3 winners of the tournament.
1. The value of life is an important mathematical feature of tournament poker
In the world of tournament poker, this is used to be called the ICM Factor, although in fact the value of tournament life is much broader than the standard definition of the former. This factor invisibly begins to be present already from the middle of the tournament, and reaches its apogee to the final table. (and on the dough)
It is the presence of tournament life (ICM factor) that makes tournament poker the most exciting, interesting and mathematically ambiguous discipline among all varieties of the game.
Chip EV model
A model for calculating the plus value of strategic actions that takes into account only the earnings of chips at a the long run.
ICM (Independent Chip Model)
The procedure by which the stacks of all remaining players in a tournament are converted into their equivalent tournament shares of the cash prize pool. The conclusions about the profitability of the solution take into account the growth of prize money and the ratio of our stack with other players.
Bubble factor is the main mathematical tool
The difference between your odds in chips and your odds in money. In other words, this is the ratio of the received chips to the lost chips from the point of view of the ICM share. Even easier - imagine that the chips of different players have different values, although their denomination is the same. For example, our chips are made of metal that is 10% more expensive than the one from which the opponent's chips are made. If the bubble factor = one, then if you lose 1000 chips, you lose ICM equity as much as you would have gained if you won. That is, bubble factor 1 = chip EV model. If the opponent's chip bubble factor is 1.2, then if you lose 1,200 chips, you will lose the same amount of ICM equity that you could have gained by winning 1,000 chips. That is, the opponent's chips are more valuable than ours.
2. Example of Bubble Factor
The basic principle of ICM is that when we play the pot, we win less equity than we can potentially lose. This is due to the tournament payout structure. Consider the example of an SNG game for $100 per 10 people with 1000 chip stacks and $500/$300/$200 payouts. Without rake and ante, blinds 50/100.
Before the hand, each player has an equity of $100 equal to the buy-in. Suppose SB and BB are all-in and SB loses.
What happens to equity?
The player who loses loses all equity – his share falls from $100 to $0. The winner does not receive $100, but only $84.44, and the remaining $15.56 is redistributed among the rest of the players. Each of them gets $1.94 without risking chips. The loser risked $100, but the winner earned only $84.44. This shows that the losses in tournaments are more tangible than the winnings. In cash, players risk $100 to win $100 (ChipEV), but in tournaments due to the payout structure, the winnings are always less risky (if there is no bounty).
Bubble Factor formula: $EV loss on loss / $EV win on win = Bubble Factor.
In the example above: 100 / 84.44 = 1.18
Knowing the Bubble Factor, you can calculate the necessary equity for the all-in call:
Required equity = BF / (BF + 1)
1.18 / (1.18 + 1) = 54%
If it were a cash table, the equity for a call would be 50%. But since this is a tournament, the threshold rises to 54%, even in the early stages.
3. What affects the Bubble Factor?
The bubble factor measures ICM pressure, which is affected by:
- Structure of payments;
- Tournament stage;
- Stack sizes.
4. Payout structure
The higher the difference in prizes, the greater the ICM pressure. In tournaments where only the winner takes everything - Bubble Factor = 1 (we play according to ChipEV). In satellites (where all prizes are equal), ICM pressure is maximum – sometimes it is even reasonable to fold AA preflop.
In PKO tournaments, the Bubble Factor can be below 1 as bounty counts. So in the very first PKO hand, all players have BF = 0.82 (the required equity for the call is 45%).
Tournament Stage
The closer to the money or the final table, the higher the ICM load.
The graph of the bubble factor for the Sunday Million per 10,000 people shows that the bubble factor rises sharply before the bubble and the final table, reaching 1.7. “Teeth” means local elevations when approaching the pei jump.
5. Stack size
- Chipliders have a low bubble factor – they can play wider.
- Medium stacks are under the most pressure – it is important for them to avoid early departure.
- Shortstacks can play wider, as they have little tournament equity.
How does the Bubble Factor affect strategy?
- The chipliders should press on the medium stacks, avoiding large stacks.
- Medium stacks should avoid collisions with large stacks and focus on survival.
- Shortstacks can play more aggressively, especially against other shortstacks.
Conclusion: In simple terms, this means that in MTT, the value of chips won and lost may vary depending on the growth of prize money in the tournament, the stack size of other players, the availability of knockouts that we can get, and other factors.
Tournament poker is so interesting and defies linear mathematical logic that even the ICM model with the calculation of the bubble factor does not accurately describe the mathematical processes taking place in the game. Therefore, another model was later invented, which is also imperfect for calculations, but very suitable for intuitive use.
The most important examples of the use of the bubble factor:
- The value of our chips increases greatly on the stack and pre-bable of the tournament and makes playing on the stack unprofitable for more than half of the standard range. (bubble factor 2x+)
- On the prefinal table, the value of our chips begins to slowly grow. (bubble factor 1.1-1.5x)
- At the final table, the bubble factor makes our chips more valuable than usual, but no more valuable than on the tournament bubble (bubble factor 1.3x+)
- Having a knockout for an opponent's stack, which we can get, increases the value of his chips (he is credited with a multiplier of the bubble factor)
The most accurate calculations and indicators of the application of the ICM model are presented in the preflop game courses Optimal preflop range LEVEL 2 and LEVEL 3 on our website.
FGS (Future Game Simulation) – a factor of the future
The impact of future hands on the profitability of the decision that is made in the present.
This model includes:
- The presence or absence of our advantage over rivals at the table;
- The presence of strong reg players in the position or fish, against which there will be a high winrate of the game in the future;
- Structure of blind growth;
- The psychological state of the players at the table (metagame);
- How lucky we are today)), etc.
Example: imagine the same final table with the same number of players and the same stacks in 2 variants:
The first one is 7 players, all strong players.
The second – 7 players, but 2 very weak recreational players and one of them is a chiplider.
If you make a calculation in the chip EV model, only the mathematical profitability of the action is taken into account, no matter who it is against. If we take into account the ICM model, it will take into account the distribution of prize money and the distribution of all tournament chips by stack, and this will affect the profitability of our solution.
But even according to the ICM model, the calculation will not take into account that in the second option, having weak players at the table, we get a higher winrate of future hands and a better chance of paying for our strong hands, thereby increasing the likelihood of winning a tournament with such a squad. Mathematically, this can not be taken into account, since there are no buttons in the calculators to indicate who is fish or not fish, and set the winrate for players and the like. Therefore, any calculations still have a far from perfect result. Tournament poker is so interesting compared to other types of games. There is still an intuitive human factor that cannot be counted.
