# The value of poker chips in a poker tournament We already know that the value of chips in poker tournaments does not match the starting value during the tournament. So, let’s try to calculate the fair value of poker chips in a certain phase or situation of the tournament :). So what is it really about in a certain phase or situation of the tournament?

Let’s say we play a 10-man, \$ 10 buy-in with an initial 1000 buy-in poker with a 50% / 30% / 20% prize structure. 1st place – 50 euros, 2nd place – 30 euros, 3rd place – 20 euros.

The value of poker chips at the beginning and end of the tournament

So at the very beginning of the tournament, our token value is 10 euros / 1000 chips = 0.01 euros.

If we won first place, we would collect a total of 10,000 chips and win € 50. The value of one chip at the end of the tournament would be: € 50 / € 10,000 = € 0.005. Thus, the value of one chip at the end of the tournament doubled.
The value of poker chips remains with a few players left

But let’s say if there are only 4 players in Litq: players A, B, C and D who have 4000, 3000, 2000, 1000 chips respectively, what is the value of each poker chip?

1. First of all, you need to calculate the odds for each poker player to take first place.

It is easy to do this, as you only need to know the percentage of each one’s chips. These players A, B, C, D have 40%, 30%, 20%, 10% respectively. These are the odds to rank first and are respectively: Player A takes 40% of the time, Player B 30%, Player C 20%, Player D 10%.

First place odds for all poker players:
Players Chip Count Probability of Win 1 Chance of Win 2 Probability of Win 3 Chance of Win 4
4,000 40%? ? ?
B 3000 30%? ? ?
C 2000 20%? ? ?
D 1000 10%? ? ?

2. Secondly, find out what the odds for each poker player are in second place. Doing this is a little harder.

There are three ways for Player A to get to second place: 1) Player B wins first place, Player A wins second place. 2) Player C wins first place, Player A wins second place. 3) Player D wins first place, Player A wins second place. By knowing the probabilities of all the variants and adding up those probabilities, we get the answer to the probability of Player A taking second place.

1) BA variant, if player B wins first place, which happens 30% of the time, then player A wins against other players: 4000 / (4000 + 2000 + 1000) = 4000/7000 time. This is BA = 0.3 * (4000/7000) ~ 17.14%. Similarly, we count other variants.

2) CA = 0.2 * (4000 / (4000 + 3000 + 1000)) = 0.2 * (4000/8000) ~ 10%

3) DA = 0.1 * (4000 / (4000 + 3000 + 2000)) = 0.1 * (4000/9000) ~ 4.4%

This is A’s chance of winning second place: A = 17.4% + 10% + 4.4% = 31.8%. Answer:. 31.8%.

There are three ways for Player B to get to second place: 1) Player A wins first place, Player B wins second place. 2) Player C wins first place, Player B wins second place. 3) Player D wins first place, Player B wins second place.

1) AB = 0.4 * (3000 / (3000 + 2000 + 1000)) = 0.4 * (3000/6000) = 20%

2) CB = 0.2 * (3000 / (4000 + 3000 + 1000)) = 0.2 * (3000/8000) = 7.5%

3) DB = 0.1 * (3000 / (4000 + 3000 + 2000)) = 0.1 * (3000/9000) ~ 3.3%

This is B player’s second chance of winning: B = 20% + 7.5% + 3.3% = 30.8%. Answer:. 30.8%.

There are three ways for Player C to get to second place: 1. Player A wins first place, Player C wins second place. 2. Player B wins first, Player C wins second. 3. Player D wins first place, Player C wins second place.

1) AC = 0.4 * (2000 / (3000 + 2000 + 1000)) = 0.4 * (2000/6000) ~ 13.33%

2) BC = 0.3 * (2000 / (4000 + 2000 + 1000)) = 0.3 * (2000/7000) ~ 8.57%

3) DC = 0.1 * (2000 / (4000 + 3000 + 2000)) = 0.1 * (2000/9000) ~ 2.2%

This gives C player the second chance of winning: B = 13.33% + 8.57% + 2.2% = 31.8%. Answer:. 24.1%

To calculate the probability of a D player coming in second place, I would just ask: Just subtracting 100% of the probability of other players getting to second place is 100% – 31.8% -30.8% – 24.1% = 13.3%. Answer:. 13.3%

Second chance for all poker players:
Players Chip Count Probability of Win 1 Chance of Win 2 Probability of Win 3 Probability of Win 4
A 4000 40% 31.8%? ?
B 3000 30% 30.8%? ?
C 2000 20% 24.1%? ?
D 1000 10% 13.3%? ?

3. Third, calculate the odds of all poker players winning third place. More complicated here, but let’s try to calculate :).

There are six ways for Player A to get to third place: 1) BCA, 2) CBA, 3) BDA, 4) DBA, 5) CDA, 6) DCA. Let’s add the odds of all the options and find out the overall probability of getting to player A in third place.

1) BCA. If BC variant happens 8.57% of the time, Player A wins third place 0.0857 * (4000 / (4000 + 1000)) = 0.0857 * (4000/5000) ~ 6.87% of the time. Similarly, we calculate other options.

2) CBA = 0.075 * (4000 / (4000 + 1000)) = 6%

3) BD = 0.3 * (1000 / (4000 + 2000 + 1000)) ~ 4.29%

BDA = 0.0429 * {4000 / {4000 + 2000

)) ~ 2.86%

4) DBA = 0.033 * (4000/4000 + 2000)) = 2.2%

5) CD = 0.2 * (1000 / (4000 + 3000 + 1000)) = 2.5%

CDA = 0.025 * (4000 / (4000 + 3000)) ~ 1.43%

6) DCA = 0.022 * (4000 / (4000 + 3000)) ~ 1.26%

This is the overall probability for A poker player to finish third: A = 6.87% + 6% + 2.86% + 2.2% + 1.43% + 1.26% = 20.62%

There are six ways for Player B to get to third place: 1. ACB, 2. CAB, 3. ADB, 4. DAB, 5. CDB, 6. DCB. Let’s add the odds of all the options and find out the overall probability of Player B getting third place.

1) ACB = 0.1333 * (3000 / (3000 + 1000)) ~ 10%

2) CAB = 0.1 * (3000 / (3000 + 1000)) = 7.5%

3) AD = 0.4 * (1000 / (3000 + 2000 + 1000)) ~ 6.67

ADB = 0.0667 * (3000 / (3000 + 2000)) ~ 4%

4) DAB = 0.044 * (3000 /(3000+2000))=2.64%

5) CD = 0.2 * (1000 / (4000 + 3000 + 1000)) = 2.5%

CDB = 0.025 * (3000 / (3000 + 4000)) ~ 1.07%

6) DCB = 0.022 * (3000 / (3000 + 4000)) ~ 0.94%

This is the overall probability of a B poker player coming in third place: B = 10% + 7.5% + 4% + 2.64% + 1.07% + 0.94% = 26.15%

There are six ways for C player to get to third place: 1) BAC, 2) ABC, 3) BDC, 4) DBC, 5) ADC, 6) DAC. Let’s add the odds of all the options and find out the overall probability of C getting to third place.

1) BAC = 0.1714 * (2000 / (2000 + 1000)) ~ 11.43%

2) ABC = 0.2 * (2000 / (2000 + 1000)) ~ 13.13%

3) BD = 0.3 * (1000 / (4000 + 2000 + 1000)) ~ 4.29%

BDC = 0.0429 * (2000 / (4000 + 2000)) = 1.43%

4) DBC = 0.033 * (2000 / (4000 + 2000)) = 1.1%

5) AD = 0.4 * (1000 (/ 3000 + 2000 + 1000)) = 6.67%

ADC = 0.067 * (2000 / (2000 + 1000)) ~ 4.47%

6) DAC = 0.044 * (2000 / (3000 + 2000)) = 1.76%

This is the overall probability of a C poker player coming in third place: C = 11.43% + 13.13% + 1.43% + 1.1% + 4.47% + 1.76% = 33.32%

To calculate the probability of a D player coming in third, I would ask: Just subtracting 100% of the probability of other players getting to third place is 100% – 20.62% -26.15% -33.32% = 19.91%. Answer:. 19.91%

Third place chances for all poker players:
Players Chip Count Probability of Win 1 Chance of Win 2 Probability of Win 3 Probability of Win 4
A 4000 40% 31.8% 20.62%?
B 3000 30% 30.8% 26.15%?
C 2000 20% 24.1% 33.32%?
D 1000 10% 13.3% 19.91%?

4. Fourth, we calculate the odds of all poker players winning fourth place.

Just by 100% subtracting that player’s chances of getting to other places and getting a fourth place chance.

The probability for a poker player to place fourth is 100% -40% -31.8% -20.62% = 7.58%

The probability of a B poker player getting fourth place: 100% -30% -30.8% -26.15% = 13.05%

The probability of a C poker player to finish fourth: 100% -30% -24.1% -33.32% = 12.58%

The probability of a D poker player getting fourth place: 100% -10% -13.3% -19.91% = 56.79%

Chances of all poker players getting to certain places:
Players Chip Count Probability of Win 1 Chance of Win 2 Probability of Win 3 Probability of Win 4
A 4000 40% 31.8% 20.62% 7.58%
B 3000 30% 30.8% 26.15% 13.05%
C 2000 20% 24.1% 33.32% 12.58%
D 1000 10% 13.3% 19.91% 56.79%

5. Calculate the value of players’ poker chips.

Player Poker Chips Value:

A poker player = 0.4 * 50 euros + 0.318 * 30 euros + 0.2062 * 20 euros ~ 33.66 euros

Poker Player B = 0.3 * 50 Euro + 0.308 * 30 Euro + 0.2615 * 20 Euro = 29.47 Euro

C poker player = 0.2 * 50 euros + 0.241 * 30 euros + 0.3332 * 20 euros ~ 23.89 euros

D poker player = 0.1 * 50 euros + 0.133 * 30 euros + 0.1991 * 20 euros ~ 12.97 euros