Reclaimer
April 23, 2012, 09:55 PM
I've long wondered how many players were left in the Liar Game, but to my knowledge, we've never seen any official statements from the Liar Game office (some of the unofficial statements comes off as absurd after the calculation. I'm thinking the statement that prompted the play-in game before round 4) as to how many players are left, so I decided to attempt to calculate approximately how many players are left using what information we do have.
Here are the assumptions I made and the resulting calculations:
Assumption #1: The 99,999:1 odds of being selected (That is, one person is chosen per every 100k) applies to all of Japan which has an approximate population of 130 million. We have no way of knowing if it applies to all of Japan, and not, for example, just a city like Tokyo with a population of 35 million, but the fact that players are transported for lengths of time allows for players to be grouped from a larger area than a single city, so we it is possible that players are being drawn from larger regions. Also, if you are trying to find the best liar, you'd likely want to find the best liar in the whole country rather than a single city.
Assumption #2: Every player entered in the Liar Game decided to play the Liar Game. Every player entered in the game was delivered the same box with 100 million yen. As we have no way of knowing if anyone ignored the temptation of curiosity, assume that no one did.
Assumption #3: All of the various groups play the same games, or at least games with identical player survival rates. As we haven't seen any other groups in action, we have no way of knowing if this is true or not, but without such an assumption, there is absolutely no way of estimating how many players survive to the next round.
Assumption #4: Nao's group is representative of the whole, except when otherwise noted. If X players survive a round in her game, that same X players survive in every other game. If Y players participate in her revival games, then Y players participate in every other revival game.
This is, of course, incredibly problematic because it is extremely unlikely that every group would have an overly naïve player trying to get everyone to work together which would result in more players winning each game than normal (e.g. the Pandemic game) but also more players dropping out than normal. Because we have absolutely no other information, we just have to hope that the two things balance each other out and give something of an accurate representation of the rest of the games.
Assumption #5: Approximately 10% of all round winners will drop out of the game. This can either be attributed to the player having made enough money to be happy or having finally gotten back into the black and getting out before they go back into the hole. Realistically, you'd probably have a lot more people dropping out earlier rather than later, but for the sake of simplicity, I'll use a single uniform rate.
Starting #: 1,300
Game 1 Finish: 650 survive (this number should actually be less since there would be games played in which neither player wins, but let's ignore that for the sake of simplicity.)
Game 2 (Minority Game) Start: 585 players playing at 26 games. (Nao's game had 22 players, so assume they sent 25 of the original 650 to each game and 3 of the 25 dropped out.)
Game 2 Finish: 52 players (at most 2 players per location could win and pass on to the next round. For the sake of being conservative, let's assume that 2 players get out of each location, rather than 1 or 1.5)
Revival Game 1 (Downsizing Game) Start: 228 players playing at approximately 25 games. (9 of 21 losers of Nao's game 2 participated in the revival game. The 228 number was determined by applying that same ratio to the 533 losers of game 2)
Revival Game 1 Finish: 203 players (I'm assuming that 8/9 players per location get on to the next game.)
Game 3 (Contraband Game) Start: 250 players (203 + 47. That includes the 10% attrition from game 2 winners)
Game 3 Finish: 125 players (250/2)
Revival Game 2 (3-on-3 team battle) Start: 42 players at 7 locations. (3 of 9 losers of Nao's game 3 participated in the revival game. The 42 number was determined by applying that same ratio to the 125 losers of game 3)
Revival Game 2 Finish: 21 players (42/ 2)
Game 4 Preliminary Round (Pandemic Game): Completely irrelevant. Losers are automatically made into Gaya and are thus precluded from winning Game 4, but they are still eligible to participate in the 3rd revival game.
Game 4 (Musical Chairs Game) Start: 133 players at 6 locations. (21 + 112. That includes the 10% attrition from game 3 winners)
Game 4 Finish: 6 players. (Each location has 1 winner)
Revival Game 3 (Bid Poker) Start: 111 players at 10 locations (20 of 23 losers of Nao's game 4 are participating in the 3rd revival game. The 111 number was determined by applying that same ratio to the 127 losers of game 4)
Revival Game 3 Projected Finish: 101 players (10 of 11 players can survive to next round)
Game 5 projected Start: 105 players (101 + 4 players. That includes the 10% attrition from game 4 winners)
If you apply the math to a base population of 35 million, such as is found in the greater Tokyo area, the projected number of remaining players going into round 5 is 29.
Here are the assumptions I made and the resulting calculations:
Assumption #1: The 99,999:1 odds of being selected (That is, one person is chosen per every 100k) applies to all of Japan which has an approximate population of 130 million. We have no way of knowing if it applies to all of Japan, and not, for example, just a city like Tokyo with a population of 35 million, but the fact that players are transported for lengths of time allows for players to be grouped from a larger area than a single city, so we it is possible that players are being drawn from larger regions. Also, if you are trying to find the best liar, you'd likely want to find the best liar in the whole country rather than a single city.
Assumption #2: Every player entered in the Liar Game decided to play the Liar Game. Every player entered in the game was delivered the same box with 100 million yen. As we have no way of knowing if anyone ignored the temptation of curiosity, assume that no one did.
Assumption #3: All of the various groups play the same games, or at least games with identical player survival rates. As we haven't seen any other groups in action, we have no way of knowing if this is true or not, but without such an assumption, there is absolutely no way of estimating how many players survive to the next round.
Assumption #4: Nao's group is representative of the whole, except when otherwise noted. If X players survive a round in her game, that same X players survive in every other game. If Y players participate in her revival games, then Y players participate in every other revival game.
This is, of course, incredibly problematic because it is extremely unlikely that every group would have an overly naïve player trying to get everyone to work together which would result in more players winning each game than normal (e.g. the Pandemic game) but also more players dropping out than normal. Because we have absolutely no other information, we just have to hope that the two things balance each other out and give something of an accurate representation of the rest of the games.
Assumption #5: Approximately 10% of all round winners will drop out of the game. This can either be attributed to the player having made enough money to be happy or having finally gotten back into the black and getting out before they go back into the hole. Realistically, you'd probably have a lot more people dropping out earlier rather than later, but for the sake of simplicity, I'll use a single uniform rate.
Starting #: 1,300
Game 1 Finish: 650 survive (this number should actually be less since there would be games played in which neither player wins, but let's ignore that for the sake of simplicity.)
Game 2 (Minority Game) Start: 585 players playing at 26 games. (Nao's game had 22 players, so assume they sent 25 of the original 650 to each game and 3 of the 25 dropped out.)
Game 2 Finish: 52 players (at most 2 players per location could win and pass on to the next round. For the sake of being conservative, let's assume that 2 players get out of each location, rather than 1 or 1.5)
Revival Game 1 (Downsizing Game) Start: 228 players playing at approximately 25 games. (9 of 21 losers of Nao's game 2 participated in the revival game. The 228 number was determined by applying that same ratio to the 533 losers of game 2)
Revival Game 1 Finish: 203 players (I'm assuming that 8/9 players per location get on to the next game.)
Game 3 (Contraband Game) Start: 250 players (203 + 47. That includes the 10% attrition from game 2 winners)
Game 3 Finish: 125 players (250/2)
Revival Game 2 (3-on-3 team battle) Start: 42 players at 7 locations. (3 of 9 losers of Nao's game 3 participated in the revival game. The 42 number was determined by applying that same ratio to the 125 losers of game 3)
Revival Game 2 Finish: 21 players (42/ 2)
Game 4 Preliminary Round (Pandemic Game): Completely irrelevant. Losers are automatically made into Gaya and are thus precluded from winning Game 4, but they are still eligible to participate in the 3rd revival game.
Game 4 (Musical Chairs Game) Start: 133 players at 6 locations. (21 + 112. That includes the 10% attrition from game 3 winners)
Game 4 Finish: 6 players. (Each location has 1 winner)
Revival Game 3 (Bid Poker) Start: 111 players at 10 locations (20 of 23 losers of Nao's game 4 are participating in the 3rd revival game. The 111 number was determined by applying that same ratio to the 127 losers of game 4)
Revival Game 3 Projected Finish: 101 players (10 of 11 players can survive to next round)
Game 5 projected Start: 105 players (101 + 4 players. That includes the 10% attrition from game 4 winners)
If you apply the math to a base population of 35 million, such as is found in the greater Tokyo area, the projected number of remaining players going into round 5 is 29.