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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.
Last edited by Reclaimer; April 24, 2012 at 10:47 PM. Reason: I was an idiot
I think your numbers are waaaaay off lol. At least IMO the 1 in 100000 thing was not the actual number but rather an statistic. The sheer amount of money and the amount of places that would be required for 100000 places is astounding and dificult to control. More so, the guys in charge of the game seem to be doing it for fun and a bit of a social experiment. In this regard, 100000 people would be hard to keep track of and largely unnecessary for the ones viewing. Around 1300 players (which is what the statistic would reflect) makes a lot more sense from every point of view.
---------- Post added at 09:29 PM ---------- Previous post was at 09:27 PM ----------
Also note that I did mean 1300 players in the other thread, not 13000.
Holy crap, on a second very close reading, you are right. The phrasing on that translation is very conducive to misunderstanding (mixing spelled out numbers and written numbers. A convoluted way of saying that she has been selected out of 100,000 people to play). The initial number is not 100,000.
I assume your 1300 number comes from taking an approximate Japanese population of 130 million and dividing it by 100k?
What makes you think it applies to the whole country and not just, for example, Tokyo with a population of 35 million?
Either way, I'll edit the first page for the new numbers. Luckily I did this all in an excell sheet and so I don't have to do much. =P
Last edited by Reclaimer; April 24, 2012 at 10:47 PM.
That's really interesting.
I wish we could try to predict how many more rounds they will need to finally get to 1 winner.
I think we are going towards the end now.
And I can't really see it going much further than Round 7-8.
Although, I could be totally wrong.
1)Game with 50% win rate (First Game and Contraband Game)
2)Revival game with 50% win rate (3-on-3 team game)
3)Game with 5% win rate (Minority Rule and Musical Chairs)
4)Revival game with theoretically very high win rate (Downsizing Game and Bid Poker)
We can get an idea of how many games there are left.
If the starting population is 350 from the 35 million in Tokyo, the game likely ends at game 6 (i.e. finish bid poker, game 5, another revival round, then the final game which is game 6)
If the starting population is 1300 from the 130 million in all of Japan, then there are theoretically 5-6 more games (plus as many revival games) depending on how many participants they want the final round.
For the sake of the series, I hope that game 6 is approximately projected end time because that is enough time to get info into the Liar Game tournament without it being too drawn out. If the author wants to continue it, do something like a world Liar Game tournament afterwards. You could possibly squeeze a game or 3 out of that.