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Taking apart the gamble: dissection of Kaiji, Liar Game, Etc

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TheyCallMeTomu Since: Jan, 2001 Relationship Status: Anime is my true love
#1: Apr 20th 2014 at 3:17:07 PM

Think Kaiji, Liar Game, or Gamble Fish.

Okay, so, I couldn't find a decent thread to babble about this sort of thing, so I lazily made my own.

I've been rewatching the Kaiji anime recently, and I was thinking, hey, there's a cheat to restricted rock paper scissors, that lets not just one person win, but the entire ship.

Simply this: since everyone starts with 3 stars and only needs 3 stars to win, all they have to do is give away their cards. So if one "sacrifice" decides to take EVERYONE'S cards, the game is over instantly. Ah, but then the sacrifice is screwed.

So the sacrifice would take the cards of everyone but one person. For the purposes of describing this gamble, we will call this "sacrifice" and "partner."

Neither the sacrifice nor the partner can win unless they get rid of all of their cards. Thus, the partner gives the sacrifice all but two of his cards, both the same set. They play, and have a draw. During this time, the sacrifice can't betray the partner, because if he does, then he'll have no one to cooperate with to get rid of his cards. After all, at any point, if one member refuses to cooperate, both members automatically lose.

Let's say we start by eliminating rock. At all times, the partner has 2 rock in his hands, and the sacrifice has every other card still in play. They repeatedly play rock against one another, and every time they do, the sacrifice gives the partner another rock.

The first hiccup occurs when there are only two rock cards left. You can't allow the partner to keep only one card, because if you do, then he'll "escape" on a draw. Thus, at this point, the sacrifice gives the partner two paper in exchange for the two rock. The sequence is then repeated, until there are only two paper left in play. The sacrifice takes the partner's paper, and gives him two scissors. They then proceed until there are only two scissors left in play.

This leads to a situation where the partner has one scissors, and the sacrifice has two rock, two paper, and one scissors. Sacrifice gives partner 1 rock. They play rock against each other, eliminating rock.

But what happens if sacrifice tries to steal one of partner's stars, by playing paper here?

Sacrifice will have 1 paper, 1 rock, and 1 scissors left. Partner will have 1 scissors. He'll be down one star. If sacrifice were to give partner his remaining scissors, then over the next two plays, partner would lose once, and win once, meaning partner would be at 2 stars. Thus, sacrifice would be able to extort partner of his entire war funds for the privilege of one star. But again, since both partner and sacrifice need to play until they are out of cards, each can threaten mutually assured destruction upon the other. Therefore, partner could simply say "Well, if you don't give me a star, I'm not going to play against you, so we both die." Therefore, no extortion can take place.

So what's the problem with this model? Well, obviously, it'd take forever. With only two people going through hundreds of cards, there's no way they'd be able to finish within the four hour time limit. So what's an alternative?

Instead of the sacrifice being willing to accept ALL of everyone's cards, the sacrifice could accept all but one suit. If everyone but the sacrifice only has rocks, then people could play against one another in order to do nothing but get rid of the rocks. I'm still running through models of "person tries to cheat" in my head in this model. The biggest disincentive to cheating here is that, once you cheat, you'll have to find another person to play against. Since everyone else is likely to already have buddied up by that point, you waste extra time, and due to the interest rule, time is money.

Thoughts? Alternative workarounds? The time limit is the real nasty part.

And of course, if anyone has any fun workarounds to other games, it'd be fun to hear it.

EDIT: It occurs to me I'm overthinking this. Instead of one sacrifice, there can simply be six sacrifices. Then, cards are divided such that two people have only paper, two people have only scissors, and two people have only rock. Each of the six know who their partner is, and thus also know who their partner isn't. Therefore, no one will be willing to play against the person who will defeat them, so everyone would only be able to play against their partner.

EDIT EDIT: Fridge Logic just set in. The number of stars is constant throughout the game (excluding when that one guy tried flushing his cards). The only way stars leave the game is through victory or through people ending the game with cards remaining (while they still possess stars).

In short, unless the baddies buy bonus stars directly (rewatching the series; I forget if they do), literally everyone could be saved no matter who has what stars. Certainly, people would want to extort others for cash, but on the other hand, there'd be no value in excess stars.

EDIT EDIT EDIT: Oh, okay. So this strategy is flawed because of the "repeaters need 4 stars" nonsense. What a shame; I totally forgot about that (not to mention it's an arbitrary rule Tonegawa never mentions). I am now APPALLED AND DISMAYED by this thread.

edited 20th Apr '14 10:04:37 PM by TheyCallMeTomu

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