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תגובות
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In the chinese town of Ruili (near the Burma/Maynmar border), the locals play a street gambling game.
There are 3 identical (giant) game cubes, each with 6 figures: dog, rooster, dragon, elephant, turtle and fish. Each participating player bets some money on one of the 6 figures, and a betting "round" is performed by rolling the 3 cubes.
After watching the game for a while, I learned that-
1) If 0 cubes show your figure, you just lose the money.
2) If 1 cube shows your figure, you break even (meaning: you just get your original bet back, no money lost and none won).
3) If 2 cubes show your figure, you get double the money you bet on (e.g. you bet 10 yuan – you get the 10 back plus another 10).
I didn´t watch long enough to see what happens if all 3 cubes show your figure
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Definitions:
a) a ´simple´ gambling game is a game in which you always get a positive integer ("shalem") multiplication of the money you bet on, or lost all the money (e.g. you bet 10 yuan, you either lose everything, get the 10 yuan back, get 20 yuan, 30… etc, but you can´t get 15 yuan). This is an important characteristic of a ´street-game´, as it helps the game flow better.b) a ´long-term fair´ gambling game is a game in which if you play all possible rounds (theoretically), the final outcome would be that that the ´house´ wins, but only the least possible amount of money. Obviously, the house must always WIN in the long-run (otherwise the game wouldn´t take place to begin with). For example, according to the Las Vegas Gambling Commitee a ´fair´ slot machine is one in which the house only wins 1% of the money in the long run.
c) a ´short-term fair´ gambling game is a game in which the above also applies (statistically) even when not all possible rounds are played (let´s say only 10% of all possible rounds are played).
Example 1: consider a gambling game in which a single cube is thrown, if the outcome is 6 you win 5 times your bet, and any other outcome – you lose your bet. This is a ´simple´ game which is also ´long-term fair´ (the house will win in the long-run, but only 1 Yuan per all rounds played) but not ´short-term fair´.
Example 2: Betting on colors on a Las Vegas roulette is ´simple´, ´long-term fair´ and also ´short-term fair´.
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Questions:
1. How much money should you win (assuming you bet on 1 Yuan) in the Ruili gambling game when all 3 figures are ´yours´, to make the game ´long-term fair´ while keeping it ´simple´ ?
2. Assuming the answer to (1) is the one actually used in reality (I seriously doubt it, but nevermind…) – the Ruili game is not ´short-term fair´. Change all ratios to make it both ´long-term fair´ and ´short-term fair´ while keeping it ´simple´.
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