66 is a dice game that's usually played with 2-3 players, using a pair of six sided dice.
Each players tosses their dice in turns and the highest number determines the tens of the score, which is then combined with the lower number to get the total. If a player rolls a 6 and a 2, the score is 62. If the player rolls a 1 and a 4, the score is 41. Scores rank from 12-65 and doubles from 11-66. A score of 65 beats a 64 and lower, while an 11 (double-1) beats 65. A 66 (double-6) is the highest possible score, beating everything else, which is why the game is called 66.
The game is made interesting because the resulting score isn't initially shown to the other players. A player could announce any score they wish, so long as it beats the previously announced score. The next player can believe and attempt to beat the announced score, or call the possible bluff and ask to see the dice. With every turn, each player throws a few coins into the pot. If a player is called and their announced score matches the actual roll, they take the pot, otherwise it goes to the calling player. It costs three times the rolling amount to call a player.
In part one, the AI is simple. In brief:
- It will only lie when it has to
- When it is forced to lie, it will pretend to reroll the dice until it gets an acceptable number, then claim that.
- It will call lies based entirely on the number claimed, based on a d12 roll. The situation or The Princess' ranks in bluff are not considered.
This means that there is no clue for when it has told a lie. When attempting to guess whether or not Dara has told a lie, the player should look at Kenny's claim, not at Dara's. The higher Kenny claimed, the more likely it is that Dara's actual roll is lower.
If there are three antes in the pot (as would be the case if The Princess were the last one to call), the break even point is 62 - IE, if Kenny's claim was 62 or higher, Dara has a 2/3 chance of having been forced to lie (and The Princess is spending four antes to get two).
Kenny and Dara are much more likely to call claims in the 60-range than in the 50-range. If The Princess makes a claim of 61, there is a >50% chance that either Kenny or Dara will call it before it comes back to her, resulting in lost money. Claiming 53 or 54 is much safer.
These findings motivate the following strategy.
- If you have doubles, always tell the truth. Kenny will probably call you and give you a lot of free money. This supercedes the rest of the strategy.
- If you have the first move, claim 54, even if your actual roll is 61-65. Claiming something in the 60's will usually cause Dara to call Kenny on his roll, and you will get nothing.
- When it comes back around to you, if the pot is at least three antes (due to Kenny and Dara both not calling), call Dara regardless of her roll. Even if Kenny only claimed 61, you will lose less money calling Dara (for a 60% chance of payout) than you will for rolling (for a nearly guaranteed call by Kenny or Dara and no payout)
- If Kenny or Dara has called and the pot is not at least three antes, claim 54 if you can, otherwise, take the lowest option available, unless the truth is higher. Calling with less than three antes in the pot is almost never worth it.
- Lying downward doesn't count as a lie. If you have 65, claim 54, and are called on it, it counts as if you told the truth.
- The AIs will never lie if the pot is empty, because there is no number for them to beat.
In part two, the AI and objective have both changed dramatically, and the above strategy is very unlikely to work.
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