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A Puzzling Situation

Puzzle created by Anthony Kam

Euphrat & Tigris 1.0

It's the last turn of a closely fought two player game. Your opponent leads the game with 10 VPs of every color plus 3 treasures, to your 9 VPs of every color plus 4 treasures. To solve this puzzle, you need to remember the tie-breaker rules, to wit: your opponent's VP subtotals in four colors, arranged in increasing order, are 10/11/11/11, whereas your subtotals are 10/10/10/10, and therefore you are losing right now.

During his last turn, he tried to end the game by using both actions to swap all six tiles. To his dismay, there is one tile left, and you have one more turn. The board situation is as follows with you as the Lion player (only the relevant section of the board is displayed):

 

Your hand consists of both disaster tiles and the following:

As often happens in Euphrat & Tigris, there is no move which guarantees a win. If you knew what tiles your opponent has, you might be able to find a guaranteed win, but since you don't, you can only find a move that gives you the greatest chance of victory. The puzzle is exactly this: what is the move which maximizes your chance to win?

Please specify both actions (if necessary), and in case of external conflicts, specify the ordering of colors in which you wish to resolve them. Also please specify the conditions under which you will win the game (e.g., "Will win if opponent has no green tiles.")

Since the opponent just swapped all six of his tiles, you may assume that each tile in his hand can be any of the four colors, with equal probability, and each tile is independent. The solution of the puzzle requires some simple intuitive judgments comparing relative probabilities of success among different moves. However, no complicated probability calculation is required.

Solution

- Anthony Kam

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