# Analysis Stratego

Precision, put in 100 or 1000 or 10000
 1 2 3 4 5 1 2 3 4 5

x1: x2:

#### The game where higher cards beat lower cards, except 1 against 5, which is a tie (both cards are replaced)

Solution of the 1,2,4,5 Game: In the first move, play 1 with probability 0.3268, play never 2, Play 4 with probability 0.2693, and play 5 with probability 0.4039.

For the 1,2,3,4,5 game we need games beyond 3*n. This is done, using an online applet. Here is the data:

 1234 1235 1245 1345 2345 1234 0 -0.25 -0.431 -0.5 -0.75 1235 0.25 0 -0.573 -0.643 -0.318 1245 0.431 0.573 0 -0.454 -0.161 1345 0.5 0.643 0.454 0 0 2345 0.75 0.318 0.161 0 0
 1234 1235 1245 1345 2345 12345 1 0.749 0.602 0.494 1
 1 2 3 4 5 1 0 -1 -1 -1 0.75 2 1 0 -0.494 -0.494 -0.494 3 1 0.494 0 -0.602 -0.602 4 1 0.494 0.602 0 -0.749 5 -0.75 0.494 0.602 0.749 0

Solution of the 1,2,3,4,5 Game: At the beginning, play 5 with probability 0.4, 1 or 4 both with probability 0.3, but never play 2 or 3 at the beginning.

May 23-25, 2007

### Complete Strategy:

 Ann Beth 1: 2: 3: 4: 5: --- 1: 2: 3: 4: 5: --- exp 12345 12345 0.3 0.3 0.4 0.3 0.3 0.4 0 12345 1235 0.15 0.59 0.26 1: 2: 3: 4: 5: 0.749 12345 1245 0.65 0.03 0.32 1: 2: 3: 4: 5: 0.602 12345 1345 0.31 0.31 0.38 1: 2: 3: 4: 5: 0.494 12345 125 0.2 0.58 0.22 1: 2: 3: 4: 5: 0.893 12345 135 0.25 0.52 0.23 1: 2: 3: 4: 5: 0.85 12345 145 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: 0.72 12345 15 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: 1
 Your Hand Opponent 1: 2: 3: 4: 5: --- 1: 2: 3: 4: 5: --- exp 1234 1234 1 1 0 1234 2345 0.25 0.75 0.75 0.25 -0.75 1235 1235 0.3268 0.2693 0.4039 0.3268 0.2693 0.4039 0 1235 1245 0.2542 0.5702 0.1756 0.6184 0.0403 0.3413 -0.573 1235 1345 0.2417 0.4463 0.3121 0.0631 0.6241 0.3128 -0.643 1235 2345 0.1478 0.0418 0.6626 0.1478 0.4289 0.1067 0.1235 0.3409 -0.318 1245 1245 0.3268 0.2693 0.4039 0.3268 0.2693 0.4039 0 1245 1345 0.2561 0.5313 0.0154 0.1973 0.2676 0.062 0.2604 0.41 -0.453 1245 2345 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp 1345 1345 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp 1345 2345 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp 2345 2345 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp You Opponent 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp You Opponent 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp You Opponent 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp You Opponent 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp You Opponent 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp
 Your Hand Opponent 1: 2: 3: 4: 5: --- 1: 2: 3: 4: 5: --- exp You Opponent 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp You Opponent 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp You Opponent 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp You Opponent 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp You Opponent 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp You Opponent 1: 2: 3: 4: 5: 1: 2: 3: 4: 5: exp