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AA BB CC DD EE FF GG HH II JJ KK LL MM NN OOPrepared by: Mike PangburnDate: Feb. 6, 2013Question 1
One play of game12 players' choices69396748686719078949288
# unique values? 11Was there match? Yes
Simulate 1000 plays (trials) using a Data TableMatch?
Yes1 Yes2 No3 No4 No5 No6 No7 No8 No9 No
995 No996 No997 No998 No999 No1000 Yes
% of games with match? 48%
Question 2
One play of game
Player A's visible die 6Player A's hidden die 4
Player B decides how many dice to roll: 1, 2, or 3. Let's call these Options a, b, c.Player B's subsequent dice (not all will apply-‐-‐unless she chose Option 3)Die 1 4Die 2 2Die 3 5
Player A's sum 10 (Note: this is unknown to Player B until after she chooses between Options a,b,c)Relevant player B sums with Option…Option a Option b Option c
4 6 11
Would player B win? No No No
Simulate many plays of gameScenario: A's visible die is a 1 Scenario: A's visible die is a 2 Scenario: A's visible die is a 3
1000 trials below No No No 1000 trials below No No No 1000 trials below No No No1 No No No 2 No No No 3 No Yes No1 No No No 2 No No No 3 No No No1 No No No 2 No No No 3 No No No1 No No No 2 Yes No No 3 No No No1 No No No 2 Yes No No 3 No No No1 No No No 2 Yes No No 3 No No No1 No No No 2 Yes No No 3 No Yes No1 No No No 2 No No No 3 No Yes No1 No No No 2 No No No 3 No No Yes1 No Yes No 2 No No No 3 Yes No No1 Yes No No 2 No No No 3 No No No1 No No No 2 No No No 3 No No No1 No No No 2 No No No 3 No No No1 Yes No No 2 No No No 3 No No No
% games player B won? 28% 10% 3% % games player B won? 17% 12% 6% % games player B won? 8% 13% 10%
Scenario: A's visible die is a 4 Scenario: A's visible die is a 5 Scenario: A's visible die is a 61000 trials below No No No 1000 trials below No No No 1000 trials below No No No
4 No No No 5 No Yes No 6 No No No4 No No No 5 No No No 6 No No No4 No No No 5 No No Yes 6 No Yes No4 No No No 5 No No No 6 No No No4 No No Yes 5 No Yes No 6 No No No4 No No No 5 No No Yes 6 No Yes No4 No No No 5 No No Yes 6 No No Yes4 No No No 5 No No Yes 6 No No No4 No No No 5 No No No 6 No No Yes4 No No No 5 No No No 6 No No No4 No No Yes 5 No No No 6 No No No4 No No No 5 No No No 6 No No Yes
% games player B won? 3% 13% 19% % games player B won? 0% 13% 25% % games player B won? 0% 10% 34%
Therefore, based on the results you find above, what will your strategy be? I will choose to roll 2 dice whenever I see my opponent's first roll is:I will choose to roll 1 die whenever I see my opponent's first roll is:I will choose to roll 3 dice whenever I see my opponent's first roll is:
(Remember here that winning with 2 dice gets you 2 points, but winning with 1 or 3 dice gets you only 1 point.)
Your opponent's 2nd random die's value is here, between 1 and 6, but you don't get to see it uncl you decide how many dice you will roll (to emphasize that, I colored the cell black). For this parccular trial, we can see from cell B1039 (=B1030+B1031) that this value must be 4
