Certain problems like the product sum game can have their permutations listed out in a table.
In the example of the Product sum game, the rules are, Player A and Player B have 3 numbers to choose from: {1,2,3}. If the sum of Player A’s number and Player B’s number is greater than the product of both, then Player A gains a point If the product of Player A’s number and Player B’s number is greater than the sum of both, then Player B gains a point
The tables are shown as such:
so, lets find which is bigger, sum or product?
for (1,1) the SUM. PLR A
(1,2): PLR A
(1,3): PLR A
(2,1): PLR A
(3,1): PLR A
(2,2): Nobody wins
(2,3): PLR B
(3,2): PLR B
(3,3): PLR B
5/9 is PLR A 3/9 is PLR B 1/9 is Nobody
Therefore the following conclusions can be make: Player A wins if either player draws a 1. Player B wins if no player draws a 1.