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« on: August 27, 2012, 06:54:55 am »
I'm not sure if this counts as off topic, but i solved -stef-'s game
i will be listing turns as 1-9 so 1st player plays the odd ones, 2nd player plays the even ones
1st player turn 1: +3
1st player turn 3: +5 if (losing by 11 or 12) otherwise +3 if (losing by 10 or less) +10 if (losing by 13 or more)
1st player turn 5: +5 if (losing by 5, 6, 11, or 12), otherwise +3 if (losing by 10 or less) +10 if (losing by 13 or more)
1st player turn 7: +5 if (losing by 4, 5, or winning by 8, 9, 10), otherwise +3 if (losing by 8 or less), +10 if (losing by 9 or more)
1st player turn 9: logical, try for the win (behind by 3 or 4 need a 5, behind by 5 or more needs a 10, losing by 2 or less needs 3's)
2nd player turn 2: +10 if (losing by 10) otherwise +3 [ignores impossible cases]
2nd player turn 4: +10 if (losing by 6 or more) +3 if (losing by 5 or less)
2nd player turn 6: +5 if (losing by 1,2,8) otherwise +3 if (tied or winning) +10 if (losing)
2nd player turn 8: +5 if (losing by 1,2 or winning by 5,6,7), otherwise +3 if (tied or winning) +10 if (losing)
overall the odds of 1st player winning is 59%
the 5's seem to not effect the overall strategy, and instead are tactical options due to special cases (if 2nd is losing by 1 or 2, missing a 5 is no worse than missing a 3, but is alot better if it hits)