The python narging I mentioned earlier came out of a quick diversion to monte-carlo the Shut The Box pub game. The varient I was testing is:
- Start with numbers 1 through 9 "up".
- Roll two 6-sided dice
- Put down one or two numbers that exactly total the sum of the dice roll.
- Repeat until either you cannot exactly total the roll (a lose), or you've put down all the numbers (a win).
Assuming I've fixed all the bugs, given perfect play (i.e. effective foreknowledge of all throws), you have somewhere around an 8.8% chance of winning.Update:
Hm... my results disagree with those on a random web site
There's also an analysis here
of a varient where you get to choose to roll one die if the total is 6 or less. The numbers given on those two sites for that varient agree, which leads me to suspect my result for the varient above may be wrong.
I haven't yet tried programming various strategies that rather than evaluating the whole tree. I'd guess something like "try to put down the numbers that aren't near 7" might be a good one to try. Rules on the web suggest that you can play it by attempting to minimise your score, rather than just going for an outright win, which might suggest a different strategy.