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I want to make sure of the rules. I may write a program to play this game a million times to see a histogram of the outcomes.

You move first and can select to move +1d6 or +10 or -10. The mouse always moves +1d6 or not at all(if a +-10 is made).

Do both happen at the same time? Ex: the mouse is on 20. I roll 1d6 and land on 20. Is this a win? Or does the mouse still get a 1d6 move? If so then you catch the mouse running by going past and letting the mouse catch up. Ex: I am on 20 and the mouse is on 22. I roll a 6 and the mouse rolls a 4 for my win.

Now do I still win if he rolls a six? Or does he always sneek past me?

Is the mouse movement always in the positive direction? Or does the + refer to always away from you? In this case you also should be able travel -1d6. Ex: you are at 30 and and the mouse is at 32. You roll a 5 placing you at 35. The mouse rolls a 2 and goes to 34 because at the start of the turn you were less. If you are at 60 and the mousecond is at 58, can you roll a 6 and go back to 54 knowing that if the mouse rolls a 4 you win?