Essentially, I'm playing a game, where two players each roll a 6 sided die, where the higher die roll wins. For some reason my die roll gets a +1 to whatever it lands on. What is the probability that my die roll is higher than my opponents die roll (assuming they get no bonuses)? We each get one roll per game.
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2$\begingroup$ Welcome to MSE! Did you make a table like this one? That should make it easier to visualize what's happening. $\endgroup$– MasonCommented Dec 4, 2018 at 19:36
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2 Answers
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HINT:
If you get the $+1$ bonus, but the other person doesn't, you can simplify that to being wherever your score is at least the value of theirs.
In other words, ignoring the bonus, if $A$ is your score and $B$ is theirs, you want:
$$P(A\ge B)$$
answered Dec 4, 2018 at 19:46
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$\begingroup$ To give an example of what I'm saying, suppose you both roll a $6$ on the die. You will win because of the $+1$ bonus $\endgroup$ Commented Dec 4, 2018 at 19:48
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If $2$ die are rolled there are 36 different outcomes. $(1,1),(1,2) \dots (1,6),(2,1), \dots$ and so on. It is an empirical fact that for rolls with $2$ "normal" die all of these outcomes will occur with equal probability. So now if you count all the outcomes where you win and divide it by $36$ you will have the probability of winning.
