1d6+1 vs. 2d6 high die.

What are the odds that 1d6+1 will tie or be higher than the high die of 2d6? What are the odds that 1d6+1 will be higher than the high die of 2d6? Odds if 2d6 rolls a double then add 1 to high die?

We don't do homework assignments.

Quote: DJTeddyBear

We don't do homework assignments.

But I think a hint is in order.

For the first two questions, figure out:
What is the probability that the high die of 2D6 will be a 5?
What is the probability that the 1D6+1 will be greater than (or equal to) 5?

Quote: DJTeddyBear

We don't do homework assignments.

It is not homework, it is for a game I'm designing. I think I have the answers by comparing the probabilities of attaining each value 1 through 7.
2D6 adding 1 to doubles has a probability of high die being 5 or higher @0.583 while 1d6+1 is @0.5.

We could do homework.

a: 1d6+1 has a probability state of (2: 1/6, 3: 1/6.... 7:1/6)
b: 2d6 high dice: (1: 1/36, 2: 3/36, 3: 5/36, 4: 7/36, 5: 9/36, 6: 11/36)

Then you combine:

Odds of a >= b.

1/6*4/36 + 1/6*9/36 + 1/6 * 16/36 + 1/6 * 25/36 + 1/6 * 36/36 + 1/6 = 58.333%

Odds of a > b

1/6 * 1/36 + 1/6 * 4/36 + 1/6 * 9/36 + 1/6 * 16/36 + 1/6 * 25/36 + 1/6 = 42.1296%


If you're going to invent games based on dice then you need to learn 7th grade combinations and probabilities.

Thanks boymimbo for laying it out for me, it is much clearer now. My game is not based on dice although it uses dice for the element of chance. Probability is very unintuitive and I do not use it enough to maintain a working knowledge of the formulas.