Dice for Non-Mathematicians - 301

Besties
The the previous two posts, we've talked about how adding dice together changes the weight of different kinds of rolls.  But what if we AREN'T adding the dice together? What if people roll several dice and keep only the best roll?

Let's assume you have a game where a player rolls 1d6 and scores a point if it's a 4 or higher. What are his chances? 50%: [1,2,3] don't score and [4,5,6] do. Same as flipping a coin, right? So what would happen to his chances if you let him roll 3 times and keep the highest roll? Would his odds of scoring improve?

Dice for Non-Mathematicians - 201

Rolling At Leasts
Let's imagine a game where you I roll 1d6 and you roll 1d6 and have to tie or beat me.  So, I roll a 5. Sweet. What were the odds that I would roll a 5? Well, obviously 1 in 6.

Now, what are the odds that you will tie or beat me? Your possible roll table is [1,2,3,4,5,6], meaning out of 6 possibilities, you have 2 chances. Ergo, your odds are 2-in-6 (33%).

You probably could have worked that out without a roll table. What you probably didn't do, but is at the heart of this topic, is to add together the individual chances for each winning roll... but that's exactly how it works.

Dice for Non-Mathematicians - 101

Six Times Two Doesn't Equal One Times Twelve
When I was in college, I had a conversation with a friend of mine who was insistent that one 12-sided die was equivalent to two 6-sided dice.

He was adamant. I was... trying to be patient.

If you don't immediately see why he and I disagreed, that's okay. You've probably never been introduced to ideas like "roll tables." You maybe never had a statistics class (actually, neither did I).

That's okay. This isn't complicated.  In fact, when you actually see it, it's pretty intuitive.