Play your odds to see if you can uncover the answer.
➡ The Problem
From Monopoly to Backgammon to Yahtzee, our first experiences with board games almost always feature sets of six-sided dice. They’re a great way to create some randomness and chaos in a game, but players have always struggled with the odds of rolling specific outcomes. How likely is a Yahtzee in three rolls? What are the chances you land on Boardwalk? Should you pay the fine or wait to roll doubles to get out of Jail for free?
One main dice mechanic involves rolling two dice and adding up the total. So you might start to recognize that the odds of rolling a 7 are higher than the odds of rolling an 8. Another mechanic involves rolling lots of dice and looking at individual dice. The odds of rolling a 5 on one of four dice are higher than the odds of rolling a 5 on one of two dice. Usually, a game picks one of these two mechanics. But some games like to play on the edge…
Let’s say you’re playing a game that gives you a single roll of two six-sided dice. In this game, you roll a specific result k if the sum of your two dice add up to k or if either of the dice is showing a k.
In this game, given a single roll of the two dice, what are the odds that you roll a 5?And is it more likely for you to roll a 5 or an 8?
➡ The Hint
There are a host of equations you could use to solve this problem, but visualizing the answer is the easiest way to get started.