2 ... 2.8% (or 1 in 36)
3 ... 5.6% (or 2 in 36)
4 ... 8.3% (or 3 in 36)
5 ... 11.1% (or 4 in 36)
6 ... 13.9% (or 5 in 36)
7 ... 16.7% (or 6 in 36)
8 ... 13.9% (or 5 in 36)
9 ... 11.1% (or 4 in 36)
10 ... 8.3% (or 3 in 36)
11 ... 5.6% (or 2 in 36)
12 ... 2.8% (or 1 in 36)

You can see the number 7 shows up most often at 16.7% of the time, accompanied by the Robber. So it turns out you're not just paranoid after all, this game really is out to get you!

Check out this picture below.

Mid-range numbers can get made out of a stack of many different dice combos (e.g. a throw of 7 has a stack of 6 possible combos).

High and low numbers are only formed from much fewer dice combos, so your chances of seeing them are much smaller (e.g. the numbers 2 and 12 can each be made from a only single dice combo),

In Catan that's why the red 6 and 8 tiles are so great, but building next to the 2 and 12 tiles is only for desperadoes.

Drawing by Tim Stellmach

Wow, three 7's in a row! The next roll has gotta be different right?

Sadly this is the mistake made by many amateur gamblers looking for that 'hot table' they believe is overdue to throw their lucky numbers.

This is because dice combos never get used up (unlike cards dealt out from a Blackjack deck which are used up). So regardless of how much grief the Robber has given you already, the odds of throwing another 7 always remains a steadily menacing you 16.7%.

So you see, Reality really doesn't care about your long-term welfare.

If you didn't already know all this stuff you're in good company. In the old days the great fortunes of noblemen were lost gambling at the two-dice game of Backgammon. That's until some smart cookies worked out what was really going on. And with just that, they kicked off the whole maths field of Probability Theory.

Mastering the dice of Settlers of Catan is a key step towards mastering Probability Theory. And this field is the very basis of Quantum Physics, which once fully understood, may well unlock stable fusion reactions for unlimited clean energy, delaying the impending Apocalypse by centuries.

So good luck with all that.