Tumbler Three

A cage, not a table

Three dice tumble in a cage and stop on three faces. You choose one of the six numbers before the tumble.

What a number pays

One appearance pays one to one, two pays two to one, three pays three to one. If your number does not appear at all, the cover is lost.

Why it looks generous

Paying three to one for a triple feels large, and the number appearing at all feels likely. Both instincts are slightly off, which is what makes the field worth reading carefully.

The instinct that misfires

Three dice, six faces, so a number 'should' appear half the time. In fact it appears at all in 91 of 216 throws — about 42 percent. The gap between those two figures is the whole game.

Where 7.87 percent goes

Working the payments through: 75/216 pay one, 15/216 pay two, 1/216 pays three, and 125/216 pay nothing. It comes out 7.87 percent short — the widest single-cover margin on this site.

Everything is countable

Two dice have thirty-six outcomes and three have two hundred and sixteen. You can write them all down on one page, which is why dice are the best place to learn where odds come from.

The shape of a total

Seven appears six times out of thirty-six and twelve appears once. Nothing is weighted; the shape comes purely from how many ways a total can be built. Most confusion about dice starts with forgetting that.

Wide margins hide in exotic covers

The simple covers on a dice table are among the fairest anywhere. The exotic ones — an exact triple, a rare total — carry the widest margins on this whole site, and they are the ones printed largest.

Rituals and results

Blowing on the dice, throwing harder, choosing a moment. None of it moves a single outcome. The rituals are old and human and completely without effect, and that is worth knowing before you start attributing results to them.