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Consecutive values

After making such a set of dice for fun, I noticed something I initially found surpising. After rolling all three dice, three consective values appeared e.g. 3, 4, 5. Nothing surprising in its own right but it happened immediately again, this time 4,5,6. In fact I struggled to throw any combintation that wasn't consecutive.

I found this very funny and strange, I think one's brain must be conditioned to not seeing a pattern and I think one also subcontiously fortget these are not normal dice. So when one sees
a sequence almost every time, you can't help but smile.

I did a few sums and I think the probability of this happening is about 83%. With a normal set of 3 dice you would expect this to happen 1.9% of the time. This I think expains why I am so amused by the effect.

This lead me to wonder if there is a similar set of dice that pushes the odds above 83%? I would like to know what set of 3 dice, covering all the usual numbers (1 to 6) yields the maximum probability of the 3 die values being consecutive?

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