"An unusual pair of dice. One has sides 1,3,4,5,6,8. The other has sides 1,2,2,3,3,4. ..."

The piece says that the odds of rolling any of the totals is the same, and I'll take their word for that, but it also says that "any game that you can play with a normal set of 2 dice can also be played with a set of Sicherman Dice, with no difference in the outcome". That's only correct for games where the total is used, not the individual dice.

Allowing that we want the different doubles behaviour, there's also a marked change to the odds of single dice - an additional 3 and the loss of both a 5 and a 6. That, along with and the appearance of an 8, no less, would affect the game more than the changed odds of doubles.

I think it would make quite a difference in the way that the game was played. For instance, in the home table, closing the 3-point would be more important than before due to the three 3s - odds of 16/36 instead of 11, while the 5-point would be slightly less useful because the odds of re-entry there would be 6/36 instead of 11/36. (The change would only be slight because the 5-point has other considerable strategic value)

Jumping primes would be harder with the loss of a 5 and a 6 so the value of smaller primes would go up - except that the 8 would make even a 6-prime escapable!

The increased long-arm potential would make for some very unexpected hits - an opponent's backrunner that escapes to your 9-point could be knocked back by one of your own backrunners with an 8-6 from your opponent's 4-point!