[GZG] [DICE MATH] Dice Pain... Never... Ending

I haven't seen anyone necessarily refute my approach of working backward from
all possible combinations producing 19 points on two dice. It's vaguely Monte
Carlo-ish. (It may
contain mistakes)

Now, I see the point about 11 in 36 for 1+ 6's. And in fact, I suppose a
similar logic applies further along.

First roll: Odds of 6 on dice A: 6 in 36 Odds of 6 on dice B: 6 in 36 The 6,6
result is really one result, so 11 in 36. But we know that
really means 10/36
chance of getting ONE six, 1 in 36 chance of 6,6. But wait, some of those
other numbers are significant too! 6,4 6,5 5,6 5,4 are all significant because
they actually cause an extra damage point.

So really, we have options to score 2, 3 or 4 points in the first roll and
still proceed with the further analysis. The 2 point case isn't complete
though, because 4,4 4,5 5,5 5,4 all score two but don't let us go on.

Odds of scoring 2 points and being able to go on: 6/36
Odds of scoring 3 points and being able to go on: 4/36
Odds of scoring 4 points and being able to go on: 1/36

Each of these leads to a separate analysis, of sorts. If you've scored 4,
you've just got the same analysis all over again (roll 2D, what are our odds
of various outcomes that let you proceed?). If you rolled 3, you have 1D to
proceed with. Similarly, if you scored 2, you've got 1 die to proceed with.

Anyway, this all goes ugly places. And really, other than as some mathematical
masochism, I'm not sure it serves much gainful purpose. We really should give
this thing a tag or take it offline to another forum. We're not really
discussing much GZG stuff anymore.

Tomb