Posted by Woodstock on 2010-09-10 14:22:04
Luck or no luck, that is the true question ;)
Posted by DonTomaso on 2010-09-10 15:07:33
Always go for the intuition... I'm not in this to solve maths problems.
Posted by Calcium on 2010-09-10 16:41:51
My head hurts....
Posted by Fela on 2010-09-10 17:18:49
I'm coming up with about 11% for the 2d+1d scenario with pro.
And that's if ONLY the turnover is critical, if you need a PB on your first block, odds are worse.
35/36 * 5/6 approx 81%
35/36 * 1/6 * 1/2 * 5/6 approx 6.7%
1/36 * 1/2 * 35/36 * 5/6 approx 1%
1 - Sum of that will fail
Posted by Fela on 2010-09-10 17:23:49
Which is not to imply your decision was wrong, just the dimensions were not as far removed as you thought and the deciding factor was the slayer's pro skill. :)
Posted by Rabe on 2010-09-10 19:17:48
@Woodstock: Or Nuffle's appreciation... ;-)
@Fela: You're right, of course. I didn't mention all my assumptions: I counted 32/36 possibilities as success (every 2d roll with at least one push), for I only wanted to compare the cases where the assist would make a difference. I also ignored the other 4/32 combined with pro failure, since they do not lead to a second block. And there I did a mistake (again): Double pows on the first block shouldn't have been counted in either, since they lead to an immediate knock-down and the assist doesn't matter in those cases, too. :-D
So in 28 of 36 cases a second block with pro is possible. In 4 out of 72 cases (4/36 * 1/2) it's a second block without pro. I would have certainly rerolled a double both down result, since I needed that push (though this decision wouldn't have been based on calculation, but intuition... maybe I should calculated that through, too...? ;-) ).
Correction:
...turnover (in relevant cases) without assist on 2nd block: 1,94 %
...turnover (in relevant cases) with assist on 2nd block: 0,32 %
...turnover on gfi: 16,67 %
Choosing gfi increases the odds on a turnover by 15,05 %. And this is the interesting number here!
Posted by Fela on 2010-09-10 20:50:34
Sorry, but your numbers are still off.
It is true that for simplicity's sake you can more or less ignore the first block since you need it anyway and just keep the 1/8 chance of the pro reroll being wasted.
Still leaves us with:
5/6 (gfi) * 35/36 + 5/6 * 1/36 * 1/2 * 7/8 * 35/36 =~ 5/6
vs.
5/6 + 1/6 * 1/2 * 7/8 * 5/6
So the 1/6 * 1/2 * 7/8 * 5/6 must make up the difference and we can easily estimate that to less than 8%.
Posted by Wreckage on 2012-03-24 10:21:11
I like to think of my gut feeling as a super computer that is too quick for my consciousness to comprehend. Sadly because i can't follow it, the statements aren't veryfiable, they are also approximations, therefore they can be wrong.
Math can never be wrong because it is verifyable. However your gut feeling about how to use math can be more wrong then your gut feeling about what makes more sense to do.