/sci/ - Science & Math

>>9043917
you have to reroll 1/8th of your rolls
and then 1/8th of those rerolls
and then 1/8th of those rererolls
and so on

so if you do decide you'll do N rolls then you'll do N + N/8 + N/64 + N/512 + N/4096... rolls
which comes out to N*(8/7) rolls. So you increase your rolls by about 14%

>>9043926
Oh, no, it's not rerolling all ones. It's if you get a one you reroll but have to keep the reroll even if it's another one.
I want to know how much higher the average result on a die will be.

>>9043929
the average value won't change, then

Your average score not rerolling 1s:
[math]\frac{1}{8}+\frac{2}{8}+\frac{3}{8}+\frac{4}{8}+\frac{5}{8}+\frac{6}{8}+\frac{7}{8}+\frac{8}{8}=\frac{9}{2}=4.5[/math]

Your average score rerolling 1s:
[math]\frac{1}{8}(\frac{1}{8}+\frac{2}{8}+\frac{3}{8}+\frac{4}{8}+\frac{5}{8}+\frac{6}{8}+\frac{7}{8}+\frac{8}{8})+\frac{2}{8}+\frac{3}{8}+\frac{4}{8}+\frac{5}{8}+\frac{6}{8}+\frac{7}{8}+\frac{8}{8}=\frac{79}{16}=4.9375[/math]

>>9043946
he said you keep the rerolled 1
so the average isn't going to change

>>9043929
>I want to know how much higher the average result on a die will be.
Well, the average without re-rolls is 4.5.
1+2+3+4+5+6+7+8 = 36
36/8 = 4.5

If we re-roll any initial 1's, the re-rolls will average 4.5,so we can substitute 4.5 for 1 above:
4.5+2+3+4+5+6+7+8 = 39.5
39.5 / 8 = 4.9375

So the average goes from 4.5 to 4.9375, which is a 9.7222....% increase.

>>9043949
>he said you keep the rerolled 1
No, he said:
>>9043929
>if you get a one you reroll but have to keep the reroll even if it's another one.

>>9043951
So, it's an increase if a little less than .5 per die? Okay, then I'd get more value out of not taking that option.
Thanks for the maths guys

>>9043960
>Thanks for the maths guys
You're welcome.

>>9043917
wouldn't this just eliminate 1 from the possible outcomes?
if that's the case, your expected roll would be 5 instead of 4.5

>>9043970
>wouldn't this just eliminate 1 from the possible outcomes?
I'm going fr a walk.
Only two possible outcomes: either I'll get hit by lighting or I won't.
must be 50-50, right?

>>9043970
No, because you only get to re-roll once.

If you could re-roll forever, then yes, you're effectively rolling a seven-sided die numbered 2-8, so the average score would be:
(2+3+4+5+6+7+8)/7=35/7=5