MrWaeseL at [unixtime wrote:1110378816[/unixtime]]On another board I visit, a poster asked for help on a problem of chance:
guy wrote:What I need to know is this:
What are the odds of a success when using this die sequence?
First roll a d4, whatever number you result in from that roll write down. You then need to roll that number or higher on a d6. Then roll the result or higher on a d8, d12, and d20 as before.
If possible, I would like to know the odds of success for the entire series and the odds of success if you omit the d4; the d4 and d6; the d4, d6, and d8; and omitting the d4, d6, d8, and d12.
I am totally unclear as to what the actual question here is. But it seems to be small enough that we can largely use lisitings of possiblities in the sample space to solve it:
# on d4 1
chance of rolling equal or higher on d6: 6/6
#on d4 2
chance of rolling eqaul or higher on d6: 5/6
#on d4 3
chance of rolling equal or higher on d6: 4/6
#on d4 4
chance of rolling equal of higher on d6: 3/6
overall chance of rolling higher on d6 than on prior roll on d4: 18/24
# on d4 1
chance of rolling equal or higher on d8: 8/8
#on d4 2
chance of rolling eqaul or higher on d6: 7/8
#on d4 3
chance of rolling equal or higher on d6: 6/8
#on d4 4
chance of rolling equal or higher on d6: 5/8
overall chance of rolling equal or higher on d8 than on a prior roll on a d4: 26/32
now, I'm going to state a general hypothesis: the overall chance of rolling equal or higher on a second die of size B than on a prior roll on a die of size A, (where B >=A, and each die is numbered with succesive positive integers can be represented as
(B) + (B-1) + (B-2).......(B-A+1)] / A*BNow what I'm unclear about is wheather the question is asking if each sucessive roll just has to beat the initial d4 roll, or whether each successive roll has to beat the imeddiately preceeding roll which had to beat the roll which preceeded it and so forth. I'm also unclear if success is determined solely by beating the initial die on all dice involved, or whether partial successes matter or not
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