Geeky math help requested.

[Elbows]

I couldn't figure out how to properly phrase this in google, so I'm curious if one of you math nuts can explain this to me.

I was calculating percentages of some dice rolls (putting together a game). I am using the following.

1) D4 (four sided dice)
2) D6 (six sided dice)
3) D8 (eight sided dice).

Each dice, when rolled, is "open ended" meaning if a value of 4, 6 or 8 (the highest possible value) is rolled, you may roll the dice again, adding to the original value. This can continue indefinitely.

I am trying to establish the percentage chance of rolling the following values:

4+
5+
6+
7+

The D6 and D8 are quite simple.

D6
4+ = 50%
5+ = 33%
6+ = 16%
7+ = 16% (if a 6 is needed, and rolled, the minimum total will be 7)

D8
4+ = 63%
5+ = 50%
6+ = 38%
7+ = 25%

...now the D4 is what I can't figure out (it's been a few too many years since my last math class).

D4
4+ = 25%
5+ = 25% (Again, if a 4 is needed, and rolled, the minimum value is 5)
6+ = a 25% chance, followed by a 75% chance ---- what overall chance does this equate to?
7+ = a 25% chance, followed by a 50% chance ---- what overall chance does this equate to?

I don't remember the formular to combine two percentage chances into one number - anyone?

Thanks.

PS: Part of me wants to simply say the chance is 75% of 25%...or 18.75% --- but it's not that simple right?

[GeoffD]

A pair of D4 gives you the following 16 possible combinations:
1-1
1-2
1-3
1-4
2-1
2-2
2-3
2-4
3-1
3-2
3-3
3-4
4-1
4-2
4-3
4-4

Just add them up and divide by 16 to get your percentage
4+ is 12 out of 16 or 75% odds
5+ is 10 out of 16 or 62.5% odds
6+ is 6 out of 16 or 37.5% odds

My university probability theory course was back in 1978. The math behind this is long gone.

[Elbows]

I agree, but I'm not initially rolling two dice at once - a second dice is only rolled if the initial result is a 4.

[VegasJetta]

[lipprandt35]

Done!!
/thread

[GTiTOM]

D4
4+ = 25%
5+ = 25% (Again, if a 4 is needed, and rolled, the minimum value is 5)
6+ = a 25% chance, followed by a 75% chance ---- what overall chance does this equate to?
7+ = a 25% chance, followed by a 50% chance ---- what overall chance does this equate to?

I don't remember the formular to combine two percentage chances into one number - anyone?

Thanks.

PS: Part of me wants to simply say the chance is 75% of 25%...or 18.75% --- but it's not that simple right?

I think it is that simple. I believe you just multiply the odds of the first roll (1/4) times the odds of the second roll.

The odds of a 4 on the first roll are 1/4, and then the combined odds are then conditional on the second roll:
5+: 25% (1/1 x 1/4 = 1/4)
6+: 18.75% (3/4 x 1/4 = 3/16)
7+: 12.5% (2/4 x 1/4 = 1/8)
8: 6.25% (1/4 x 1/4 = 1/16)

Similar to how if you roll two dice, your odds of rolling a 2 (1/6 x 1/6) are the same as rolling a 12 (1/6 x 1/6) or 1/36.

[Elbows]

Gotcha. I actually just called my mother, the accountant/super math wiz and we came to the same conclusion. Thank ye kindly.

[Kameirocco]

[Inkarnata]