Gratchoof
Joined: Mar 29, 2013
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 Posted:
Nov 29, 2019 - 14:09 |
 
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Heya
What are the odds of:
Getting at least one Double
AND
Getting at least one +Agi
Out of 5 skill ups?
My maths is failing me today :/
Thanks |
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Harad
Joined: May 11, 2014
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Nov 29, 2019 - 15:05 |
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Probability of a double is 1 in 6 - probability of not a double is 5 in 6.
Probability of AG is 1 in 18 - probability of not AG is 17 in 18.
Probability of not getting a double in 5 rolls is therefore 3125 in 7776.
So probability of getting at least one double is 4651/7776
Probability of not getting AG in 5 rolls is 1,419,857 in 1,889,568
So probability of getting at least one AG is 469,711 in 1,889,568.
Now your question of and should just be a multiplication as the events are mutually exclusive:
This gives 4651*469711/(1889568 * 7776) = 2,184,625,861 / 12,693,280,768
Or about 1 in 6 
I've included all the sums as my experience is that probability is one of the easiest areas to make slips as we are not well suited to thinking probabilistically. |
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JackassRampant
Joined: Feb 26, 2011
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Nov 29, 2019 - 15:45 |
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A double is 1/6, yes, but double-sixes aren't really doubles, in that you don't usually take a skill when you roll [6,6] — except for bigs, but they usually don't take +AG when rolling an 11 (yes, yes, Stonetroll's leaping Minotaur, but you know what I mean). So it's really only 5/36 at best. And then there are the players you'd take MA on, or maybe even AV once in a blue moon. So it's really more like 4.5/36, or 1/8, to get a double qua doubles skill. But you also have 11 players, and several of them would probably end up with +AG and a double if given the chance.
As for the odds of getting at least one double and one AG, Harad's math is basically right from a back-of-the-envelope perspective, but if you wanna get nitpicky, you can't roll doubles and AG on the same roll, so the actual odds are a little more complicated.
Doubles can be 1/6 (if you'd take doubles over +ST), 5/36 (if not), or 1/9 (if you would take +MA or +AV on [5,5]). +AG is 1/18. Let's assume we're talking about a baller-type who would take +MA on [5,5]). So for our math, +AG is 1/18 and a double (non-stat) is +2/18.
D = Double (2), A = Agility (1), N = not Double/Agility (15), X = anything (18).
18^5 = 1,889,568 permutations
ADXXX = 1 x 2 x 5832 = 11,664
ANDXX = 1 x 2 x 15 x 324 = 9,720
ANNDX = 1 x 2 x 225 x 18 = 8,100
ANNND = 1 x 2 x 3375 = 6,750
and then double that for the doubles-first results (DAXXX, DNAXX, DNNAX, DNNNA), and you've got 72,468 out of 1,889,568, or a bit over 3.8%. Multiply that by the number of players who would take a double and +AG.
Now, if you'd take the double as a double even on [6,6], this math changes as follows: D becomes 1/6, which is 3/18, stealing a permutation from N results. So A = 1, D = 3, N = 14, and X = 18.
ADXXX = 1 x 3 x 5832 = 17,496
ANDXX = 1 x 3 x 14 x 324 = 13,608
ANNDX = 1 x 3 x 196 x 18 = 10,584
ANNND = 1 x 3 x 2744 = 8,232
Added together and doubled, that's 99,840 out of 1,889,568: about 5.3% per player. |
_________________
Lude enixe, obliviscatur timor.
Last edited by JackassRampant on %b %29, %2019 - %15:%Nov; edited 1 time in total |
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Gratchoof
Joined: Mar 29, 2013
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Nov 29, 2019 - 15:45 |
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Thanks, but I don't think that's quite right as that's doesn't account for you not being able to get the double and the agility on the same skill up
I tried it written out by hand with simpler numbers (get at least one 3 or at least one 4 from 3 rolls of a 4-sided die) and the answer is 18/64 which your method doesn't give. |
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Gratchoof
Joined: Mar 29, 2013
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Nov 29, 2019 - 15:49 |
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| JackassRampant wrote: | A double is 1/6, yes, but double-sixes aren't really doubles, in that you don't usually take a skill when you roll [6,6] — except for bigs, but they usually don't take +AG when rolling an 11 (yes, yes, Stonetroll's leaping Minotaur, but you know what I mean). So it's really only 5/36 at best. And then there are the players you'd take MA on, or maybe even AV once in a blue moon. So it's really more like 4.5/36, or 1/8, to get a double qua doubles skill. But you also have 11 players, and several of them would probably end up with +AG and a double if given the chance.
As for the odds of getting at least one double and one AG, Harad's math is basically right from a back-of-the-envelope perspective, but if you wanna get nitpicky, you can't roll doubles and AG on the same roll, so the actual odds are a little more complicated.
Doubles can be 1/6 (if you'd take doubles over +ST), 5/36 (if not), or 1/9 (if you would take +MA or +AV on [5,5]). +AG is 1/18. Let's assume we're talking about a baller-type who would take +MA on [5,5]). So for our math, +AG is 1/18 and a double (non-stat) is +2/18.
D = Double (2), A = Agility (1), N = not Double/Agility (15), X = anything (1 .
18^5 = 1,889,568 permutations
ADXXX = 1 x 2 x 5832 = 11,664
ANDXX = 1 x 2 x 15 x 324 = 9,720
ANNDX = 1 x 2 x 225 x 18 = 8,100
ANNND = 1 x 2 x 3375 = 6,750
and then double that for the doubles-first results (DAXXX, DNAXX, DNNAX, DNNNA), and you've got 72,468 out of 1,889,568, or a bit over 3.8%. Multiply that by the number of players who would take a double and +AG.
Now, if you'd take the double as a double even on [6,6], this math changes as follows: D becomes 1/6, which is 3/18, stealing a permutation from N results. So A = 1, D = 3, N = 14, and X = 18.
ADXXX = 1 x 3 x 5832 = 17,496
ANDXX = 1 x 3 x 14 x 324 = 13,608
ANNDX = 1 x 3 x 196 x 18 = 10,584
ANNND = 1 x 3 x 2744 = 8,232
Added together and doubled, that's 99,840 out of 1,889,568: about 5.3% per player. |
I hadn't considered the double 6 in my thoughts.
Basically my mate and I were wondering how likely it'd be to get an Ag4, leaping, very long legs, pass block, disturbing presence chaos warrior |
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JackassRampant
Joined: Feb 26, 2011
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Nov 29, 2019 - 15:50 |
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Considering the number of players most of us go through, 3.84% is actually pretty good odds. |
_________________
Lude enixe, obliviscatur timor. |
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Gratchoof
Joined: Mar 29, 2013
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Nov 29, 2019 - 15:56 |
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I have 11.43% chance to do it, assuming you do take double 6 as ST instead of the desired double skill.
Formula:
1-((1-2/36)^5+(1-5/36)^5-(1-2/36-5/36)^5)
1-(P(no Agi) + P(no Double you'd take) - P(no Agi and no double)) |
Last edited by Gratchoof on %b %29, %2019 - %16:%Nov; edited 1 time in total |
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JackassRampant
Joined: Feb 26, 2011
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Nov 29, 2019 - 15:58 |
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| Gratchoof wrote: | | Basically my mate and I were wondering how likely it'd be to get an Ag4, leaping, very long legs, pass block, disturbing presence chaos warrior |
Ah, well, I hate to burst your bubble but those odds are much smaller. You wouldn't bother with Leap unless you already had +AG, and none of the normals makes sense without considering Leap. So you'd need do go the route ADXXX, and what's more, those X's can't be double-6.
So now we've got 1 x 2 x (17.5^3) / 1,889,568. 0.57%. A little better than your odds of rolling an 18 on 3d6. If you'd really bypass +ST, your math improves to 1/162, or 0.62%. |
_________________
Lude enixe, obliviscatur timor. |
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JackassRampant
Joined: Feb 26, 2011
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Nov 29, 2019 - 15:59 |
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| Gratchoof wrote: | I have 11.43% chance to do it, assuming you do take double 6 as ST instead of the desired double skill.
Formula:
1-((1-2/36)^5+(1-5/36)^5-(1-2/36-5/36)^5) |
Remember, you don't get 5 rolls for each. You get 5 rolls for both. If you get +AG on the third roll, you can't get a double on the third roll. |
_________________
Lude enixe, obliviscatur timor. |
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Gratchoof
Joined: Mar 29, 2013
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Nov 29, 2019 - 16:03 |
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| JackassRampant wrote: | | Gratchoof wrote: | | Basically my mate and I were wondering how likely it'd be to get an Ag4, leaping, very long legs, pass block, disturbing presence chaos warrior |
Ah, well, I hate to burst your bubble but those odds are much smaller. You wouldn't bother with Leap unless you already had +AG, and none of the normals makes sense without considering Leap. So you'd need do go the route ADXXX, and what's more, those X's can't be double-6.
So now we've got 1 x 2 x (17.5^3) / 1,889,568. 0.57%. A little better than your odds of rolling an 18 on 3d6. If you'd really bypass +ST, your math improves to 1/162, or 0.62%. |
Yeah, I was more contemplating it as if I'm going to head towards that build with every chaos warrior and fire the ones who don't make it!
Purely theoretical, but then the math is stuck in my head for 8 hours |
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Gratchoof
Joined: Mar 29, 2013
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Nov 29, 2019 - 16:05 |
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| JackassRampant wrote: | | Gratchoof wrote: | I have 11.43% chance to do it, assuming you do take double 6 as ST instead of the desired double skill.
Formula:
1-((1-2/36)^5+(1-5/36)^5-(1-2/36-5/36)^5) |
Remember, you don't get 5 rolls for each. You get 5 rolls for both. If you get +AG on the third roll, you can't get a double on the third roll. |
Yep, that's what the last bit is for, removing the probability of getting both at the same time assuming it was possible.
Phrased poorly, but it seems to work with the variations I've tried by hand |
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Relezite
Joined: May 21, 2007
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Nov 29, 2019 - 16:28 |
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Harad
Joined: May 11, 2014
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Nov 29, 2019 - 16:29 |
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| Gratchoof wrote: | Thanks, but I don't think that's quite right as that's doesn't account for you not being able to get the double and the agility on the same skill up
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Thanks, I thought I was wrong that they were independent. |
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MattDakka
Joined: Oct 09, 2007
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Nov 29, 2019 - 16:55 |
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| Gratchoof wrote: |
Basically my mate and I were wondering how likely it'd be to get an Ag4, leaping, very long legs, pass block, disturbing presence chaos warrior |
Why on earth should somebody build such a player?
Not worth the calculation effort!  |
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JackassRampant
Joined: Feb 26, 2011
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Nov 29, 2019 - 17:39 |
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| Gratchoof wrote: | | Yeah, I was more contemplating it as if I'm going to head towards that build with every chaos warrior and fire the ones who don't make it! |
Funny enough, if you shoot for that build with every player, you'll never get there, because your silly bloaty rookie team will just get mauled and you'll not build super stars. |
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Lude enixe, obliviscatur timor. |
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