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  1. #1
    Son of LO Manu_Forti's Avatar
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    Mathematically, how bad is my luck?

    Hi,

    So, Im wondering if theres anyone who can help me calculate the probability of this..

    2 Chariots taking a Stupidity test on Ld9, for 6 turns of a game. Thats 12 tests..
    The odds of failing on Ld9 = 1/6..
    (logic = Rolls of: 5,5 5,6 6,5 4,6 6,4 6,6 = 6/36 combos for 2D6 = 1/6.. correct?)

    Can anyone tell me the odds of failing 8/12 tests, considering its a 1/6 chance?

    I dont need maths to know its bad, but im curious to know :lol:

    Dark Elves - Game #28 vs High Elves: Draw
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  3. #2
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    The long answer:
    For those that will question my working (and you're welcome to, as it's a long time since I've done this) I basically figured that:

    Using the combination equation

    n!/(n-k!)k!

    where you're picking k tests (in this case 4) of n possible tests (in this case 12) to be successful. I used combination rather than permutation since the order that the tests are passed/failed is irrelevant (and can't actually change, since you'll always do the Turn 1 Chariot A test before the Turn 2 one ).

    Note that you can also use the equation to determine the combination of 8 possible tests out of 12 to be failed, and it yields the same final number.

    12!/(12-4)!4! = 12!/(12-8 )!8! = 495

    This is the number of different ways that the 8 failed tests and 4 passed test can be ordered.

    Now we work out the probability of just one of these results happening. For example, we can work out the probability that you'll failed the first 8 tests you roll, and pass the last 4.

    You worked out that there's a 1/6 chance of failing, and therefore there is a 5/6 chance of passing. Therefore the probability of failing the first 8 tests and passing the last 4 is:
    (1/6)*(1/6)*(1/6)*(1/6)*(1/6)*(1/6)*(1/6)*(1/6)*(5/6)*(5/6)*(5/6)*(5/6)
    = [(1/6)^8]*[(5/6)^4]
    = 2.87 x 10^(-7)
    = 0.000000287

    To work out the final probability of you failing 8 of 12 tests, we multiply the probability of failing that one way of failing 8 of 12 by the number of different ways you could fail 8 in 12.

    0.000000287 x 495 = 0.000142

    The short answer:

    As a percentage, this comes out as 0.014%. To give an idea, that's about 1 in 7000.

    So chances are fair that in your lifetime of playing Warhammer, that will never happen again. Of course, you could always get a worse result! (although that's even less likely)
    Last edited by SilentTempest; December 11th, 2006 at 00:07.

  4. #3
    Son of LO
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    523 (x8)

    Yeah it's binomial distribution

    So it's (12 choose 8 )x[(1/6)^8]x[(5/6)^4]

    Which yields the answer given above(Y)

    Ciao

    Stonehambey

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    sometimes... i hate maths...

  6. #5
    Senior Member Djones9916's Avatar
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    How about the odds of a Librarium with 7 attacks on the charge against Lysander, not inflicting a single wound(with actually rolling 5 wounds), and then getting insta-killed with one swing in retaliation?

    I'll qoute myself from last night...

    "Never before have I been so demoralized by a single dice roll."

    And that was all after he survived 36 Bolter Shots, and 3 Melta shots...

    Can someone do that math?
    Last edited by Djones9916; December 10th, 2006 at 17:35.
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  7. #6
    Son of LO Manu_Forti's Avatar
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    117 (x6)

    The short answer:

    As a percentage, this comes out as 0.014%. To give an idea, that's about 1 in 7000.

    So chances are fair that in your lifetime of playing Warhammer, that will never happen again. Of course, you could always get a worse result! (although that's even less likely)
    Holy moly That's pretty bad considering it happens most games....those chariots are cursed I tells ya!..cursed!

    Thanks *repped*
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  8. #7
    Benevolent Dictator CaptainSarathai's Avatar
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    Um, about the cursed thing... are they painted?
    I am not even joking, the dice gods favor painted models. I could show math to prove it, but my brain is sluggish.


    hrm hrm... funny word
    sluggish...
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    Quote Originally Posted by Manu_Forti View Post
    Holy moly That's pretty bad considering it happens most games....those chariots are cursed I tells ya!..cursed!

    Thanks *repped*
    Keep in mind that doesn't give the probability of them failing 12 of 12, or 11 or 10 or 9 or 7 of 12. It just gives the probability of failing 8 of 12. But if you felt like it you could always use the method above to work out the probabilities for each of these and then just add the results together for the probability of, say, failing more than half. (7 or more tests failed out of 12).

    Quote Originally Posted by Djones9166
    How about the odds of a Librarium with 7 attacks on the charge against Lysander, not inflicting a single wound(with actually rolling 5 wounds), and then getting insta-killed with one swing in retaliation?

    I'll qoute myself from last night...

    "Never before have I been so demoralized by a single dice roll."

    And that was all after he survived 36 Bolter Shots, and 3 Melta shots...

    Can someone do that math?
    As for this question, I'm not sure whether you mean you rolled 5 dice to wound, or rolled 5 wounds and he got his invulnerable save against them, so I'll just do it from the top. I'll assume the Librarian has his normal force weapon and isn't using the re-roll psychic power (whatever it's called), since it looks a little like he's using the +d3 attacks one (either that or they have some way of gaining extra attacks I don't know about).

    The easiest way to work out the probability of him failing in a single attack is to work out the chance of him succeeding, and subtracting that from 1 (otherwise it's a pain to work out, given he can fail in the To-Hit, To-Wound, or the target can pass saves.

    Chance to hit = 1/2
    Chance to wound = 1/2
    Chance Lysander fails his Inv save = 1/2

    Therefore there's a 1/8 chance any given attack will hurt Lysander. Therefore there's a 7/8 chance the attack will fail. So the chance of 7 attacks failing will be (7/8 )^7 = 0.393 = 39.3% chance of all attacks failing. That's not a bad chance at all. It's mainly because of his decent Invulnerable save, and the fact that the units are actually fairly evenly matched (as opposed to if a Daemon Prince or something like that came to smack Lysander down, because it would only be needing 2s and 3s, not 4s).

    As for the chance of Lysander smacking you back and instant-killing you, I'm assuming because of his thunderhammer... and I've just realised it's master-crafted, which makes this whole thing much more of a pain to do. Basically, the best way to do it would be to work out the probability of Lysander inflicting no wounds, and then subtract that from 1 to work out the chance of 1 wound or more, which would then, of course, instant-kill your Librarian. But normally I'd get paid for teaching this sort of stuff, and I'm not, so I'll leave this one to some other keen forum-dweller.

  10. #9
    Son of LO Manu_Forti's Avatar
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    Quote Originally Posted by CaptainSarathai View Post
    Um, about the cursed thing... are they painted?
    I am not even joking, the dice gods favor painted models. I could show math to prove it, but my brain is sluggish.


    hrm hrm... funny word
    sluggish...
    lol Yes they are well painted, theres pics in the DE forum. I did notice my opponent had pretty bad luck in general, and his army looked like a 3 year old made it.. (hence why I felt the need to score a massacre victory (& did), I hate poor quility armies )

    Most of my other rolls werent too bad. The Cold one Knights passed all 6 of their stupidity tests
    Dark Elves - Game #28 vs High Elves: Draw
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  11. #10
    is a Brother of Arterius Bleyden's Avatar
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    I seem to go through bouts of good luck and bad luck in a game. The outcome usually depends on what time these events occur.

    Example 1: both good and bad luck come early
    Im playing Dwarfs vs Chaos. In turn 1 my anvil of doom explodes, giving away 300 odd VPs . In turn 2or3 my organ gun wipes out a whole unit of 6 Chosen Chaos knights .
    Overall result Draw

    Example 2: Bad luck early good luck late
    Playing Dark Angles vs Eldar. A heavy weapons platform kills my predator in turn 1. Predator was my only heavy support unit and his falcon-heavy army sweeps through my tactical squads and scouts killing all until 10 howling banshees are killed by my Librarian and his command squad, who then place melta bombs on the falcon and destroy it.
    Overall result Solid Loss

    Example 3: Good luck early bad luck late
    Playing SoC Slayers vs Skaven. My axe thrower manages to kill all of his tunnelling gutter runners unit in one turn, earning me a few VPs. This same axe thrower then goes onto kill a unit of Rat Ogres, a rat swarm AND about 8 slaves, forcing them to flee. Later in the battle, my dragon slayer gets killed by 2 rat swarms due to dreadful dice rolling.
    Overall result Massacre

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