99.4% & Some Math (!!)

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edited June 2014 in MPQ General Discussion
Not that I'm gonna buy these new "no guaranteed" packs as oppose to the old packs that guaranteed a 3* cover. It's history now. But I was just wondering how the pull probability works. So I did a little math, just on the Lord of Thunder tokens.

10/42 packs probability
LThor 6.1%
IW 1.2%
WXF 1.2%
BP 0.7%
BWGS 0.7%
LCapA 0.7%
LDaken 0.7%
DD 0.7%
Falcon 0.7%
HT 0.7%
IM40 0.7%
MagC 0.7%
Psy 0.7%
Sentry 0.7%
SpidieC 0.7%
Hood 0.7%
Greenie 0.7%
Pun 0.7%
Patch 0.7%
Doom 0.5%
Loki 0.5%
Rag 0.5%
Subtotal 3* & 4* 21.2%

Ares 6.9%
OBW 6.9%
Cap 6.9%
Hawkeye 6.9%
MagMN 6.9%
Moons 6.9%
Bagman 6.9%
StormC 6.9%
Thor 6.9%
YellowWolvie 6.9%
Bulls 4.6%
Daken 4.6%
Subtotal 2* 78.2%

Total 78.2% + 21.2% = 99.4%

I know this is probably not a pdf, hence the total p may not be 100%. But if it's intended to be 100%, I wonder where that 0.6% has gone... icon_question.gif

If you have time, keep this checking going and see if other packs have total p less than 100% as well. icon_e_wink.gif

Unit Pricing - daily special
10 pack - 3800: 380/token
42 pack - 15800: 376.2/token (Saving - 160 comparing to 10 pack)

Upgrade vs Packs - daily special
Upgrade LThor - 1250 each

10 pack to breakeven - 3800/1250 = 3.04
42 pack to breakeven - 15800/1250 = 12.64

According to D3P, "drop rates are per draw". i.e. independent. Hence, binomial distribution can be applied with p = 0.061.

Probability to get:
At least 3 LThor in 10 pack: 0.01968916
At least 4 LThor in 10 pack: 0.00215722
At least 12 LThor in 42 pack: 0.00000521
At least 13 LThor in 42 pack: 0.00000077

Comments

  • OnesOwnGrief
    OnesOwnGrief Posts: 1,387 Chairperson of the Boards
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    My guess is that .6 missing is most likely distributed among the hundredths place to skew the tokens even more. Notice how it cuts off at the tenths.
  • Unknown
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    Chance of getting the hp draw probably. Though I swear it feels its been removed, if all it is ...is the equivalent to a 3*** cover...then it would make sense never seeing it.
  • OnesOwnGrief
    OnesOwnGrief Posts: 1,387 Chairperson of the Boards
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    soenottelling wrote:
    Chance of getting the hp draw probably. Though I swear it feels its been removed, if all it is ...is the equivalent to a 3*** cover...then it would make sense never seeing it.
    HP draw I believe is only through standard tokens.
  • Unknown
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    OnesOwnGrief wrote:
    soenottelling wrote:
    Chance of getting the hp draw probably. Though I swear it feels its been removed, if all it is ...is the equivalent to a 3*** cover...then it would make sense never seeing it.
    HP draw I believe is only through standard tokens.

    And was removed at some point. Without telling us officially I think.
  • OnesOwnGrief
    OnesOwnGrief Posts: 1,387 Chairperson of the Boards
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    j12601 wrote:
    OnesOwnGrief wrote:
    soenottelling wrote:
    Chance of getting the hp draw probably. Though I swear it feels its been removed, if all it is ...is the equivalent to a 3*** cover...then it would make sense never seeing it.
    HP draw I believe is only through standard tokens.

    And was removed at some point. Without telling us officially I think.
    considering the draw rate is that of a 4*, that could just be anecdotal evidence. I pulled some HP after it was brought up that they may have been removed. Haven't seen any since though. Plenty of 3*s though.
  • Unknown
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    Easy, those are simplified values, 6.9% might be 6.95% for example, or even less, like 6.89%. In the end the whole simplification can make the total look less or more than 100%.
  • mohio
    mohio Posts: 1,690 Chairperson of the Boards
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    I've noted this elsewhere before, but one way you can tell there is a rounding issue is by looking at the 2-cover vs. 3-cover characters. In the example you noted, the 3-cover characters have a .7% chance while the 2-cover ones have .5%. So, it clearly looks like each individual cover (i.e. each separate color) has it's own specific chance of being pulled, but .7 is not 3/2 of .5. So, maybe it comes out to something like .24% per cover which would make the 2-cover guys ACTUAL percentage .48% and the 3-cover ones .72%. Something similar is no doubt happening with the 2* characters as well. All those missing thousandths add up to the "missing" .6% in their stated percentages.
  • Unknown
    Unknown
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    I'm pretty sure it's something like 15% chance to pull a 3* in a heroic and then that's distributed by each cover, so 3 cover characters gets 3/(total number of 3* covers) * 15% and 2 cover character get 2/3 that. It's rounded to the nearest tenth so it's not going to always add up to 100%. You can see that the % goes down as new characters are released. There used to be a time where they're 1.0% if I recall per 3*, now it's down to like 0.7% or so because there are more of them.
  • Unknown
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    OnesOwnGrief wrote:
    j12601 wrote:
    OnesOwnGrief wrote:
    soenottelling wrote:
    Chance of getting the hp draw probably. Though I swear it feels its been removed, if all it is ...is the equivalent to a 3*** cover...then it would make sense never seeing it.
    HP draw I believe is only through standard tokens.

    And was removed at some point. Without telling us officially I think.
    considering the draw rate is that of a 4*, that could just be anecdotal evidence. I pulled some HP after it was brought up that they may have been removed. Haven't seen any since though. Plenty of 3*s though.

    The 25 HP fixed daily rewards replaced token HP.

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