99.4% & Some Math (!!)

Unknown
Unknown
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
    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
    Unknown
    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
    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
    Unknown
    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
    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
    Unknown
    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
    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
    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
    Unknown
    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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