I will share some secrets of RaffleBot here. If time permits, I will analyze how RaffleBot gives the prize, and try to answer the question that whether RaffleBot is fair.

Remarks:
* I am a mathematician, not a statistician. I only have very limited knowledge of statistics, and below are only some very basic analysis.
* All the percentages given below are approximations.
* I would like to thank JK_3 for providing the chat history of RaffleBot.
* All data is based on raffles from Apr 13, 2021 to Jul 22, 2021.
* If a user changes the user name, then it may not be reflected correctly here.

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Type of raffles
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There are 3 possible types of raffles.
* Raffle: 95%
* Waffle: 3.5%
* Wafaffle: 1.5%

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Message at the end
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If nobody entered the raffle, the message is
Nobody entered the raffle! These coins will be added to the next one. Be ready for it!

There are 3 possible messages otherwise.
* Stay tuned for the next raffle!: 93%
* Stay tuned for the next waffle!: 3%
* Stay tuned for the next wafaffle!: 2%
* You are all ruthless!: 2%

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Start time of raffles
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The start time in a day follows an uniform distribution.

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Gap between raffles
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The gap between raffles in minutes follows a discrete uniform distribution between 11 minutes and 120 minutes.

* This means that the gap is always in full minutes (plus possibly < 1 second error).
* There was two very special raffles on July 4, 2021, 06:53:24 and 09:23:24. The gap is 150 minutes. This is the only occurrence of raffles that do not follow the distribution above. Was RaffleBot an American busy with celebrating July 4 and forgetting to give us raffles?

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Coin prize of raffles
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If nobody entered the raffle, the coin prize will be added to the next raffle. Let
effective coin prize = coin prize of the current raffle - coin prize saved in previous raffles.

There are two type of effective coin prize:
* Small: 95%
* Big: 5%

The small prize follows a binomial distribution with mean value 5.
* 8 coins: 1.5%
* 7 coins: 12.0%
* 6 coins: 21.5%
* 5 coins: 30.0%
* 4 coins: 21.5%
* 3 coins: 12.0%
* 2 coins: 1.5%

The large prize follows a Poisson distribution with mean value 55.

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Power prize of raffles
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You cannot get a power prize and an artifact prize at the same time.

There are 8 possible power prizes.
* Free Cache: 25%
* None: 15%
* Supercharge Army Camp: 15%
* Supercharge Mine: 15%
* Time Warp: 15%
* Fog Buster: 5%
* Market Raids: 5%
* Inspire Mercenaries: 5%

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Artifact prize of raffles
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You cannot get a power prize and an artifact prize at the same time.

There are 2 possible artifact prizes.
* None: 95%
* Poor artifact: 5%

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Participation rate leaderboard
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Below are the participation rate of users, chopped at 5%, which means roughly 1 raffle per day.

37.5% krinid
35.1% JK_3
34.8% awaythro
33.1% Captain Ab
31.3% faxfox
24.1% Z
22.3% John Smith
21.2% Hodop
18.5% Lefty
18.2% Gunk
16.5% Ocean0.1
15.2% #BanPlajer
14.4% ZombieSlay
13.6% Kcebnroh
13.2% Ursus
12.9% Splat
12.5% stonemende
11.5% Legolas
10.0% Shin
9.3% Mythos1618
9.2% Kratt
9.1% Sevban
8.8% Arrow838™
8.0% nonolet
7.2% KaelF
6.6% riskboy88
6.5% Xxylox
6.5% Leia - Pri
6.2% Thorben
5.5% TrapdoorSp
5.3% GODZILLARE

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Coin leaderboard
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The percentage of coin prized earned are listed here, chopped at 1%. This is correlated to the previous section.

6.46% krinid
5.47% awaythro
5.44% Captain Ab
5.16% JK_3
3.47% Z
3.19% John Smith
3.17% Hodop
3.15% faxfox
3.08% Lefty
3.06% Gunk
2.91% Ursus
2.60% Ocean0.1
2.51% Kcebnroh
2.48% ZombieSlay
1.77% Legolas
1.71% stonemende
1.65% Splat
1.65% #BanPlajer
1.52% Sevban
1.35% Shin
1.33% Kratt
1.28% Arrow838™
1.23% GODZILLARE
1.13% qweds
1.07% IMaq AQ
1.06% Xxylox
1.04% Madkytle
1.04% Leia - Pri
1.01% nonolet

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Luck
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Below are the luck of players who attend at least 5% raffles (roughly 1 raffle per day). A 5% luck means at the player has a 5% more possibility to earn the prize of a random raffle. I would say -5% to 5% is well in the margin of error. So, we can conclude that, so far, no one had abused the RaffleBot, and vice versa.

4.91% Ursus
4.67% Legolas
3.73% Xxylox
2.94% Thorben
2.12% Lefty
1.92% nonolet
1.43% Arrow838™
1.01% Leia - Pri
0.72% riskboy88
0.22% krinid
0.20% Gunk
0.19% Sevban
0.08% Hodop
0.08% awaythro
0.04% Kcebnroh
-0.12% #BanPlajer
-0.47% Ocean0.1
-0.53% stonemende
-0.56% ZombieSlay
-0.62% Z
-0.83% GODZILLARE
-0.99% Kratt
-1.37% Splat
-1.37% Shin
-1.45% Mythos1618
-1.58% John Smith
-1.66% JK_3
-1.75% Captain Ab
-1.98% faxfox
-2.42% TrapdoorSp
-4.74% KaelF

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Winning time
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The percentage of winning by the time remaining is shown in the plot below. The horizontal axis is the time remaining, with -1 means "announced soon" and -2 means nobody entered. The vertical axis is the percentage of wins. This is for the people who believe that correlation implies causation, and I would advise them to join a raffle in the first 10 seconds.

https://imgur.com/a/wigQ5KZ

Edited 7/23/2021 02:25:02

Nice man!

Damn, you went deep onto RaffleBot. Not to mentions he levels up once in awhile :D

Spicy

can u tell my the secrets to why my gf left :'(

Nice analyses @functor

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can u tell my the secrets to why my gf left :'(

You didnt play tactical enough...

Unless it is possible to get both a poor artifact and a power, I think you should merge those into one category.

The start time and gap between raffles are updated.

@awaythro
I agree with you that they could be merged, but I like separating them better, just in case RaffleBot decides to behave differently in the future. To address your concerns, I have updated those two sections a bit.

Here's a parallel universe version replacing the power and artifact sections:

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Idle prize of raffles
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There are 8 possible WZI prizes.

* Free Cache: 25%
* Supercharge Army Camp: 15%
* Supercharge Mine: 15%
* Time Warp: 15%
* none: 10%
* Fog Buster: 5%
* Market Raids: 5%
* Inspire Mercenaries: 5%
* poor artifact: 5%


(edit: I just noticed that the numbers don't add up to 100% here or in the original)

(edit #2: realized it was missing Supercharge Mine)

(edit #3-4: minor stuff)

Edited 7/22/2021 19:28:03

The large prize follows a Poisson distribution with mean value 55.

No upper limit?

range is 40 to 68 iirc

To 68?
:/

Three sections are added.
* Participation rate leaderboard
* Coin leaderboard
* Luck

@καλλιστηι
In the dataset I use, I only see 41 (effective) coins to 67 (effective) coins. Even if it is unbounded, we should not expect a very large prize, since it follows Poisson distribution, unless nobody joins the raffle for a long time.

I love the information provided, I hope we can get another one of these in the next 100 days!

I'm getting different luck results for number-of-second-remaining.

59 won 2 of 13 (expected 1.73849206349206)
58 won 36 of 245 (expected 34.3091522040052)
57 won 88 of 601 (expected 89.8972265264837)
56 won 133 of 831 (expected 119.161123224901)
55 won 127 of 875 (expected 131.389544193337)
54 won 98 of 748 (expected 108.604187560805)
53 won 121 of 721 (expected 102.696696092865)
52 won 101 of 689 (expected 97.6584762846375)
51 won 102 of 629 (expected 95.3255513878968)
50 won 75 of 566 (expected 82.0766291285257)
49 won 73 of 565 (expected 83.0581447920846)
48 won 69 of 516 (expected 75.4950102357226)
47 won 66 of 489 (expected 71.7103620622585)
46 won 67 of 419 (expected 59.5620950944483)
45 won 72 of 389 (expected 58.5170724270571)
44 won 58 of 369 (expected 53.497428285509)
43 won 51 of 330 (expected 47.8494397544321)
42 won 44 of 292 (expected 41.0765154565078)
41 won 30 of 226 (expected 32.772079717668)
40 won 42 of 239 (expected 34.6884853708384)
39 won 33 of 233 (expected 34.6115664564194)
38 won 38 of 242 (expected 36.3507737145895)
37 won 27 of 208 (expected 30.8759094663506)
36 won 31 of 202 (expected 29.824113794702)
35 won 26 of 177 (expected 27.9517814486855)
34 won 29 of 182 (expected 27.768803255568)
33 won 23 of 180 (expected 25.8378013927936)
32 won 19 of 138 (expected 21.8287823287823)
31 won 27 of 151 (expected 22.3259132207661)
30 won 21 of 135 (expected 20.0556253387136)
29 won 20 of 146 (expected 24.1014415108455)
28 won 25 of 128 (expected 19.9330400593558)
27 won 18 of 137 (expected 21.3007510463393)
26 won 23 of 131 (expected 20.5933959014841)
25 won 9 of 98 (expected 14.6887158593041)
24 won 29 of 119 (expected 19.2602701220348)
23 won 27 of 158 (expected 24.2468947718948)
22 won 20 of 135 (expected 21.5467457379222)
21 won 14 of 87 (expected 13.8945998445998)
20 won 12 of 97 (expected 15.1494089244089)
19 won 18 of 102 (expected 17.0164613164613)
18 won 7 of 70 (expected 11.8815337440337)
17 won 9 of 100 (expected 14.5849761349761)
16 won 16 of 111 (expected 15.8892320098202)
15 won 9 of 87 (expected 14.8343026856185)
14 won 11 of 87 (expected 12.9754041709924)
13 won 18 of 105 (expected 17.7451261157143)
12 won 21 of 103 (expected 15.3455271036153)
11 won 28 of 117 (expected 18.3685041265923)
10 won 13 of 96 (expected 15.6795518808677)
9 won 15 of 81 (expected 13.3210539460539)
8 won 7 of 78 (expected 11.289319014319)
7 won 11 of 80 (expected 12.5140159676924)
6 won 16 of 99 (expected 18.1305740011622)
5 won 11 of 86 (expected 15.2281819487702)
4 won 13 of 92 (expected 16.9727605727606)
3 won 10 of 90 (expected 13.9576451326451)
2 won 10 of 77 (expected 13.113217746306)
1 won 7 of 64 (expected 10.3094239094239)
0 won 5 of 60 (expected 8.61314241314242)

"will be announced in 11 seconds" is the luckiest (won 28, expected to win 18-ish).

thanks a lot functor and all other fellow RB analysts here! You were faster and more in-depth than me analyzing RB secrets. :-)
I am not there yet and too tired now to try and format/upload/share my list now.

looking at "luck" factor for individual players - have we taken into account different number of participants in each raffle causing different statistical chance to win?

Overall RB algorithm seems to be sufficiently randomized and differences between individual players winrate are (maybe?) primarily related to being online and participating at different times - some time windows are generally "busier" than others - leading to higher or lower # of entrants in raffles.

Yes, my luck calculations (which appear to match functor's) take the amount of competition into account. The expected number of wins is sum_k (1/n_k) where 'n_k' is the number of participants in raffle 'k', and 'k' ranges over the raffles in which a given person participates. We compare that to the actual number of wins.

Damn this is interesting. @AT, could we see a % breakdown for your table of seconds and win/expectation?

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I'm getting different luck results for number-of-second-remaining.

59 won 2 of 13 (expected 1.73849206349206)
58 won 36 of 245 (expected 34.3091522040052)
...

Edited 7/23/2021 02:19:16

@functor, could you compile a winrate for the seconds entered as well as factoring in the # of participants? Like, maybe something like # of wins for each second / total participants?

Edited 7/23/2021 02:31:19

functor for pres! Hats off for some excellent analysis.

Why not show the actual # of coins won rather than just a % of total coins? And total # of raffles won. %'s also good, but raw #'s are also interesting.

plajer in the -ve surprised me initially ... but then again, he hasn't won a lot recently. It used to be "plajer always wins", now it's "faxfox always wins". Oh wait, faxfox is even more -ve than plajer! Ok, I suspect fraud here ... or better yet, just blame JK. JK rigged it all!

#JKisToBlame

Edited 7/23/2021 02:49:56