DeletedUser2424
Guest
Background:
I felt like nerding out on some probability math. Since you can win snowflakes which in turn increases the number of possible attempts it makes for an interesting yet solvable math puzzle. In my quest for how to properly apply "binomial distribution models" to the problem... I ended up just writing a simple python script to simulate the probability of getting Grand Prize 2 & Grand Prize 3. Here's the results.
TL;DR:
- You have < 1% chance of getting the 3rd grand prize without diamonds.
- You will be able to get the 2nd grand prize (no luck needed) if you complete all quests.
- You will earn about 14 event buildings (if you complete all quests).
- If you buy small chests, you'll end up with more daily exclusive buildings then you would the large chests (assumes your trading in lots of snowflakes not a single chest) but you have a slightly lower chance of getting the grand prizes and will get less KP, etc.
Results
More Detailed
Includes all 3 box options as well as the amount of runes, KP, and relics you will gain.
So, which box is the best?
Well it turns out the choice isn't as obvious as we all once assumed... Large Box seems like the best option but for many of you I suspect the medium box or small box will be your best bet.
Large Box:
Pros: Most KP, and a practically negligible 1% better chance of getting a 3rd Grand Prize
Cons: Least Tier 3 Relics
Medium Box:
Pros: Most Rune Shards (~10 more at 6000)
Cons: Least KP (about 50 less than Large)
Small Box:
Pros: Most Daily Exclusive Buildings (about 2 more)
Cons: Least Rune Shards
More on test methodology:
- The test essentially simulates how the game works... you trade in 140 snowflakes and have 7% chance of getting 200 snowflakes, a 13% chance of getting 140 snowflakes, and 25% chance of getting a building. It uses a random number generator for each trade in and increases or decreases snowflakes accordingly until you can't play anymore. The simulation is run over 100,000 times to get a statistically accurate result.
- Only the big chest is used (140 flakes for 20 globes)
- Someone on SoggyShort's spoilers thread (which is awesome, sorry couldn't find the exact post) estimated of number of Snow Flakes you could earn (1156 daily quests / 4128 secondary quests / 1104 dropped snow crystals) giving you 6388 flakes without diamonds. I used those.
- 650 globes are needed for Grand Prize 2
- 1450 globes (in total) are needed for Grand Prize 3.
- Source Code for the python script: http://pastebin.com/amAREij0
Anticipated Questions...
> Something must be wrong with your math... There is only a 25% chance of getting a building...
Yes, you have a 25% of building for each chest opened. But! since you have 20% chance (13% + 7%) of getting a free chest by winning snowflakes. This improves the probability to at least 25/80 or 31.5% (it's actually even better since 7% of the time you get 1.42 chests). Doing a simple math of say i have 4000 snowflakes / (140 flakes / chest) * .25 is not taking all this into account.
> So am i better of buying snowflakes or a premium building?
While, i haven't thought this through completely since I don't plan on buying either. I would think of it like this... You'd need about 2000 snowflakes to comfortably assure you'll get the Grand Prize 3 (which is 8500 diamonds to buy). After reading this post... the Mario Patron Saint is "more efficient" than the 3rd Grand Prize (the tower) and at only 3000 a pop you could buy almost 3 of them. Which is most likely a much better spend. On the other hand, you'll stand to pickup an extra 4-5 daily exclusive buildings and other goodies in the process... but placing 18 3x3 buildings you'll likely be straining your coin supply anyway.
EDIT: 12/20 Added Large vs. Small Chest
EDIT2: 12/20 Added Medium Box and comparison of runes, shards, and relics gained.
I felt like nerding out on some probability math. Since you can win snowflakes which in turn increases the number of possible attempts it makes for an interesting yet solvable math puzzle. In my quest for how to properly apply "binomial distribution models" to the problem... I ended up just writing a simple python script to simulate the probability of getting Grand Prize 2 & Grand Prize 3. Here's the results.
TL;DR:
- You have < 1% chance of getting the 3rd grand prize without diamonds.
- You will be able to get the 2nd grand prize (no luck needed) if you complete all quests.
- You will earn about 14 event buildings (if you complete all quests).
- If you buy small chests, you'll end up with more daily exclusive buildings then you would the large chests (assumes your trading in lots of snowflakes not a single chest) but you have a slightly lower chance of getting the grand prizes and will get less KP, etc.
Results
Includes all 3 box options as well as the amount of runes, KP, and relics you will gain.
So, which box is the best?
Well it turns out the choice isn't as obvious as we all once assumed... Large Box seems like the best option but for many of you I suspect the medium box or small box will be your best bet.
Large Box:
Pros: Most KP, and a practically negligible 1% better chance of getting a 3rd Grand Prize
Cons: Least Tier 3 Relics
Medium Box:
Pros: Most Rune Shards (~10 more at 6000)
Cons: Least KP (about 50 less than Large)
Small Box:
Pros: Most Daily Exclusive Buildings (about 2 more)
Cons: Least Rune Shards
More on test methodology:
- The test essentially simulates how the game works... you trade in 140 snowflakes and have 7% chance of getting 200 snowflakes, a 13% chance of getting 140 snowflakes, and 25% chance of getting a building. It uses a random number generator for each trade in and increases or decreases snowflakes accordingly until you can't play anymore. The simulation is run over 100,000 times to get a statistically accurate result.
- Only the big chest is used (140 flakes for 20 globes)
- Someone on SoggyShort's spoilers thread (which is awesome, sorry couldn't find the exact post) estimated of number of Snow Flakes you could earn (1156 daily quests / 4128 secondary quests / 1104 dropped snow crystals) giving you 6388 flakes without diamonds. I used those.
- 650 globes are needed for Grand Prize 2
- 1450 globes (in total) are needed for Grand Prize 3.
- Source Code for the python script: http://pastebin.com/amAREij0
Anticipated Questions...
> Something must be wrong with your math... There is only a 25% chance of getting a building...
Yes, you have a 25% of building for each chest opened. But! since you have 20% chance (13% + 7%) of getting a free chest by winning snowflakes. This improves the probability to at least 25/80 or 31.5% (it's actually even better since 7% of the time you get 1.42 chests). Doing a simple math of say i have 4000 snowflakes / (140 flakes / chest) * .25 is not taking all this into account.
> So am i better of buying snowflakes or a premium building?
While, i haven't thought this through completely since I don't plan on buying either. I would think of it like this... You'd need about 2000 snowflakes to comfortably assure you'll get the Grand Prize 3 (which is 8500 diamonds to buy). After reading this post... the Mario Patron Saint is "more efficient" than the 3rd Grand Prize (the tower) and at only 3000 a pop you could buy almost 3 of them. Which is most likely a much better spend. On the other hand, you'll stand to pickup an extra 4-5 daily exclusive buildings and other goodies in the process... but placing 18 3x3 buildings you'll likely be straining your coin supply anyway.
EDIT: 12/20 Added Large vs. Small Chest
EDIT2: 12/20 Added Medium Box and comparison of runes, shards, and relics gained.
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