Vault Statistics Part 2: The benefit of hoarding

halirin

Lately I've been having a very difficult time playing because every time I open the game I'm tempted by the little indicator that says I have 22 tokens to open. 22? Seriously? As someone who typically has trouble waiting long enough to get above 1k and shield before opening the 900 point token in pvps, these taco vault tokens are really testing my resolve. So I decided to follow my economics training and find out whether I was really gaining anything for all this costly self-control.

Sadly, it turns out that most of the potential benefit from the vault comes from hoarding (or whaling, presumably).



This shows the difference in your chance of drawing at least one 4* from X# of tokens based on your drawing method (Blue is vault with hoarding - conventional tokens with 1/100 4* odds; red is vault with hoarding - vault w/o hoarding; green is vault w/o hoarding - conventional tokens with 1/100 4* odds).

I generated this graph by starting with the same data as last time and calculated the odds of drawing a 4* from the vault without hoarding by using the odds from 1-10 vault tokens repeated through every week.

As with my last post, this doesn't include any discounting for the value of time (rewards now are more helpful than rewards later), and that matters! One of my alliance-mates has decided to split the difference by opening one set as they come and hoarding the other set. That seems pretty sensible to me, and I'll probably do the same once the self-control reserves have dwindled down to zero.

Here's the file with all the data: https://www.dropbox.com/s/7gtshfgu16pbt ... .xlsx?dl=0

Unknown

Please define your drawing methods more clearly. You may want to double check your calculations too. No drawing method should be able to produce an "at least one 4-star" chance that is below 1% when starting from a fresh vault.

halirin

I thought the breakdown was pretty clear, but I can try again.

The highest probability method is to open X# tokens all in the same vault (call this type 1). The next version is to use ten tokens per vault in X#/10 vaults (type 2). Last would be X# of iid (https://en.m.wikipedia.org/wiki/Indepen ... _variables) draws (type 3). The graph just shows the differences in probability among pairs of these three types. So from top to bottom it's type 1 - type 3; type 1 - type 2; and type 2 - type 3.

As for probabilities less than 1%, I don't see any. The first row is .01 for all three probability columns. The color coded columns are all differences, which is why they all start at 0 (all types start with that 1% chance).

Pylgrim

A less stated benefit for hoarding: there's been a lot of player feedback on the vault, most of it positive about the feature itself but negative about the numbers and proportions, so I'd expect Demiurge to tweak those numbers in the future, making them more favourable, thus making tokens earned now get better odds then.

Unknown

halirin wrote:

I thought the breakdown was pretty clear, but I can try again.

I was unclear with my question then. Why is the green curve below 1%?

This confused me, so I did not understand how your graph, its legend, and your description of the whole thing fit together

XandorXerxes

By your graph, the apex seems around ~175 so I'll just go up to 180.

10 tokens, % chance of 1 or more 4*s in a single vault: 9.702%
10 vaults, using 10 tokens each time - chance of getting 1 or more 4*s is 63.96%
18 vaults, using 10 tokens each time - chance of getting 1 or more 4*s is 84.069%
100 tokens, 1 vault - chance of getting 1 or more 4*s is 70.519%
180 tokens, 1 vault - chance of getting 1 or more 4*s is 93.696%

10 tokens, % chance of getting 2 or more 4*s in a single vault: 0.2956%
10 vaults, using 10 tokens each time - chance of getting 2 or more 4*s is 2.917%
18 vaults, using 10 tokens each time - chance of getting 2 or more 4*s is 5.189%
100 tokens, 1 vault - chance of getting 2 or more 4*s is 25.851%
180 tokens, 1 vault - chance of getting 2 or more 4*s is 64.848%

That's where hoarding helps - going for multiple rewards. Your chances of getting a 4* from burning your tokens every week isn't bad, it's comparable to saving your tokens (you lose out on a 9% chance over 18 weeks). But the ability to not re-pull all those 2*s is what helps you get MORE rewards.

Using the 10/100 comparison, you're losing out on a 4* every 400 tokens per vault. Noting that DPD rotates vaults, that means essentially waiting out 200 tokens to open your two vaults, or 20 weeks of daily DPD with all 3*s. Over a long period of time, on average you'd have to do that twice to get the extra 4*. Is only spending in your vaults twice in 40 weeks to get that extra 4* worth it to you, versus having the 4* cover earlier?

Even using the 10/180 comparison, every 5 times you'd run that simulation you'd get 3 extra 4*s. That's 450 days by math, but because DPD rotates it's really 540 days, if you have every 3* and play every day. You'd have to wait 180 days to open two vaults. If we're looking only at 4* rewards, you have to ask yourself how much you value getting the specific 4*s in that vault - maybe when you spend every day after a while you get a vault of 4*s you don't want so you hoard a week (which boosts your chances two weeks later, and decreases the value of hoarding).

Are you willing to hoard on 180 day intervals for 540 days in order to get 3 extra 4* covers over you spending your tokens every day? Some people will say yes. Sounds to me like you're not one of those people. Also, if it's not fun for you to hoard, don't do it. When you sacrifice enjoyment for odds, you've already made the wrong choice (imo).

This of course completely ignores the 3* rewards as well.

Unknown

I was unclear with my question then. Why is the green curve below 1%?

This confused me, so I did not understand how your graph, its legend, and your description of the whole thing fit together

The green line is not below 0, it just appears that way because of the thickness of the green line. The graph uses the center of the green line to chart the value - it should be just a hair above 0, which is correct.

evildead666

I rarely comment on this but ,your theory mite be flawed. I must have been the luckiest of tiny kitties on this or it's just off , just pulled 2 iron fists of different colors , 1000 hp, and 10000 iso off 4 tokens.

evildead666

Sorry, me again did not notice you were talkin tacos pulled mine from the independence day vault w 1 taco thrown in lol, guess i just mite have been lucky.

halirin

The green line is so low because it is a difference (subtraction) of two very similar numbers. Basically there isn't much difference between regular tokens and the vault without hoarding.