Stats homework: trying to decide whether to save Tacos or no

Cousin Simpson

Not really homework, but I've sort of forgotten all of the stats I've taken in the past and want to figure out if I should cash in (eat?) all my tacos now or save them for a rainy day.

So let's say I have t tacos, with a vault of v total possible covers, and u covers that would be useful to me. I figure the correct math involves some nCr magic, and is more involved than (u / v) * [(u-1) / (v - 1)] * ... [(u - 4) / (v - 4)].

Killinstinct

I have tried to calculate some stuf, but the number of different combinations with 300 items is too high for both my calculator as Excel.

Unknown

The math will be very complicated because the taco vault is a random draw without replacement. The problem is even harder to solve if you are trying to optimize outcomes when there is the option to wait and hoard. I would suggest you use one of two heuristic approaches towards the taco vault instead.

1. Count the maximum number of desirable rewards you can possibly have in the vault (e.g. there are 83/300=28% rewards that are not 2-stars or med packs). Use this number to set a reasonable threshold for the chance to obtain a desirable aware, above which you will begin to redeem tokens, and below which you will hoard. If your target is 25% for example, then you should start redeem your tokens whenever there are more than 75 desirable rewards in the full vault, and continue to do so until the probability of getting something useful drops below 25%. If you luck out and draw one of the extremely rare rewards, then stop and wait for the next vault to refresh that reweard. Adjust your target threshold over time to avoid accumulating a huge stockpile of tokens, and the outcome of this strategy will be very close to what is optimally possible for using an active vault.
2. Forget about the active taco vault entirely, and save all your tokens until they transfer to the post-event vault. The contents of the post-event vault can be reset at will, so you can keep resetting it until you see favorable rewards, redeem a token, then repeat as much as you want. This approach has the additional benefit of allowing you to generate med packs on demand from a large stockpile of tokens, which can be useful during crunch time in PvE or PvP. In circumstances where you do not have many fully covered 3 and 4-star characters, this strategy will generally be the most efficient use of taco tokens, though it may also incur a significant cost in time.

GuntherBlobel

I can't post links right now but you should go to Wolfram Alpha and type in the following:

For typical tokens use a "binomial distribution" calculator.

Try: "binomial distribution, p = 0.014, n = 40" for odds of getting a featured 4* in a 40x pack.

For vault tokens use a "hypergeometric distribution." Same idea, except without replacement. N = 300 for taco tokens. m = 3 if you a gunning for the 3 4* tokens. n = tokens you will spend at one time.

Edit: If this is really something you would do in Excel using complicated formulas, may I suggest trying out RStudio? It's free and better suited for statistics.

Killinstinct

GuntherBlobel wrote:

Edit: If this is really something you would do in Excel using complicated formulas, may I suggest trying out RStudio? It's free and better suited for statistics.

Thanks, I will look at it