Made this for the subreddit, thought I'd post it here also.

In table form:

No. of crates (USD) | Chance of win | Chance of No Tank |

2 crates ($9.99) | 9.75% | 90.25% |

6 crates ($50) | 26.49% | 73.51% |

12 crates ($100) | 45.96% | 54.04% |

18 crates ($150) | 60.28% | 39.72% |

24 crates ($200) | 70.80% | 29.20% |

30 crates ($250) |
78.54% |
21.46% |

Some thoughts:

- Unlike some crate offers, there is no secondary mechanism which secures the tank with X number of crates. Conceivably, you can spend forever and still never win.
- Your chance of winning the tank doesn’t get above 50% until 14 crates.
- Therefore the 2-crate deal plus two 6-crate bundles will give you a 51.23% chance of winning the T-22 for the bargain price of $109.97 USD.
- You can spend $250 on 30 crates and still have a greater than 1 in 5 chance of winning no tank at all. This is a mug’s game.

My recommendation: *NEVER BUY CRATES!*

But, if you absolutely must have a go, the one-time 2 crate deal for $9.99 offers the best value. And you won’t feel sick if you lose.

Every time there's a post like this, there's someone who pops up and says *"This is wrong, percentage chance is always the same no matter how many you buy!"* This is both true and not true.

To explain I'm going to shamelessly steal an analogy from someone else.

- If you have 1 covered basket with 1 red ball and 9 white balls and you put your hand under the cover to blindly grab a ball, you have a 10% chance of getting a red ball.
- If you have 100 such baskets, you still have only a 10% chance of getting a red ball .... true, but only on a per-basket basis.

Remember your objective is to ~~own the tank once~~ leave with a red ball.

Imagine you go to a Fair with your girlfriend and for some reason, she really wants a red ball. You really want to get one for her but there's only a 10% chance, right? But it turns out that you get to choose between two tents.

- Tent A has 1 basket.
- Tent B has 100 baskets. You get to try them all!

Do both tents offer an equal chance of leaving with a happy girlfriend? At this point it should be intuitively obvious that Tent B, with 100 * 10% chances, offers a vastly better chance of leaving the Fair with a red ball (probably more than one, but not what we need) than Tent A. Binomial probability is a way to put a number on that chance. You can read more about that here.

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**Edited by HugGigolo, 16 August 2019 - 07:07 PM.**