Hi all,

This isn't for homework - it's related to an online game I play.

There is an item I want but it can only be purchased by luck - like rolling a dice.
You pay between 250 - 2,000 in-game currency (diamonds) and you receive an item.
There are 6 possible items which drop.
The more you pay the higher the chance one of the rarer items will drop.

(Item) 1. Mayfly's Horn, 2. Dragon-scale Shield, 3. Dragon Essence, 4. Roar of the Dragon, 5. Wrathful Dragon, 6. Ring of Dragon's Breath
(Cost) (Probability)
Layer 1 (250 Diamonds) 77% 10% 10% 1% 1% 1%
Layer 10 (500 Diamonds) 64% 15% 15% 2% 2% 2%
Layer 30 (1,000 Diamonds) 48% 20% 20% 4% 4% 4%
Layer 50 (2,000 Diamonds) 26% 25% 25% 8% 8% 8%


The item I want to get is the Roar of the Dragon.
If I pay 250 diamonds there is a 1% chance I will get it.
If I pay 500 diamonds there is a 2% chance I will get it and so on.

I want to get a Roar of the Dragon but I want to get it as cheaply as possible. No one will sell me one so I have to get it myself.

My question is 2 fold.

1) Which is the best layer (250, 500, 1,000 or 2,000 diamonds) to use to get the item?
(There is a cost/probability trade-off here as layer 50 has an 8% chance to drop versus Layer 1's 1% chance - but at Layer 1 you would get 8 tries versus 1 try at Layer 50).

2) How many diamonds would I need to guarantee getting the item?
i.e. how many times must I do it to make sure it drops (luck aside).

Thanks

This post was edited by FeelGoodInc on Jun 3 2015 11:16pm

There's no way to guarantee you get your item at a certain number of buys and that's just because you could buy any of the layers 100 times(really any amount) but you could basically just get screwed and get mayflys or whatever every time

We can give you a threshold if you'd like such as if you buy layer 1 x times there will be a 90% chance to get your item

Or another question might be expected value of buying the layer so you know even if you don't get the item you want you know which layer has the highest expected payout when you sell whatever item you get


Anyways good luck

This post was edited by brigadier on Jun 4 2015 12:13am

there's actually not much difference in the chances of rolling at least one with different layers.
although layer 50 is always higher chance, by less than 1%

here's how much you need to spend to have 95% chance of getting it.
first column is diamonds spent
ignore 2nd column
then 3rd and rest are layer 1,10,30,50



This post was edited by Exx on Jun 4 2015 12:17am

Thanks guys
Sent Exx the fg

Table above is correct.

However, the fact is that the medium price (in diamonds) you'll have to pay, in regard to the number of desired item you get, is the same whatever Layer is used.