FaringdonSwirl wrote:
Would be interested in the math if you can be bothered
Yes, of course. The gist of it is pretty simple. The detail can get a little complicated.
First, the math assumes that each of the five outcomes are 50-50, and that each are independent. Both these assumptions can be argued, but generally fair to assume both I reckon.
Then, in terms of figuring out what cut the house (draft stars) is taking:
For the option where you need to pick 5 out of 5, that is a one in 2x2x2x2x2 = 32 chance. This means that of 32 different people each take one combination (and all combinations are taken), one will get it correct.
So 32 people pay $20 = $640 but draft stars only pays out $400. So their cut is $240 profit out of $640 invested = 240/640 = 37.5%
For the option where you need to get 3/5 (or more) correct, the math is a little more complicated. Its based on something called a Bernoulli trial. A Bernoulli trial is a random experiment with two outcomes, success and failure, where the probability of success is the same every time.
This online calculator https://planetcalc.com/7044/ allows you to calculate the probability of k success outcomes in n Bernoulli trials with given success event probability.
In short though, out of the 32 potential outcomes from the 5 options, 50% of them reflect 3 or more successes. I.e. if you randomly chose 5 guys in the draftstars comp, you will get 3/5 (or more right) on average.
So, if 2 people pay $20 = $40 draft starts will pay out on average $1.8 *20 = $36, So their cut is $4 profit out of $40 = 10%
Hopefully that is explained well enough...?
Edit: Its actually calculating the probability of k successes where the math gets a little intense (but still very much learnable)
P(k)={n \choose k}p^{k}q^{n-k}
see https://en.wikipedia.org/wiki/Bernoulli_trial
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