I I finding the EV of the possible outcomes

[Alanay]

I'm making a Bitcoin gambling game with some developers. But I need help from you crazy good mathematicians out there! I need to know the "kelly criteron" or "EV" of the possible outcomes in the game.

How the game works:

The game is basically a grid of 1-100 numbers. Every 10 seconds a number range will be generated. So you choose to bet on 40-60 so that the generated range won't crash into your bet range. You will get a 250% payout. 200% for the 20 numbers. 50% for the 5 prime numbers in there. So prime numbers are your friend!

You can also click once on any number. If you click on a prime number you are betting the generated range will not crash into at least 1 prime number, if you're correct you will get a 112.5% payout. If you click on only one even or odd number you're betting there will be more of that number (even or odd) in the total range that is not crashed into. So If I click on an even number and the generated range is 21-31 I will win, the payout would be 150%. Because between 21 and 31 there are more even numbers.

 

[mfb]

If the Kelly criterion tells players to bet any money, your game is broken. The bank always has to win.

You can freely choose the range to bet on?
How does the generated number range get determined? For most reasonable systems, I guess betting on the first N numbers will be the most efficient bet.

What is payout if you bet on an even number and the generated range is 20-29?
If you pick a prime, are odd numbers also included (or even numbers for 2)?

Why don't you just simulate enough games to determine the expectation values?

 

[Alanay]

If the Kelly criterion tells players to bet any money, your game is broken. The bank always has to win.

You can freely choose the range to bet on?
How does the generated number range get determined? For most reasonable systems, I guess betting on the first N numbers will be the most efficient bet.

What is payout if you bet on an even number and the generated range is 20-29?
If you pick a prime, are odd numbers also included (or even numbers for 2)?

Why don't you just simulate enough games to determine the expectation values?

They freely bet what range or even/odd/a prime they will to choose during a 10 second count down until the next random range is chosen. If the next random range is 10-90 and I chose a range within that range I win but if I chose something like 5-15 then I crashed into 5 tiles and I lose.

If they bet an even number and it the random range is 20-29 they lose, they only win if it's mostly evens. So they have a 1 in 3 chance.

If you pick a prime and you chose an even prime then odd primes are still included yes. It just has to be any prime number.

We will be working on prototypes soon but I need to make sure the team all know exactly how it works before we start. Some of them got a little confused with small things.

 

[mfb]

If they bet an even number and it the random range is 20-29 they lose, they only win if it's mostly evens. So they have a 1 in 3 chance.

1 out of 4, approximately (a bit less), for some reasonable assumptions about your still unspecified algorithm to generate the random range.

If you pick a prime and you chose an even prime then odd primes are still included yes. It just has to be any prime number.

That was not my question.
I pick 7, the random range is 8-14. Do I win the "mostly odd" payout?
I pick 7, the random range is 14-16. Do I win the "mostly odd" and the "prime number" payout?

 

[Alanay]

No if you choose a prime number you're only betting the range will include a prime number. If you want to be an even/odd then bet on one that isn't a prime number.