The pigeonhole principle translated into math when applied to roulette outcomes is:

nlog2(1/37)+.....+nlog2(1/(37-(r+1))+.....nlog2(1/(x-r+1))+.....nlog2(1/2)

Hope that helps

Cheers

Hi Drazen , thanks for that. Tbh , that type of equation does not come easily to me , I think I was hoping for the other thread that was mentioned.

This statement made by you seems to be key.

" Or in other words, is it possible to play roulette like drawing cards from a deck and not putting them back? "

You have to narrow down the options by eliminating other choices , this is what I understand by pigeon hole principle from reading the link given.

Look at this example :-

" If you pick five numbers from the integers 1 to 8, then two of them must add up to nine.

Let's say 1 of our multiple streams comes out 1,2,3,4. then no matter which one of the 5,6,7,8 comes out first then we have a pigeon hole created/filled according to our rule above. Now how do we know what to bet and when? I don't have the answer yet. The answer might be to combine this pigeon hole with something else like a cycle , another stream creating another pigeon hole that we can cross reference etc., or something else ?

Just throwing this out there.

Cheers.