In a game, there’s a spin wheel with 8 segments. The odds for a reward are displayed:

0 for 1 in 16. 1 for 1 in 2. 2 for 1 in 3. 0 for 1 in 16. 6 for 1 in 25. 8 for 1 in 50. 15 for 1 in 100. 50 for 1 in 200.

The percents add up to 103%. The odds add up to 412. Calculating the expected value both ways gives 1.97 spin value.

If I wanted to do a how and why, say 206 spins will land on the 1, so it has a 50% chance, and say 1 in 2 sounds like a 50% chance but it isn’t 50% out of 103% so you can’t add them that way. If you adjust 100 to 103 then it gives the same expected value.

So you can check another calculation and see how you might explain all these numbers representations:

8 for 1 in 50. 412/50 = 8.24 and 412/50 * 8 = 65.92 reward from this odd in 412 spins. Yet, when you do 1/50 * 8 = .16 reward, that .16 is out of 1.03 so it’s really 103%/50 chance.

For second reference, the total expected reward is 810.27 in 412 spins.

Asking for ways you might explain figuring out odds and payout reward, getting the same value 1.97.

Just in case, this game sometimes shows rounded values in info details, so the small difference between 100% and 103% may just be a rounding thing. I just want to see some comparison between probabilities and odds description and the difference it does make should show different explainations.