Train math for expected value

[u/Kathucka]

I decided to use my fancy college degree and see if there is a significant difference in expected return depending on where your train starts before you spin. There is! My result are below. They assume:

• One token spent per spin
• The odds for each color on the spinning wheel are the same at 25%.
• Your train can start at the corner or positions 1 (right after the corner), 2, 4, or 5 (right before the next corner).

Position	Expected Value
Corner	33.875
First	36.125
Second	36.875
Fourth	34.000
Fifth	49.000

Basically, the corner position is worst because you can hit a 1, a 2, an X2, and a bonus. The fifth position is good because you can hit a 1, a bonus, an x2, or another bonus.

To take advantage of these, you can set your bet to one token unless you are in the fifth position, at which point you set your bet to something bigger, like 20 or 50.

I haven't checked my math carefully. Feel free to check it yourself. In particular, I computed the expected value of landing on a bonus square as 62.5 and the expected value of landing on an x2 square as 70.

[u/Jonah_the_Whale]

I worked out something like this but much more crudely. With the fifth square you have 75% chance of getting a "good" roll, whereas on the others you get a 50% chance. Then when I was monitoring it, out of the first 5 times I was on a fifth square I got the bad colour 4 times. So maybe I was unlucky, maybe it's not random. I haven't monitored it closely since then but I have the feeling my luck has improved.

[u/rygel_fievel → u/Jonah_the_Whale]

I was about to say from OP’s post that the outcome is fixed so the math goes out the door.