Lonesome Gambler said:
Great! Would you mind sharing the math on that? Thanks!
Sure!
So we have a wheel with 12 spaces. Four of them pay $2, another four pay $3, two of them pay $5 and one pays $10. So far we have a pretty straightforward EV calculation.
EV Excluding the 2x Multiplier:
(4/12)$2 + (4/12)$3 + (2/12)$5 + (1/12)$10 = $3.33
The only part we are missing is the 2x multiplier space (hereafter “Multi”). We know that it has a 1/12 probability so we’re almost done. All we need to know is the average payoff (EV) of the Multi space.
After we hit the Multi space we are only concerned with the spaces that give a payout (spaces $2, $3, $5 and $10). If we hit the Multi space again nothing happens so we can ignore that outcome. That leaves 11 spaces on the wheel. Of those 11 spaces, four of them pay $4, another four pay $6…you get the picture. The EV for the Multi space is:
EV of Multi Space:
(4/11)$4 + (4/11)$6 + (2/11)$10 + (1/11)$20 = $7.27
Including that in our original calculation gives us a total EV of $3.94 per attempt. I use the word ‘attempt’ instead of ‘spin’ because it may take several spins before the bet is resolved. In fact, the average length of a turn is 1.09 spins. If we divide $3.94 by 1.09 then we get an EV of $3.61 per spin, although that number is kinda pointless. I can’t imagine a scenario where you would quit playing, willingly or otherwise, after only a single spin, especially after your EV has more than doubled. Still, in the interest of pointless calculations, I included it in my earlier post. If anyone wants to see some more pointless math I’ll be happy to show how I calculated the average number of spins.
-Sonny-