^ Sammy's question
I may have done this completely wrong, but:
$1*0.4 + $2*0.3 + $3*0.2 + $4*0.1 = $2 EV for a single spin.
Therefore, optimal would be to quit when you hit $3 or $4. Odds of totally missing $3 or $4 in 3 spins is 0.7*0.7*0.7 = 34.3%
34.3% of the time you hit $2 or less in 3 spins.
65.7% of the time you hit $3 or more in 3 spins.
42.8% of the time that you hit $2 or less you hit $2.
57.2% of the time that you hit $2 or less you hit $1.
66.7% of the time that you hit $3 or more you hit $3.
33.3% of the time that you hit $3 or more you hit $4.
0.343(0.428*2 + 0.572*1) + 0.657(0.667*3 + 0.333*4)
= 0.343(1.428) + 0.657(3.333)
= 0.490 + 2.190
= 2.68
Therefore this game is slightly +EV if you follow my rules and you should expect a ROI of 7.2%.
There is probably a better way to play if you are planning on doing multiple spins. ie. probably something about stopping if you hit $2 on the second spin to avoid taking a 40% risk on hitting $1 on the 3rd spin. This would make it much more +EV in the long run I think but I'm not sure how to figure it out. The 3rd spin obviously does not rely on whether or not you missed $3-$4 on the 1st and 2nd spins.
(I'm probably way off here and would easily get suckered into this game that is most likely -EV due to my bad math skills)
Last edited by JH1; 02-05-2009 at 09:21 PM.