No, You are wrong here. You are failing to account for the chance of the £1000 back, you are assuming you always get the £1000 back, whether you win or lose.cushelle wrote:The expected Value doesn't change if you bet on number or colour.
Expected Value of number=
£2000x36= £72,000
£72,000x (1/37)= £1945.95
EV= £1945.95 + £1,000
Expected Value of colour=
£2,000x2= £4,000
£4,000 x (18/37)= £1945.95
EV= £1945.95 + £1,000
As you're best off doing a one off spin then the least risk for one spin is given when you put £1,000 on black £1,000 on red. Your expected value is the same, but the risk for a given spin is lower. Your best outcome is £3,000 though, whereas if you do a number £73,000. Basically there is no right or wrong bet as your expected value is the same, just how much risk/reward you want.
The EV of a number from the £2000 stake lets look at that:
1/37 off the time you hit the number, so 1/37 * £72000 = £1945.95 as you say
36/37 you miss and get the £1000 back from the £2000 so thats = £973
£1945 + £973 = £2918. Minus the £2000 stake from this. The EV from this bet is then £918.
The EV of a colour now.
18/37 times u hit the colour for £4000, so as you say £4000 *18/37 = £1945
19/37 you get £1000, ie. half ur stake back that is worth in EV terms £513
£1945 + £513 = £2458, minus the £2000 stake is £458!
So count yourself WRONG cushelle please :P