What is your strategy?

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Ok, i would bet:

8% on R16,
5% on R14
24% on Red

i.e those percentages of my bank each spin, (recalculating bank after each spin)
 
kut2k2 said:
There are three R-14 slots on the wheel. There is only one R-14 bet square on the table. So yes you get paid if the ball lands in any of the R-14 slots.
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Ok, thanks for the clarification. Here are my calculations.

Optimal bet fraction = Kelly = p - (1- p) / b,
where
p = probability of winning
b = odds on the bet

Expectancy = p * b - (1 - p)
My custom score = Expectancy * Kelly

Then,
Kelly(red) = 23/37 - (1 - 23/37) / 1 = 0.24 = 24%
Kelly(black) = 13/37 - (1 - 13/37) / 1 = -0.29 = -29%
Kelly(R14) = 3/37 - (1 - 3/37) / 35 = 0.05 = 5%
Kelly(R16) = 4/37 - (1 - 4/37) / 35 = 0.08 = 8%

Expectancy(red) = 23/37 * 1 - (1 - 23/37) = 0.24
Expectancy(black) = 13/37 * 1 - (1 - 13/37) = -0.29
Expectancy(R14) = 3/37 * 35 - (1 - 3/37) = 1.92
Expectancy(R16) = 4/37 * 35 - (1 - 4/37) = 2.89

Score(red) = 0.24 * 0.24 = 0.058
Score(black) = no need to calculate, negative expectancy and negative Kelly
Score(R14) = 0.05 * 1.92 = 0.096
Score(R16) = 0.08 * 2.89 = 0.231


So, if only a single bet is allowed, the best strategy would be to bet 8% of the bankroll on R16, on every bet. Some sort of combination bet (such as R14 and R16) would probably be even better, but I have not calculated it yet.
 
The problem is the overlap between r14,r16 and red...i think i would need to bet less than what i just said for RED, maybe only 20% on RED?
 
nonlinear5 said:
Ok, thanks for the clarification. Here are my calculations.

Optimal bet fraction = Kelly = p - (1- p) / b,
where
p = probability of winning
b = odds on the bet

Expectancy = p * b - (1 - p)
My custom score = Expectancy * Kelly

Then,
Kelly(red) = 23/37 - (1 - 23/37) / 1 = 0.24 = 24%
Kelly(black) = 13/37 - (1 - 13/37) / 1 = -0.29 = -29%
Kelly(R14) = 3/37 - (1 - 3/37) / 35 = 0.05 = 5%
Kelly(R16) = 4/37 - (1 - 4/37) / 35 = 0.08 = 8%

Expectancy(red) = 23/37 * 1 - (1 - 23/37) = 0.24
Expectancy(black) = 13/37 * 1 - (1 - 13/37) = -0.29
Expectancy(R14) = 3/37 * 35 - (1 - 3/37) = 1.92
Expectancy(R16) = 4/37 * 35 - (1 - 4/37) = 2.89

Score(red) = 0.24 * 0.24 = 0.058
Score(black) = no need to calculate, negative expectancy and negative Kelly
Score(R14) = 0.05 * 1.92 = 0.096
Score(R16) = 0.08 * 2.89 = 0.231


So, if only a single bet is allowed, the best strategy would be to bet 8% of the bankroll on R16, on every bet. Some sort of combination bet (such as R14 and R16) would probably be even better, but I have not calculated it yet.
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Excellent analysis.

I agree, the best bet is almost certainly going to be some combination bet, possibly of all three +ev singles.

I love the challenge. :)
 
Visaria said:
The problem is the overlap between r14,r16 and red...i think i would need to bet less than what i just said for RED, maybe only 20% on RED?
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Yes, your original proposal (a combo bet of 8% on R16, 5% on R14, 24% on Red) is almost certainly an overbet. I am not sure if it's possible to solve for the optimal combination bet analytically, but it can certainly be done numerically using a simulation.
 
I am most certain Kelly fraction & such doesn't apply because of the 10-spin limit

Betting 1 on red every spin, the average ending P&L on 10 spins is +2.43 with a stdev of ~3.05
Betting 1 on red-16 at every spin, the average ending P&L on 10 spins is +28.92 with a stdev of ~35.4

(stdev from MC-sim on 100,000 runs in both cases, unlikely to be the "exact" value)

The information-ratio (avg/stdev) is 0.797 for red-single, and 0.817 for red-16

I would say the difference between the 2 is marginal at best, IMO those 2 plays are equivalent.

This "opportunity" still present the risk of ending with a negative P&L about 20% of the time, regardless of play red or red-16.

The optimal bet is the one that guarantees the ending P&L will stay within the player desired boundaries after the 10-spins.
 
nonlinear5 said:
Yes, your original proposal (a combo bet of 8% on R16, 5% on R14, 24% on Red) is almost certainly an overbet. I am not sure if it's possible to solve for the optimal combination bet analytically, but it can certainly be done numerically using a simulation.
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Best combo so far:

Bet 9% of bankroll on Red plus 9% of bankroll on R-16.

Kelly == 0.179 ,
Expectation == 58/37 == 1.568 ,
k*E == 0.2806
 
I was a bit confused about whether you can bet on both R14 AND R16, the opening post says :

- You are only allowed to place one of these types of bets:
-- Any single number (including R-16, R-14, G-0), which pays off at 35-1 ,
-- Red or Black, which pays off at 1-1.

But then says:

- You are allowed to place multiple bets on the same spin.
 
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