What is your strategy?

nonlinear5 · Apr 16, 2014

kut2k2 said:
A question about risk ...

Every spin you're betting your entire bankroll. But you can only lose 2.7% for any given spin. So what is the "risk", the 100% you're betting or the max 2.7% you stand to lose?

The risk is that you lose 10 times in a row, each time 2.7% of the bankroll.

kut2k2 · Apr 16, 2014

nonlinear5 said:
The risk is that you lose 10 times in a row, each time 2.7% of the bankroll.

No, I mean the risk per spin. For a single bet, the bet risk is easy: 100%, because that's how much of your bet you lose when you lose. So your risk (to your bankroll) is your bet size.

But we now have a combination of bets where your betsize is 100% of your bankroll but the most you can lose (indeed, your only possible loss) is 2.7% of your bankroll.

So does the definition of "risk" stay constant or does it change with the strategy? Trading is immeasurably less predictable than this or any other casino game (leaving aside cheating or faulty equipment). So I don't see the definition of "trading risk" being strategy-dependent, but maybe that's just me.

So is the risk per spin using this thread's optimal strategy 100% or 2.7%?

nonlinear5 · Apr 16, 2014

SplawnDarts said:
I THINK we will see both of those at zero.

Betting on each black # is strictly cheaper than bettering 1 unit on black and gives the same effect. So that's a strictly better-than expectation wise thing.

I think a similar but more complicated argument can be constructed for the individual red #s.

But probably worth checking - this is a goldmine of weird effects.

Well, I have another surprise for us all. You were right about betting on black color -- it's worthless. But as it turned out, betting on individual red numbers is much better than betting on red color, to the point that no money should be wasted in betting on red color.

Here are my latest results which allow all types of bets:
R16: bet on R16
R14: bet on R14
RC: bet on red color
RN: bet on all individual red numbers (other than R16 and R14)
BC: bet on black color
BN: bet on all individual black numbers (including Green-0)

The top strategy is:
10.8% on R16
8.1% on R14
0% on Red color
43.3% on all individual red numbers, equally distributed
0% on black color
37.8% on all individual black numbers, equally distributed

Code:

	R16	R14	RC	RN	BC	BN	F(R16,R14,RC,RN,BC,BN)
	10.8	8.1	0.0	43.3	0.0	37.8	0.5192641
	10.8	8.1	0.0	43.2	0.0	37.9	0.5192639
	10.9	8.1	0.0	43.2	0.0	37.8	0.5192606
	10.8	8.1	0.0	43.4	0.0	37.7	0.5192593
	10.8	8.2	0.0	43.2	0.0	37.8	0.5192591
	10.8	8.1	0.0	43.1	0.0	38.0	0.5192588
	10.9	8.1	0.0	43.1	0.0	37.9	0.5192582
	10.9	8.1	0.0	43.3	0.0	37.7	0.5192582
	10.7	8.1	0.0	43.3	0.0	37.9	0.5192581
	10.8	8.2	0.0	43.1	0.0	37.9	0.5192566

kut2k2 · Apr 16, 2014

nonlinear5 said:
Well, I have another surprise for us all. You were right about betting on black color -- it's worthless. But as it turned out, betting on individual red numbers is much better than betting on red color, to the point that no money should be wasted in betting on red color.

Here are my latest results which allow all types of bets:
R16: bet on R16
R14: bet on R14
RC: bet on red color
RN: bet on all individual red numbers (other than R16 and R14)
BC: bet on black color
BN: bet on all individual black numbers

The top strategy is:
10.8% on R16
8.1% on R14
0% on Red color
43.3% on all individual red numbers, equally distributed
0% on black color
37.8% on all individual black numbers, equally distributed

Code:

R16 R14 RC RN BC BN F(R16,R14,RC,RN,BC,BN) 10.8 8.1 0.0 43.3 0.0 37.8 0.5192641 10.8 8.1 0.0 43.2 0.0 37.9 0.5192639 10.9 8.1 0.0 43.2 0.0 37.8 0.5192606 10.8 8.1 0.0 43.4 0.0 37.7 0.5192593 10.8 8.2 0.0 43.2 0.0 37.8 0.5192591 10.8 8.1 0.0 43.1 0.0 38.0 0.5192588 10.9 8.1 0.0 43.1 0.0 37.9 0.5192582 10.9 8.1 0.0 43.3 0.0 37.7 0.5192582 10.7 8.1 0.0 43.3 0.0 37.9 0.5192581 10.8 8.2 0.0 43.1 0.0 37.9 0.5192566

So basically what you're saying is ...

Divide your bankroll into 37 equal parts and bet one part on each wheel slot. This works out to 4 parts on R-16, 3 parts on R-14, and one part on each of the other 30 numbers. Interesting.

k*E == 0.446, which happens to be identical to the previous strategy:

Divide your bankroll into 37 equal parts. Bet one part on each of the not-red numbers, bet 18 parts on Red, bet 3 parts on R-16 and bet 2 parts on R-14.

How exactly are you measuring these strategies?

nonlinear5 · Apr 16, 2014

kut2k2 said:
So basically what you're saying is ...

Divide your bankroll into 37 equal parts and bet one part on each wheel slot. This works out to 4 parts on R-16, 3 parts on R-14, and one part on each of the other 30 numbers. Interesting.

I didn't think of it this way, but yes, as it turns out, it is almost exactly 1/37 of the bankroll on every single number. There is a certain beauty in this, isn't there? So, what's the E*k for this?

nonlinear5 · Apr 16, 2014

kut2k2 said:
k*E == 0.446, which happens to be identical to the previous strategy:

Can you check again? The current strategy is much superior to the previous one.

kut2k2 said:
How exactly are you measuring these strategies?

The performance metric, F(R16,R14,RC,RN,BC,BN), is the geometric rate of the bankroll growth per spin. I am maximizing this function, so the resulting bets are Kelly-optimal.

kut2k2 · Apr 16, 2014

nonlinear5 said:
Can you check again? The current strategy is much superior to the previous one.

The performance metric, F(R16,R14,RC,RN,BC,BN), is the geometric rate of the bankroll growth per spin. I am maximizing this function, so the resulting bets are Kelly-optimal.

I checked again, and my k*E values are identical for the two strategies.

Can you write out the formula for F(...)? Thanks.

nonlinear5 · Apr 16, 2014

kut2k2 said:
I checked again, and my k*E values are identical for the two strategies.

Can you write out the formula for F(...)? Thanks.

F(R16,R14,RC,RN,BC,BN) =
= pR16 * log1p(35 * r16 - r14 + red - redNumber - black - blackNumber)
+ pR14 * log1p(-r16 + 35 * r14 + red - redNumber - black - blackNumber)
+ pRedSingle * log1p(-r16 - r14 + red + 35 * (redNumber / 14) - black - blackNumber)
+ pBlack * log1p(-r16 - r14 - red - redNumber + black + 35 * (blackNumber / 14))

where

pR16 = 4 / 37
pR14 = 3 / 37
pRedSingle = 16 / 37
pBlack = 14 / 37

r16 = percent of the bankroll to bet on R16
r14 = percent of the bankroll to bet on R14
red = percent of the bankroll to bet on red color
redNumber = percent of the bankroll to bet on all red numbers other than R16 and R14
black = percent of the bankroll to bet on black color
blackNumber = percent of the bankroll to bet on all black numbers (including Green-0)

log1p(x) = ln(1 + x)

nonlinear5 · Apr 16, 2014

I've spotted a typo in my code.

This:
pRedSingle * log1p(-r16 - r14 + red + 35 * (redNumber / 14) - black - blackNumber)

Should be this:
pRedSingle * log1p(-r16 - r14 + red + 35 * (redNumber / 16) - black - blackNumber)

I am re-running the simulation.

nonlinear5 · Apr 16, 2014

After fixing the typo, the top 10 strategies are almost identical to what they were before. It's just F(.) was reduced:

Code:

	R16	R14	RC	RN	BC	BN	F(R16,R14,RC,RN,BC,BN)
	10.8	8.1	0.0	43.2	0.0	37.8	0.4784760
	10.8	8.1	0.0	43.3	0.0	37.7	0.4784735
	10.8	8.1	0.0	43.1	0.0	37.9	0.4784735
	10.9	8.1	0.0	43.1	0.0	37.8	0.4784707
	10.9	8.1	0.0	43.2	0.0	37.7	0.4784705
	10.7	8.1	0.0	43.3	0.0	37.8	0.4784697
	10.7	8.1	0.0	43.2	0.0	37.9	0.4784695
	10.8	8.2	0.0	43.1	0.0	37.8	0.4784691
	10.8	8.2	0.0	43.2	0.0	37.7	0.4784689
	10.8	8.0	0.0	43.3	0.0	37.8	0.4784682