Donuts
Donuts
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Joined: Oct 17, 2014
September 3rd, 2015 at 1:38:45 PM permalink
I'm looking at the Dragon 7 baccarat side bet, specifically what kind of bankroll would be needed to avoid the risk of ruin. This bet isn't actually that great for APs, this is more of an academic exercise.

Stats:

Baccarat values per hand (Main game):
EV -0.01065
SD 0.927282
VAR 0.0859851

Baccarat values per hand (Dragon 7):
*Values extrapolated using Teliots calculations. He gives his value per shoe - I assumed 81.37 hands per shoe, divided the EV (0.5967) and VAR (43.125489) by this number, then backed into the SD per hand by taking the square root of the VAR.

EV 0.007332582 (Low due to bet only being made 9.16% of the time when TC is above 4)
SD 0.529950039
VAR 0.529950039

Combine (per hand):
>n = main bet unit, m=side bet unit
EV = -0.01065*n + 007332582*m
VAR = .927282*m+.529950039m
SD = Sqrt(.927282*m+.529950039m)

So assuming a $25 Mainbet unit and a $100 Side bet unit (when we have the advantage):
EV = -0.01065*$25 + 007332582*$100 = $0.47/hand
VAR = .927282*$25+.529950039$100 = $74.49/hand
SD = Sqrt(.927282*$25+.529950039*$100) = $8.63/hand

RoR
Using the formula ror = exp(-2*u*B/s^2)
u = EV
B = Bankroll in units
s = SD

Our unit would be:
$25*100%+$100*9.16% = $34.16
>The Dragon 7 bet is only made 9.16% of the time

Let's assuming our BR is $15,000 so we have 439 units.

ror = exp(-2*$0.47*439/$8.63^2) = 0.406%

Does this all look right? The reason I ask is when I sub in a $1000 unit for the side bet, I'm only getting an ROR of 3.7% which can't be right. I have a feeling my mistake is how I handled the bankroll units calculation but I'm honestly not sure.
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