ROR CURVE from Wizard of Vegas

**Dog Hand** · 03-23-2020, 01:30 PM

SimonEggi,

Sorry about moving this thread from Wizard of Vegas, but I got frustrated over there trying to upload an image. Norm's board is much more user-friendly in that respect... kudos, Norm!

For those of you joining the thread here, it originated at this URL:

https://wizardofvegas.com/forum/ques...ve/#post761486

In the image below, I took the graph that you posted and superimposed an Excel graph.

Fitted with redefined EoR.jpg

On the Excel graph,the colored squares correspond to results obtained by using my simple "k/(%EV)" formula discussed at WoV, while the colored lines correspond to the calculated results I obtained using the RoR formula (originally developed by Patrick Sileo) reproduced by Don Schlesinger in his seminal Blackjack Attack 3, Playing the Pros' Way, on page 113.

If we let:
SD = standard deviation in units per round
EV = expectation in units per round (note that on your graph, the EV is given on the x-axis in percent, or EV%)
RoR = risk of ruin, expressed as a fraction
EoR = Element of Ruin (note that on your graph, the EoR is given in percent, or EoR%)
BR = necessary BR
(Note that Don used different notation in his book.)
then Sileo's equation can be written as

BR = -(SD^2/(2*EV))*ln(RoR)

Now upon further reading I discovered that Uston's EoR is not the same as Don's RoR. Uston defines EoR (on pages 126-7 of Million Dollar Blackjack) as the risk of losing the BR before doubling it, with the proviso that, if half the BR is lost, the betting is cut in half. Don defines RoR (on page 114 of BJA3) as the risk of losing the BR before building it so high that ruin is no longer possible (i.e., the BR goes to infinity), without ever resizing the betting.
Don helpfully provides a method of comparing these two "ruins": on page 115 of BJA3 he states that EoR = RoR^(2/3). Thus, Uston's 5% EoR corresponds to Don's (0.05)^(2/3) = 0.1357... = 13.6% RoR.

Now the original graph shows parametric plots, for three different EoR% values, of BR vs. %EV, but naturally Uston failed to provide SD information. Thus, to get the lines on the Excel graph I had to guess the SD. In theory, the SD should be the same for all three curves, but I couldn't find ANY SD value that came close to all three. Thus, I ended up using a different SD value for each EoR curve, as shown below:

SD5%=	1.25
SD10%=	0.95
SD3%=	1.70

To get the squares on each curve, I used the simple

"k/(%EV)" formula, with the value for k differing for each EoR. I used 160 for 5%, 70 for 10%, and 330 for 3%.

Hope this helps!

Dog Hand

**simoneggi** · 03-23-2020, 01:48 PM

Thank you very much Dog Hand, this explains a lot of hidden information!!
And no problem for moving the thread, it is really annoying that you cannot post pictures.

Btw, do you think you could give me your private E-Mail or something since you are quite an expert on the topic of Blackjack and I might have more questions.