Attention Don and Others: Risk of Ruin and Standard Deviation

My thanks to Don and other masters who continue to hang out in the Free Message Board to help us out.

My question has to do with ROR. I have thankfully figured out that my ROR is .737, due to my low bankroll and high unit bet. (Note: I do not count cards and, for all purposes, flat bet only.).

I understand that ROR incorporates SD. However, I calculated my trip one SD range to be (-$33 to $378), two SD to be (-$237 to $583), and three SD to be (-$442 to $788). As you can see, these ranges seem quite favorable, especially in light of the excessive ~75% ROR mentioned above.

1) How can the trip ROR be so high while the trip SD seems so favorable?

2) Finally, and Don you touch on this on page 128 of Blackjack Attack, why are the maximum losses occurring in the early going of playing (pg. 131 of BA)? Do these seemingly very high RORs occur with flat bettors as well as spread bettors, or just spread bettors? It's just that the RORs seem very high (early on )even when the player has a significant advantage. It almost seems that the early RORs get worse when the player advantage INCREASES?

Can you tell me please where your advantage comes from, if you aren't counting? You are flat betting and not counting, so your ROR would be 100% with BS only.

Is your ROR a trip ROR or a long-term ROR? How did you calculate it?

The answer to your last question is simple, provided you actually have an edge. While e.v. is a linear function, s.d. is a square root function. So, the longer you play, the greater the fraction e.v./s.d. becomes, as the numerator is increasing much faster than the denominator. As I state in the book, the "dangerous" period is early on, when s.d. still dominates e.v. Eventually, e.v. catches up and then never looks back, as you play more and more hours.

Don

With just flat betting your long term risk of ruin is 100% so I'm thinking you are just looking at trip risk of ruin.

Assume a 6 deck, S17, DAS game. Also assume trip bankroll is $500 and you will flat bet $10 a hand for 4 hours at 100 hands per hour. Your expectation is to lose $3.50 an hour.

However 2 out of 3 times your results will be between -$246 and $218. 95 out of 100 times your results will be between -$478 and $450. Complete trip ruin is 3.53% and if your trip goal is to win $100 in 4 hours the chance of doing that is 64.87%

Blackjack Risk Manager is a nice little program.

You didn't read his numbers. One s.d. range to be -$33 to +$378. Does that look like a negative e.v. to you?

Clearly, something is very wrong.

Don

My numbers came from BJRM

Don - I just don't want to get back into our old 'loop' where we go back and forth, so right now I won't take the time to answer all of your questions. But I may later, because I value your input. Thank you.
Questions for you and anyone:

1) How does the standard deviation predict a range of outcomes that are positive for a trip but the ROR trip formula predicts catastrophe 50% of the time? Is this possible, or am I mixing apples and oranges or incorrectly using the formula(s).

2) How does one incorporate playing simultaneous hands into a ROR formula? E.g., if betting $50 on one hand, $50 on the adjacent hand, and $50 on the hand adjacent to that, do you assign $150 to the unit variable, or do you take the average of the three bets ($50) and use that for the unit variable.

1) How does the standard deviation predict a range of outcomes that are positive for a trip but the ROR trip formula predicts catastrophe 50% of the time? Is this possible, or am I mixing apples and oranges or incorrectly using the formula(s.

It's perfectly possible. If you have a positive expectation, and you know the standard deviation, you can do the traditional calculations for mean outcome, and deviation around that mean. Having a positive e.v. does NOT tell you anything about your ROR (on the other hand, having a negative e.v. means that, if you play long enough, you will, with 100% certainty, lose all your money).

So now, you need to incorporate into the formula a bankroll size, which can be anything. And, if it's too small, despite your positive e.v., you might have a large ROR. Clear?

2) How does one incorporate playing simultaneous hands into a ROR formula? E.g., if betting $50 on one hand, $50 on the adjacent hand, and $50 on the hand adjacent to that, do you assign $150 to the unit variable, or do you take the average of the three bets ($50) and use that for the unit variable.

You don't have to use a unit size in the ROR formula; rather, you can use e.v. per round, in dollars, s.d. per round, in dollars, and bankroll size, in dollars. If you are calculating a trip ROR, then you also use number of hours of play. If not, then the time is "infinite."

Hope this helps.

Don

P.S. If you're using Norm's calculators, and they ask for units, rather than dollars, then just convert from one to the other. In your above example, your bet is $150 and not $50. I know that's not the same as betting $150 on one hand; however, that will be reflected in the different s.d., which incorporates the covariance for the three simultaneous hands.

We know he's not counting since he said so. There are of course a myriad of other possible ways to get an edge at BJ. Some of these are:

Shuffle tracking - although since he specified flat betting, not likely. Then again, in his next post he did say that he entered mid-shoe on occasion....

Hole carding - entirely consistent with all info given by the OP.

Exploiting dealer errors.

2:1 BJ promo, or something similar, that makes the game +EV off the top.

Exploiting a really generous cash back comp program.

Sitting next to a high roller who lets you take all of his advantageous double downs and splits.

Match plays.

Of course, there is also always the possibility that the OP is full of shit. Who the hell knows?

In "Blackjack Attack," I did not see a clear definition of Risk of Ruin as it is used in the formulas. Is it, as another author put it, the likelihood of doubling your bankroll before losing it? Or is Risk of Ruin, as applied to the big formulas, slightly different?

"In Blackjack Attack, I did not see a clear definition of Risk of Ruin as it is used in the formulas. Is it, as another author put it, the likelihood of doubling your bankroll before losing it? Or is Risk of Ruin, as applied to the big formulas, slightly different?"

See p. 114, next-to-last paragraph for the definition you seek.

Doubling the bank has nothing to do with ROR, as used throughout BJA3. The assumption is that you keep playing until you have all the money in the world, or you are broke.

Don

You say that your trip sd is between -$33 and +$378. This means that your trip ev must be $172.5 (right in the middle).I assume a trip playing time of 16 hours. This produces an hourly ev of roughly 11$. For simplicity we assume flat betting of $100 at a rate of 100 hands an hour.
This means that your edge is 0.11% (unlikely but not impossible).Since the sd of a blackjack hand is 1.1 units, your sd per hand is $110 and therefore $1100 per hour (10*110) and $4400 per trip (40*110).
So your sd numbers have been wrong by at least a factor 10.
Since your ev is very feable, it takes a long time to catch up with sd. 10'000 hours which is more than a decade!
Your worst time would be after 2500 hours when tha gap between sd and ev reaches $27'500 (55000-27500).
In other words you would need at least 30k to survive the experience.

Francis Salmon

After about 7 attempts, I may have finally used the formula correctly. But something seems a bit wrong. Is it possible that when I flat bet $10 side by side, my short-term ROR (~12.7%) is BETTER than when I flat bet $5 side by side (short term ROR = ~ $ 24.19)? If this is possible, perhaps it's because my EV is so high.

I used +16 units after 192 rounds of side by side play to get the EV. This seems to be representative of my advantage with my non-progression, non-counting 'system' or strategy. (I believe this equates to about a 3.6% advantage.).For my trip I am going on today (down South), I have $1000 and plan to play about 192 rounds in 4 hours. I plan to do this for a grand total of 16 hours during my trip.

So, again, is it possible to have a higher risk of ruin when flat betting side by side (2 hands at a time) with a lower amount than when flat betting side by side (2 hands at a time) with a higher amount?

... but we've reached the point where I'm out of this discussion. You aren't listening anymore, and that's usually my cue to exit.

Good luck to you.

Don

It seems "You'll excuse me" is kind of a pushy way of making a statement to be excused rather than "If you'll excuse me?," which, appropriately, is stated as a question. One is actually asking permission to be excused, not informing or telling what is about to happen.

By the way, with all respect, this is a blackjack board, not a grammar or punctuation board. I know some have extensive knowledge of the game of blackjack, but it seems to me that criticizing others' grammar, punctuation, etc. is not only off-topic but potentially belittling, disrespectful, and judgmental. It also seems to create barriers and an air of formality rather than camaraderie.

In my opinion, if one does not like the way others write, perhaps they should not read the posts.

I sure feel I am listening. And Don (or others), I still don't know what Don means by his post about me not listening. And I wished I had, because I was about to play and wanted some more betting confidence.

I don't know if Don is impatient because I was not acknowledging the stuff about how standard deviation overrides EV early on, or is there some other point I missed?

Boy, if that really is true about how powerful standard deviation is, I am surprised. I was under the impression that with a 3% EV, betting $10 side by side would pose a more dangerous ROR than betting $5 side by side. You must admit this is a difficult concept, and definitely interesting.

Perhaps betting $10 side by side is safer than betting $5 side by side because one is taking advantage of the cards when that 3% manifests itself, thereby propelling the player out of the gravitational pull of standard deviation?????

if I have hurt anyone's feelings regarding what I posted about how I feel about some people posting corrections of others' grammar and spelling.