Question for Don and Norm

**MJ1** · 06-03-2017, 02:05 PM

I'm trying to forecast an ROI% for potential investors.

When I use the double barrier calculator for RoR it returns 16%. The goal calculator returns 70% assuming trying to double bank. Bankroll = 700 units. Based on these figures I would assume 14% of the time the result will fall somewhere between -700 to 700 units. How do I determine, on average, what the result will be within that 14%? This seems rather tricky. If I just multiply hourly EV * the life of the bank the result exceeds 1400 units which should have already been accounted for in the 70% goal statistic.

Is this something that would require a simulation to answer?

Thanks,
MJ

**DSchles** · 06-03-2017, 09:08 PM

"I'm trying to forecast an ROI% for potential investors."

"When I use the double barrier calculator for RoR it returns 16%. The goal calculator returns 70% assuming trying to double bank. Bankroll = 700 units. Based on these figures I would assume 14% of the time the result will fall somewhere between -700 to +700 units."

Correct. But what are your inputs?

"How do I determine, on average, what the result will be within that 14%?"

The distribution will be fairly uniform, within the interval, with an upward bias, so maybe the average result would be in the +100 range or so, skewed to the right. Depends on hours played.

"This seems rather tricky. If I just multiply hourly EV * the life of the bank the result exceeds 1400 units which should have already been accounted for in the 70% goal statistic."

Is that 1,400 units won, or total bank? How can you win 1,400 units? If you play until you double the bank, you stop when you get to +700, no? Your goal is +1,400, but that isn't the win.

"Is this something that would require a simulation to answer?"

There's probably an analytic solution to it (see BJA3, pp. 298-301, for a related problem and solution), but simming would be easier. For now, it would seem that you have +700 70% of the time (e.v. = +490); -700 16% of the time (e.v. = -126); and +100 (?) 14% of the time (e.v. = +14). Total e.v. = +376.

There is a problem with your +1,400 units based on hours. If you use the double-barrier formula, you can stipulate the number of hours of play and then calculate the probability of either going bust or doubling the bank, using the ROR and Goal formulas with a time constraint. But you can't win more than 700 units, as you stop when you double the bank.

Don

**MJ1** · 06-04-2017, 09:06 PM

The win rate per 100 hands is 6.08 units.
The SD per 100 hands is 86.52 units.

I've adjusted my bet schedule so the double barrier calculator now gives 22% RoR. The goal calculator gives 68% assuming 12000 rounds. This means there is a 10% chance of the result falling somewhere between -700 to 700 units.

I meant to write a win of 700 units in my prior post, yielding a total bank of 1400 units. I referenced the article you mentioned but that gives the average win, whenever there is a win. It does not factor in losses when there are losses. So having said that, on average, what result can I expect in those 10% of cases? The answer will clearly be somewhere between 0 and 700 units. So do you still figure +100 units to be the answer? If so, how?

Thanks,
MJ

**DSchles** · 06-05-2017, 10:00 AM

Originally Posted by MJ1

The win rate per 100 hands is 6.08 units.
The SD per 100 hands is 86.52 units.

I've adjusted my bet schedule so the double barrier calculator now gives 22% RoR. The goal calculator gives 68% assuming 12000 rounds. This means there is a 10% chance of the result falling somewhere between -700 to 700 units.

I meant to write a win of 700 units in my prior post, yielding a total bank of 1400 units. I referenced the article you mentioned but that gives the average win, whenever there is a win. It does not factor in losses when there are losses. So having said that, on average, what result can I expect in those 10% of cases? The answer will clearly be somewhere between 0 and 700 units. So do you still figure +100 units to be the answer? If so, how?

Thanks,
MJ

For the 10%, why do you figure the result has to be positive? It's not between 0 and +700; it's between -700 and +700. If hitting the goal is 68% and ruin is 22%, that's about a 3:1 ratio. So, one way to approximate the outcome for the remaining 10% might be to assume a skewed distribution where the result is three times as far away from -700 as it is from +700. That would give about +350.

Don

**MJ1** · 06-05-2017, 01:23 PM

Originally Posted by DSchles

For the 10%, why do you figure the result has to be positive? It's not between 0 and +700; it's between -700 and +700.

For the 10% the result must be between -700 and +700 units. However, since I'm playing with an edge shouldn't it stand to reason that the wins will outweigh the losses within the 10% interval? So, on average, the result will be positive. Why would you expect it to be between -700 and 0 units?

I fiddled around with the Actual Results calculator and found that 15% of the time the result will fall between -700 and 0 units. 27% of the time the result will be between 0 and +700 units. This confirms the obvious--you come out positive more often than negative.

I completed the ROI estimate for the investors using your figure of +350 units within the 10% interval. It works out to be approximately 11%. Do you think that is a good return?

MJ

**BoSox** · 06-05-2017, 02:24 PM

Don, you have damn good patience!

**DSchles** · 06-05-2017, 02:38 PM

"For the 10% the result must be between -700 and +700 units. However, since I'm playing with an edge shouldn't it stand to reason that the wins will outweigh the losses within the 10% interval?"

Yes.

"So, on average, the result will be positive. Why would you expect it to be between -700 and 0 units?"

I expect it to be positive, but that doesn't mean that it WILL be positive! Each time you sit down to play, you expect to win, no? But do you win every time, or do you lose sometimes? The expected result is above zero, but the possible result can be anywhere from -700 to +700. Surely, you understand this.

"I fiddled around with the Actual Results calculator and found that 15% of the time the result will fall between -700 and 0 units. 27% of the time the result will be between 0 and +700 units."

Well, you know that isn't true, because you just said that 90% of the time you either double the bank or go broke trying. So, that leaves only 10% for the -700 to +700 interval. So, I have no idea what the 15% and 27% refer to.

"This confirms the obvious--you come out positive more often than negative." But what do your numbers mean?

"I completed the ROI estimate for the investors using your figure of +350 units within the 10% interval. It works out to be approximately 11%."

How did you calculate that? Do the investors put up all the money? Are you getting a return of 359 units? If so, where does the 11% come from?

"Do you think that is a good return?"

Depends on how long it takes to earn it, of course. If your money is in the S&P 500, 11% is about average for a full year. But the risk of the stock market is greater than that of playing blackjack. How long will it take, on average, to earn the alleged 11% return?

Don

**DSchles** · 06-05-2017, 02:39 PM

Originally Posted by BoSox

Don, you have damn good patience!

And, as you can see, it's not over yet!

Don

**DSchles** · 06-05-2017, 03:19 PM

Originally Posted by moses

OMG. This risk of the S&P 500 is higher than blackjack. Are you serious?

Read pp. 97-98 of the old, "Bible" edition of Wong's Professional Blackjack for a discussion of this. Actually, there is no comparison. On an annualized basis, you can't even discuss the risk/reward ratio of blackjack in the same breath as that of the stock market. Blackjack is much, much better.

If I gave you $100,000 on January 1 and told you you could park it in the S&P 500 for the year, or you could play blackjack with it for the year, you'd have to be completely out of your mind to choose the stock market.

Don

**MJ1** · 06-05-2017, 08:32 PM

"I fiddled around with the Actual Results calculator and found that 15% of the time the result will fall between -700 and 0 units. 27% of the time the result will be between 0 and +700 units."

Well, you know that isn't true, because you just said that 90% of the time you either double the bank or go broke trying. So, that leaves only 10% for the -700 to +700 interval. So, I have no idea what the 15% and 27% refer to.

Hmmm...I didn't write what I intended to convey. This requires a bit of explanation. My logic here may very well be flawed so please correct me if that is the case. On the Actual Results calculator I examined various intervals of interest to determine the probability of experiencing a given result. The probability of losing 700 units or less is 93%, breaking even or more is 78%, and winning 700 units or more is 51%. So to determine the probability of being within the interval of -700 to 0 units take 93% - 78% = 15%. Likewise, to find the probability of being within the interval of 0 to 700 units do 78% -51% = 27%.

Now I suppose I would have to use these percentages to carve up the 10% interval we discussed. 15/(15 + 27) * 10% = 3.5% 27/(15 + 27) = 6.5%. Now all outcomes add up to 100%! In summary, there is a 68% chance of doubling, a 22% chance of going bust, a 3.5% chance of being behind but not broke, and a 6.5% chance of being ahead but not doubling! :-)

With that being said this analysis may be flawed due to the fact that the Actual Results calculator will allow for instances where a player loses more than 700 units but the experiment continues. The calculator doesn't know there is a hard stop at 700 units so the player never quite 'falls off the cliff'. There will be instances where someone shifts to the left 700 units but then comes back to the right of 700 units. Whereas they should have fallen victim to the RoR calculator some will manage to escape bankruptcy. Before I address the ROI topic I would like to hear your thoughts on this matter. To be continued...

Thanks,
MJ

**DSchles** · 06-06-2017, 12:09 PM

There's nothing more to say. You didn't really answer any of the questions I asked you, and you keep on confusing statistics for playing without a barrier or goal with those that have a barrier, or double barrier. Clearly, you're way overthinking this, and the answers you're getting aren't very helpful. You can't mix and match calculators.

Don

**DSchles** · 06-06-2017, 12:52 PM

Personally, I'd settle for knowing how he's earning 6+ units per hour! :-)

Don

**MJ1** · 06-06-2017, 01:00 PM

I'm not trying to mislead anyone which is why I created this thread. I'm just trying to get a feel for the likely outcomes.

Don, let's try this a different way. We both agree that 90% of the time the bank either doubles or goes bust. Now, within the 10% of outcomes that remain the result will be within -700 to +700 units. Is there a way to know how often the result will be within -700 to 0 units? 0 to 700 units? I think it would be useful information for the investors. Thanks.

MJ