Awful results playing Boss Media single deck

[Caruso]

The attached results are my last 590 initial hands playing single deck blackjack at Pharaohs Casino. The overall loss is 93.5 units, which is a 3.35 standard deviation swing.

All these sessions were characterised by uninterrupted stiffs busting with a 10, constant small cards on doubles and very few pat two card hands. The number of dealer drawouts to 21 was absolutely phenomenal, when it wasn't sitting on a pat 20 or 19. All but two of the splits were lost 100%, while one pushed.

I consider these results extremely suspicious and would like feedback. I would particularly appreciate Ken's view on this, and an exact calculation of the probability of such an awful result.

[Sonny]

Originally Posted by Caruso

The attached results are my last 590 initial hands playing single deck blackjack at Pharaohs Casino. The overall loss is 93.5 units, which is a 3.35 standard deviation swing.

By my calculations a 94 unit loss over 590 hands would be about 2.9 standard deviations:

One SD = 1.33 * sqrt(590) = 32.31 units
94 / 32.31 = 2.91 SDs

That is pretty unlikely, but not unexpected. I think Ken came to a similar conclusion after 10 hours of play at that casino:

http://www.blackjackinfo.com/blog/20...al-summary.htm

You can follow his progress "play-by-play" here:

http://www.blackjackinfo.com/blog/20...ur-1-of-10.htm

-Sonny-

[mickpk]

I don't have my stats with me as I am on the road for a few days but I have had similar results at least twice. But each time I kept playing and I returned to be above my previous high point. These results will happen. I have played more than 25,000 hands of SD BJ at Boss and whilst that is a fairly insignificant number in the mathematical scheme of the 'long term', if the casino wished to cheat me (not that I'm suggesting you are making that claim) and take my money, all they had to do was bust me a few more times when I was almost down and out. I have not had to redeposit since my starting bankroll yet twice (as mentioned above) I came fairly close to busting yet each time I recovered. I have had tremendous losing and winning sessions, as should be expected in a random game. But I am also showing a profit, also as expected.

[Caruso]

Originally Posted by Sonny

One SD = 1.33 * sqrt(590) = 32.31 units

How do you get 1.33 as the SD for single deck? Surely that's way over? I know there are more double opportunities, but it can't push it up that much. I use the generic 1.15 figure.

Originally Posted by mickpk

if the casino wished to cheat me (not that I'm suggesting you are making that claim) and take my money, all they had to do was bust me a few more times when I was almost down and out.

Yes, that's what I'm suggesting. I consider a plus 3 SD result worthy of suspicion.

I don't know the exact probability of 3.3 SDs, so I'll take a vague shot at 1 in 1000. Confirmation of that would be appreciated.

[Caruso]

Originally Posted by Sonny

One SD = 1.33 * sqrt(590) = 32.31 units 94 / 32.31 = 2.91 SDs

Norm Wattenberger gives it as 1.152, not 1.33, so the above 3.35 SD figure stands.

Originally Posted by Sonny

That is pretty unlikely, but not unexpected. I think Ken came to a similar conclusion after 10 hours of play at that casino.

I think you'll find Ken didn't experience an event anything like this.

[mickpk]

Quote:
Originally Posted by Sonny
One SD = 1.33 * sqrt(590) = 32.31 units


How do you get 1.33 as the SD for single deck? Surely that's way over? I know there are more double opportunities, but it can't push it up that much. I use the generic 1.15 figure.

I concur with your figures, Caruso. From sims and other sources, I have been using a figure of 1.15 as the sd for SD BJ. Calculating the figure on the fullest possible player advantage of 0.15312%, -93.5 units in 590 hands (as opposed to bets, which is where the 1.33 figure may have come from) is 3.38 standard deviations according to my calcs. That's a 1 in 2755 chance, or 0.0363%.

Yes, that's what I'm suggesting. I consider a plus 3 SD result worthy of suspicion.

A plus 3 sd result is just that, a plus 3 sd result. If it wasn't possible then it wouldn't be a 1 in 750 chance (-83 units in 590 hands is spot on 3 sd's). You have to accept that it will happen, on average, once per 750 sets of 590 hands. After all, for my experience to bounce back from such lows and reach new highs would mean that I have had a plus 3 sd result on the positive side of expectations and if that is possible so is the negative side of plus 3 sd's. Personally, I'm happy to continue playing it but it's your choice as to your decision, I can only relate that I have experienced what you have and have bounced back.

All the best, either way.

[Sonny]

Originally Posted by Caruso

Norm Wattenberger gives it as 1.152, not 1.33, so the above 3.35 SD figure stands.

I got 1.33 from Theory of Blackjack and Blackjack Attack (as well as a few generic CV sims). However, if Norm says that this situation is closer to 1.152 then go with that. I’ve never known Norm to be wrong before. His numbers are probably more specific than mine.

Originally Posted by Caruso

I think you'll find Ken didn't experience an event anything like this.

He played for much longer than you and still had a losing experience.

"Overall result for 2689 hands was a loss of $200.
The expected win of that action is 2689 * $10 * 0.11% = $29.58."

During his final session he hit a losing streak and tapped out after having been ahead $1,085 at one point.

"I thought I had a good chance at surviving the day, until the last twenty minutes were all downhill."

That's a swing of over 100 units in a very short time. He even ackwoledges the same thoughts that you had:

"I'm sure I'll hear from the conspiracy theorists now saying the casino must have "flipped the switch" to get my profits back. But I don't believe that for a minute. I've played many thousands of hands online over the last few years, and my results are very close to what the math would suggest."

"The main thought you should take from this monologue is that short-term results are basically meaningless, whether you are a card counter with a 1% edge, or a hopeful basic strategy player with only 0.11% the best of it.

Let me state that again:
Short-term results are basically meaningless."

I agree that your results are suspicious. They are certainly unlikely, but not unexpected.

-Sonny-

[ScottH]

Having your results be 3 standard deviations away from the EV is not that big of a deal. With all the people out playing blackjack, it happens all the time.

When your results show that you are 10+ standard deviations away from EV, then maybe you can start to be suspicous.

According to Chebechev's Theorem you will be within k standard deviations away from the mean 1- (1/k^2) % of the time. So with 3 standard deviations it is 1-(1/3^2) which is 1- (1/9), or 8/9, or 89%. That means that 11% of the time your results will be more than 3 standard deviations away.

[Caruso]

Originally Posted by ScottH

When your results show that you are 10+ standard deviations away from EV, then maybe you can start to be suspicous...11% of the time your results will be more than 3 standard deviations away.

No offence, but GIVE me a break.

10 SDs cannot happen. I don't know the figure, but it must be somewhere in the region of 1^20.

START to be suspicious??? Are you kidding? Let's not get into fantasy land.

3 SDs are a 1 in 400 shot approx - that's 0.25%. Where do you get 11% from?

This is just plain incorrect.

I would still be interested in Ken's input here.

[Sonny]

Originally Posted by ScottH

According to Chebechev's Theorem you will be within k standard deviations away from the mean 1- (1/k^2) % of the time. So with 3 standard deviations it is 1-(1/3^2) which is 1- (1/9), or 8/9, or 89%.

Chebyshev’s inequality is meant to be used when the distribution is not normal (or not known to be normal). Blackjack tends to follow a normal distribution so we can use the standard confidence intervals:

1 SD = 68.3%
2 SD = 95.4%
3 SD = 99.7%
4 SD = 99.994%
5 SD = 99.99994%
6 SD = 99.9999998%
7 SD = 99.9999999997%
8 SD = Why bother?!

Originally Posted by Caruso

10 SDs cannot happen. I don't know the figure, but it must be somewhere in the region of 1^20.

I think you made a little typo there. I assume you meant 10^20 (1^20 = 1). I don’t know what 10 SDs would be either, but judging by the numbers above it really doesn’t matter. It would be a very rare occurence to say the least.

Originally Posted by Caruso

3 SDs are a 1 in 400 shot approx - that's 0.25%.

Mickpk mentioned a 1 in 2755 shot, which sounds about right to me off the top of my head. It is definitely worthy of suspicion, but certainly not damning evidence.

-Sonny-