Awful results playing Boss Media single deck

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.

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:

(Dead link: http://www.blackjackinfo.com/blog/2005/07/pharaohs-single-deck-final-summary.htm)

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

(Dead link: http://www.blackjackinfo.com/blog/2005/07/pharaohs-single-deck-hour-1-of-10.htm)

-Sonny-

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.

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.

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.

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

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

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%.


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.

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.

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-

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.

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.

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?!

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.

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-

Are you sure? I get from that, that you will be 1 SD away 48% of the time. But I could be wrong.

From my regular online BJ play I had 130,000 hands this calendar year at 3 sd's on the negative. But the subsequent 40,000 hands were over 2 sd on the positive. Within those results I have had many plus 3 sd experiences and even a few plus 4 sd experiences. They were bad results but not unexpected. Perhaps a casino here or there has 'tweaked' the game, but perhaps they haven't and all I have experienced is mathematically acceptable variance. When you play this many hands you will see many wild swings in your play and I accept it as being that and just move on to the next game.

Caruso, I've been away travelling, and just found this thread.

3.35 SDs is certainly bothersome. Do you have other recent experience at the game, or is this your sole set of data?

Perhaps it's time for another test. It'll take me a few days to catch up around here, and then I'll hopefully have time to consider this more closely.

I imagine this scenario where there is a heap of 2755 envelopes. All of the envelopes are empty except for one, which contains a check for a million dollars.
Some guy pulls one envelope and lo and behold it is the envelope with the huge check in it.
That is far beyond suspicious in my book.

Is it even possible for awful results to be suspicious to you?

Not sure what is trying to be implied here but why would a result that we mathematically know to be a 1 in 2755 chance be suspicious? Whether it is 2755 people playing 590 hands each or one individual playing 2755 sets of 590 hands, from my understanding, what the math states is that it is possible for one of those sets of hands to be -93.5 units (as per Caruso's results). Expand that to ten times as many sets or players, ie 27550 players all play 590 hands each; is anyone really suggesting that it would be suspicious for even 1 of those 27550 players to be -93.5 units when the math states that it is possible for 10 of those players to experience such a loss. If being -93.5 units in such a sample is suspicious then the math is wrong and it shouldn't be stating that it is a 1 in 2755 chance but a 1 in NEVER chance. And that is clearly not the case. I contend that these experiences will happen and are not, of themselves, reason for suspicion. There may well be valid reasons for suspicion but that is not determined purely by a result such as this. That is determined by an in-depth analysis of the distribution of the cards. If every 1 in 2755 chance result was deemed suspicious then I'm certain I've had plenty of such results and 1000's of others have as well and I'm not just talking about online casino play for such results happen in land casino play as well. Play enough hands and you will experience it. Otherwise we may as well just throw the math out the window if we aren't going to accept it when we receive a result we're not comfortable with.

I'd like to state that this is not any commentary or imputation on Caruso. It is just my commentary on the math of the game and that we have to accept the negative variance as well as the positive variance, not just the latter (notice how they always go into the Big Winners threads without a complaint or concern about rigging or unfairness?). Of course, evidence of an unfair game at any casino is welcomed and encouraged for none of us want to lose our money by being cheated. But a 1 in 2755 chance is, surely, just that, not a 1 in never chance.

Sorry, it seems you are looking for a reply but what you wrote makes no sense.

This is the section of what you wrote that most struck me. This implies that I have to change my imagined scenario where one man pulls from a pile of 2755 envelopes, to a scenario where 2755 people pull from a pile of 2755 envelopes.
The chances of any single person getting the correct envelope is still 1 to 2755, but that someone is going to get the correct envelope has now become 100 percent.
Thanks for the clarification.

Quote:
Originally Posted by Gregory View Post
http://www.blackjackinfo.com/bb/showpost.php?p=17058&postcount=14
"I imagine this scenario where there is a heap of 2755 envelopes. All of the envelopes are empty except for one, which contains a check for a million dollars.
Some guy pulls one envelope and lo and behold it is the envelope with the huge check in it.
That is far beyond suspicious in my book."

is it possible that coincidental parallels are mathematically likely? :devil:

http://www.blackjackinfo.com/bb/showpost.php?p=16472&postcount=11

these discussions make one ponder risk of ruin. say one hundred people are playing a similar game under similar cirumstances and each as a ROR of one percent. how do you tell the one guy that ends up losing everything that it isn't awful?

best regards,
mr fr0g

This theorem isn't perfect for relating to blackjack, it's just to show that 3 standard deviations is nothing mathematically.

From the theorem, with 1 standard deviation, it would be 1-(1/1^2), which is 0. That means that at least 0% of the data will be within 1 standard deviationof the mean. That doesn't mean much. But at least 75% will be withing 2 standard deviations, and at least 89% will be withing 3.

I don't know how you got 48%...