You will never get heat at the Bellago or any MGM/Mirage property. The first bit of heat you will get is when the shift manager is tapping you on the shoulder from behind telling you that you're blackjack business is no longer welcome.
You will never get heat at the Bellago or any MGM/Mirage property. The first bit of heat you will get is when the shift manager is tapping you on the shoulder from behind telling you that you're blackjack business is no longer welcome.
I am an actuary, which makes me a mathematician to a great extent. I spend my life examining mortality tables and developing them.
As far as computing standard deviation, generally it is calculated as the root of the variance. The variance is the of sum of probability weighted squares of possible outcomes minus mean. For a sum, such as a sum of hands played, the variance is generally equal to the sum of the individual variances, assuming the individual outcomes are independent of one another (which is not strictly true in blackjack). Over a large enough number of hands, the distribution of the sum of the outcomes of those hands is roughly approximated by the normal distribution.
As far as how to calculate the variance for an individual hand, it is quite difficult. Usually, it is done via computer simulation rather than by use of strict rules of probability. Certainly, that is how I accomplish it. I've never read a full development of the variance of a blackjack hand without use of simulation, even in Griffin. But MathProf, if you can provide one, I'd love to see it. Once you have it, though, it still isn't good enough, though, because it must incorporate the spreading of your bets with count, which will tend to increase variance. It would not be at all correct to take the variance of a unit and apply it to your average unit. This would have to be an entire separate process. No, computer simulation is by far easiest for this component of the calculation.
I don't know why you doubt my mathematical credentials, but to be an actuary one ahs to pass some quite rigorous mathematical tests, the first of which is on probability and statistics.
You took 1.13 to be the standard deviation of one hand of BJ. I am not quibbling with that. It does vary with the rules and with the count. (BTW, you can compute this without computer simulation, via combinatorial analysis.)
But from what I can tell, you are estimating your SD in $$ by multiplying 1.13 times your average bet. This is only valid fi you are flat-betting (and I don�t think so foolish as to think you can make 150K a year flat-betting.)
More generally, you multiply 1.13 times the square root of you average bet-squared. This is NOT the same as your average bet; it is much bigger.
You made another error when you said: But my sessions have been quite long, and that lowers the standard deviation for the sessions somewhat.
The longer your session, the bigger the SD. If N measure the length of the session, then SD is proportional to sqrt(N). Of course, EV is proportional to N, so in relative terms SD/EV decreases with longer sessions. Maybe you meant that, but it is not what you said.
Earlier you mentioned that you played the DD game at Bellagio with a 1-5 spread. I presume this is one spot.
With an optimal spread, your average bet is about 1.85 units. Your EV is about 2% units per hand, and you SD is about 2.71. This is relatively low because of the small ebt spread. It would be higher with a 10-1 spread.
It would 19,000 hands before your SD was equal to one EV. This is in the ballpark of 200 hours, depending on the game speed.
With the data above: For a 100 hour session, your EV will be about 7.3% of your SD. That is, your SD is about 14 times your SD. This is consistent with DD�s suggestions that the ratio would be between 10 and 30.
I have trouble understanding the word �game� in you subject line. My guess is that you meant to type �gave� and made a mistake, and the spill checker changed it to game.
This happens to me all the tame. In fact, I an notorious for it.
They say that �Imitation is the sincerest form of flattery�. I appreciate the complement.
Sigh. I can see that you are going to interpret things quite literally, so I will have to be more careful with my words from now on.
Specifically, yes of course I know that a longer session will increase my overall standard deviation. But while my expected value increase proportional to N, my standard deviation only increase proportional to root N. Since DD was speaking specifically regarding the ratio of EV to SD, this is what I was addressing.
Also, I am not planning on flat-betting, nor do I believe I can calculate the standard deviation of a session by applying a factor to an average bet. This should be clear from my last post, where I said it would not be sufficient to come up with a standard deviation for a single hand. The 1.13 number used in an earlier post is not a number I use in my calculations, it was only quoted as some evidence that I understand the high standard deviation inherent to blackjack. Yes, standard deviation for a session is much further increased by the nature of the bet-spreading required. Apply a factor the root of the average (bet-squared)? I suppose, but that is really only an approximation, and like I said I don't much like it because individual hands within a shoe will tend to have some correlation if you are spreading your bet according to the count. That is why I would rather use a computer simulation to come up with the standard deviation for a particular session. Otherwise, send me the specifics of your calculation of standard deviation for a given unit, spread, and number of hours. But if it assumes independence between one hand and the next, I will have to reject it unless you can show me that the correlation is insignificant. I have no problem with your estimate of 2.71 for my 5:1 spread at Bellagio.
The truth is that the play at Bellagio was so different than my usual play that I was not considering it (though I did make a small fortune there, luckily). I cannot support a $50 unit. My play since then has been $10-$100, as I said. I believe I also mentioned that one of the advantages to the area in which I was playing was that the tables were empty and I could always spread to two hands. This allows me to somewhat lower my standard deviation, for though the hands have some covariance it is far from 1.
But as far as my response to DD, I stand by it. I am about one standard deviation above mean. That is far from incredible luck. You seem to believe I am underestimating the standard deviation inherent to a particular session. If I were, than my claim that I am only one standard deviation above mean would degenerate into something even less than one standard deviation, and make it that much more likely and less "lucky".
OK, I understand that you meant to say that the ratio of SD/EV increases with session length. Also, in your most recent post I now see that you did state Once you have it, though, it still isn't good enough, though, because it must incorporate the spreading of your bets with count, which will tend to increase variance. It would not be at all correct to take the variance of a unit and apply it to your average unit., which is what I thought you had suggested earlier in the thread.
However, you have gone on to say:
But if it assumes independence between one hand and the next, I will have to reject it unless you can show me that the correlation is insignificant.
Actually, simulations show that the correlation between hands within a shoe are almost negligible. So the method that I mentioned above would work fairly well. However, the numbers that I quoted above are based upon computer simulations, reported by BJRM.
I ran the numbers about the Bellagio game, because I know the parameters of that. I do not know about the other games where are spreading 10-100. If you tell us a little about the rules, number of decks, penetration, etc, we can compute the standard deviation for you. What do you think your EV and SD are for these game?
You mentioned that you were over-betting at Bellagio, relative ot your other games. Your Max Bet there was 250, whereas ordinarily it is only 100?
Mixing betting levels does very bad things to the EV/SD ratio that you are talking about. It raises your SD disproportionate to your EV.
Bellagio was distinct from my usual advantage play. My friends were there and I wanted to play with them, so I took a shot and closed my eyes and hoped it would be okay. Betting at those stakes is not something I will be doing again until I am willing to lose around ten grand. I thought I said something to that effect in the original post.
In terms of computer simulations, I have a little visual basic program I've written here to do my simulations. It isn't pretty, but it gets the job done. I also like to use it to check two-deckn playing strategy, since I haven't seen any tables specifically for two decks (though they must be out there).
Feanor wrote:
In terms of computer simulations, I have a little visual basic program I've written here to do my simulations. It isn't pretty, but it gets the job done. I also like to use it to check two-deckn playing strategy, since I haven't seen any tables specifically for two decks (though they must be out there).
Feanor,
If you need just the Basic Strategy, follow the link below to download Eric Farmer's Basic Strategy Calculator. Using it, you input the particular rules variations for the game you wish to study, and the program outputs a text file with the correct BS.
As a side bonus, the download includes a BJ game that you can adjust to use whatever set of common rules variations you prefer.
Hope this helps you!
Dog Hand
If Bellagio was a special case, then I would suggest that you exempt the money you made there from you cumulative winnings, if you want to get a fair picture of profitability.
If you have your own simulator, have you used it to estimate your EV and SD? I thought that you did not agree with DD�s ballpark estimates, which struck me as being reasonable estimates.
I will say that I am not sure about the details of the games you are playing. If you are playing deeply dealt double-deck, with a 1-10 spread across two spots, and your sessions are 400 hands or so, then you EV/SD ratio may not be that bad. It could be around 20% for one 400-round session. I have naively assumed that you were playing a typical shoe game.
Also, if you have your own simulator, you may wish to compute the CC between different hands of the same shoe. If you do, I think you will see that it is quite small.
If you are really planning to make some money from this game, then I would suggest some investments. One of which is BJRM. It is basically a warehouse of simulation data, together with an interface which allows you to do computations on them. It will compute optimal spreads, Risk of Ruin, etc.
You could also consider buying a simulator. I have my own custom software that I could use to set up my own sims, but if I ma just doing standard types of �Canned� simulations, I use SBA.
Finally, I would encourage you to join Green Chip. You will be able to discuss issues with far more experienced players than are here. If you do want to try make 150K, a year, or even only 10K a year, then I think it is indispensable.
Yes, I have exempted Bellagio winnings from my calculations. That was really just gambling (though with an edge).
I didn't have as big a problem with DD's numbers as his comment that I had been so lucky. I have not at all. As to his number, 30:1 SD:EV is not accurate for the sessions I've been playing. 10:1 is closer, though I think it's somewhat less than that.
As to the games I've been playing, they have been DD dealt to .8 decks left (although sometimes you can get some .5 penetration). And I have been playing twelve hour sessions (like I said, no heat yet, so why not). Presumably, when I increase the stakes I will not be able to play anything like that amount of time.
I punched these numbers into BJRM. You didn�t mention rules: I used H17 DAS. The data available are include 62, 70, and 78 cards dealt. I used the 70 cards dealt.
I pulled up the optimal 1-10 spread, playing on two hands.
BJRM reports a DI of 9.72. That means the EV/SD ratio for a 100-round session is 9.72%. In round figures, this is 10%.
If you played 400 round sessions, the EV would be 20% of SD.
If you played 900 round sessions, it would be 30%.
This was based upon High-Low, using the full I18 indices, and no cover betting. It is also based upon the optimal spread. Here �optimal� means the spread that maximizes the EV/SD ratio.
I had assumed your 10-1 spread was at a Shoe game. A 10-1 DD spread at DD for long sessions is unusual, although it is certainly easier at lower stakes.
You may want to consider busting your post. You have identified you play strategy and the general location of the game. Casinos spies can lurk here for Free. It is possible that someone from one of your local stores will read this and pay more attention to you.
Unfortunately, I don�t remember the reference to me that you are referring to. But thanks for the compliment.
I am not sure what to say about your proposed strategy. But getting $100 EV an hour on a bankroll of 100K doesn�t sound like a very good return to me. And any of the bad things that you mention could occur.
They may reshuffle. They may have someone come over and count the discards. When they see the deck is loaded, they may order a Reshuffle.
I would like to once again encourage you to join Green Chip. Try it for a quarter. I think is is only a little over $12 for the first quarter. You don�t have much to lose by trying it, and I think you will find it a valuable resource.
MathProf's post is interesting;
I tuned in after Feanor's post was gone, and so I'm curious about the
"loaded deck" -- no need to respond anyone though.
I'll just note that I think probably those noting the value of
GreenChip (MathProf, and DD' in the thread where I've been tormenting
him) are probably correct -- GC sounds like a very good value, and
as soon as I get my time together to play signifcantly again I am
going to join GreenChip.
One question about GreenChip: MathProf notes that casino types can
scan here for free, causing security concerns -- but I've "heard" that
some of them also read GreenChip, don't they?
I believe the main value of it for those in this forum is education. This is an elementary forum that addresses the same elementary issues month after month as different groups of users come and go. For the price, you'd do well to join even before you start getting in any significant play. It is not a major investment and there are also general interest forums, like politics, stock market/investing, laws and taxes, poker, etc.
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