VC Casino -- Fair BJ?

[ThodorisK]

Then this other calculator that I used, is wrong in estimating risk of ruin?
It does calculate for negative win rate.

 

[aka23]

Then this other calculator that I used, is wrong in estimating risk of ruin?
It does calculate for negative win rate.

It may produce different results because of card counting assumptions, rather than basic strategy assumptions. For example, card counters often use a varied bet size, rather than a flat bet size. This, of course, influences risk of ruin.

 

[ThodorisK]

I just remembered that the results of this "wrong" calculator were matching with the "risk of busting" tables of your site! I am getting nuts now! I have to make some tests.

 

[ThodorisK]

I just found the answer! The "risk of ruin" probability IS NOT the "ending up below expectation" probability. The "risk of ruin" SHOULD BE HIGHER than the "ending up below expectation", as the "risk of ruin" is the probability reaching the point of -123 units for the first time, whereas the "ending up" implies that one has passed that -123 point many times before ending up there. And therefore, it is much more ... lets say "probable" for the bankroll to pass for the first time the -123 point, that to ... pass it many times!

Your answer was wrong, to my question of why there is a difference between these 2 different values of 18.74% and of the 10%.
You implied that they should be the same thing! You even went that far as saying that the difference in these values proves that calculator as wrong!
Strange, as in your site it is clear that you have grasped the difference between these 2.
I made you (unwillingly) to fall into this trap by implying with that question of mine that these two different probabilities should be the same one thing. But if I had grasped the difference, I would not had this question. Anyway, matter solved. And that calculator I used is correct.

 

[ThodorisK]

Now to identify cheating, the more appropriate of these two different probabilities, is the "ending up below expectation" probability, as this refers to a greater number of hands played, i.e. all the hands played.
However, when the experiment is finished when one runs out of money (when the bankroll becomes 0), then these 2 probabilities become the same one thing.

 

[ThodorisK]

And therefore, it was a theoretical mistake of mine to use any risk of ruin calculator or formula when I still had money left in my account AND when my balance had previously fallen below the ending balance.

 

[ThodorisK]

I am still doubting if my above formulas are right though. I am trying to use your calculator to verify them, but I still dont understand your calculator. I used your directions, but ...

 

[aka23]

You even went that far as saying that the difference in these values proves that calculator as wrong!

I did not say that, nor did I say anything to that effect. I said, "I don't know how that calc works or if it is even applicable to a negative win rate. I do know how the calc on my site..." I stand by this statement. The calculator you linked to is intended to be used with card counting in which the player gains money over time, hence the positive win rate (equivalent to 1.2% player edge). There may be other assumptions related to card counting that are inherent to the calc as well.

Yes, you are correct that "risk or ruin" is not applicable to the situation for different reasons. That is not what we are measuring in this situation, so the calc results aren't expected to match. I missed that earlier, as I did not look at the other calc in detail.

 

[aka23]

I am still doubting if my above formulas are right though. I am trying to use your calculator to verify them, but I still dont understand your calculator. I used your directions, but ...

My calc reports the average gain, range of gain, and chance of making a gain. It is not designed to measure chance of a loss, but this information can be obtained. If you program the bonus size to the size of your loss, then the chance of losing this amount is 1 - chance of gain. The final complication is that you listed the hands played, rather than amount wagered. These two values differ because of splits and doubles. A simple trick to account for this difference is to change the final bet:initial bet ratio from the default to 1.

 

[ThodorisK]

I did what you said, I put 123 at the bonus box, and I get a chance of gain = 0.511. That means a 1-0.511=48.9% to lose 123 units?! Obviously I do something wrong. Should't I get 10%? It also says "expected return"=107.86.

 

[ThodorisK]

"chance of loss"? Chance of ending up below 123 units you mean?

 

[aka23]

I did what you said, I put 123 at the bonus box, and I get a chance of gain = 0.511. That means a 1-0.511=48.9% to lose 123 units?! Obviously I do something wrong. Should't I get 10%? It also says "expected return"=107.86.

You said you lost 150.5, so put that in the bonus box. Change "wagering" to hands played. Change "bet size" to your bet size.

 

[ThodorisK]

The post in which I use the "z" formula was for calculating the probability of ending up with a loss greater than 123 units (or bets). So what I want is to verify my formula somewhere.

 

[ThodorisK]

150.5$/1.22$=123 bets

 

[aka23]

The boxes must all be in a common unit.

If this unit is $, then enter it as follows:
Bonus - 150.5
Bet Size - 1.22

If this unit is betting units, then enter it as follows:
Bonus - 150.5/1.22 = 123
Bet Size - 1

 

[ThodorisK]

Here's your calculator and what I put and get:

Bonus: 123
Wagering: 5607
Bet Size: 1
Hands: 5607
House Edge (%): 0.27
Standard Deviation: 1.16
Final Bet: Initial Bet Ratio: 1

And the results it gives:

Expected Return: 107.86
Chance of Gain*: 0.511
1 Standard Deviation: -3777.41 to 3993.13
2 Standard Deviation: -7662.68 to 7878.4

How did you conclude that the probability of ending up with a loss of 123 bets (or greater loss), is 10%?
Also, I dont understand the -3777.41 to 3993.13 and -7662.68 to 7878.4

 

[niklas]

You should only put a value in the hands field if you play multi hand blackjack. You're telling the calculator to calculate the expected results when playing 5607 hands in one round of blackjack, which of course isn't possible, but explains the huge variance reported.

 

[ThodorisK]

I wrote in a previous post:

"...The "risk of ruin" probability IS NOT the "ending up below expectation" probability. The "risk of ruin" SHOULD BE HIGHER than the "ending up below expectation", as the "risk of ruin" is the probability reaching the point of -123 units for the first time, whereas the "ending up" implies that one has passed that -123 point many times before ending up there. And therefore, it is much more ... lets say "probable" for the bankroll to pass for the first time the -123 point, that to ... pass it many times!"

I have to correct this, I made many mistakes in expressing what I meant. This is what I meant:

(In each hand an initial bet of 1 unit of bankroll is wagered)

The risk of ruin probability of losing a bankroll of 123 units (until 5607 hands are played), is not the same thing with the probability of ending up with a loss of at least 123 units (after 5607 hands are played).

When one uses the risk of ruin probability of losing a bankroll of 123 units (until 5607 hands are played), which is 18.74%, what he finds is the probability that the balance will reach a downfall of 123 units. And this means the first time the balance reaches that -123 point.

Whereas the probability of ending up with a balance of -123 units or lower (after 5607 hands are played) , means that BEFORE that happens, the balance MAY HAVE passed from the -123 point either once, or many times.

Therefore the risk of ruin probability of losing a bankroll of 123 units (until 5607 hands are played), is higher than the probability of ending up at a balance of -123 units or below (after 5607 hands are played). Because it is more probable to reach the -123 point only once (until 5607 hands are played), than to pass from the -123 point once or many times (in 5607 hands) before ending up at the -123 point (after 5607 hands are played).

I was confusing these two different probabilities, and that is why I was wondering why the 18.74% result was not the same with the 10% result.

 

[happygobrokey]

the way i understand it with the figures given is that the expectation after 5607 hands of $1 with 123 to start with is 107.86. you are below expectation if after 5607 hands your balance is less than 107.86. the risk of ruin is the likelihood that you would lose the full 123 in those 5607 hands.

and i don't know what all the hooplah is now. i found their games to be fair, albeit somewhat strange in the actual hands produced (dealer rarely holds a ten in the hole, but often draws to a winner). but i broke roughly even every time i played there to earn a bonus.

 

[kingkong098]

Just want to chime in and say Chartwell is by far the most streaky blackjack I have ever seen. It is a regular occurence to win or lose 12 bets in 10 hands which are both +/-3SD happenings. The swings are truly sick and not for the faint of heart. I wish there was a way to export the log reports that you can view on the website si I ciuld graph my results.

The swings are not limited to blackjack. I can't count the amount of times I have gone 15 hands in Pai Gow without a victory. I've had sessions where I win 14 games in 100 and others where I've won 40.

Finally, 4 handed VP. In JOB normally when you hold 4 cards to a flush, you will get at least 1 flush a good portion of the time. I had a session the other day where 11 consecutive times I held 4 to a flush and did not make the flush. What are the odds of holding 4 to a flush and missing 44 consecutive times? Astronomical I would think. Later in the session though I held 4 to a straight flush(open ended). I made the straight flush on 3 of the 4 hands, for a nice win.

My long term results are pretty close to expected, probably a little over actually, but it us very odd why I consistently have sessions that fall far away from the expected return.

 

[ThodorisK]

Happygobrokey, I dont know if you really misunderstood this because of the confusion with Nolan's calculator inputs I post in the above post No 41, or if you try to confuse others. These inputs were a copy of Nolan's calculator as I tried to follow his instructions he gave me. Forget about them. I am still confused about Nolan's calculator, but since I prefer to understand the matter in depth, I prefer to do it manually so that I see what exactly I am doing with the normal distribution.
The 123 is not the starting balance - initial bankroll as you implied. The 123 is the loss in units of bankroll after playing 5607 hands. The expected loss was (as you see in a previous post of mine), the value of 15.14 units of bankroll (which perhaps I calculated wronlgy, as I assumed that the initial bet is equal to the final bet, but anyway, the right figure is about the same. In the future I will use the total wagered amount of money to calculate this, a data which I ignored in my previous analysis. So, if I wagered e.g. 6000$, the expected loss is 6000*house edge = 6000*0.27%=16.2$. So, I finished far below "expectation", i.e. far below the average-expected loss.

 

[ThodorisK]

I am forced to give a name to these two different probabilities-methods of prooving cheating:
1.) The one is the “ending up that low or below” which is the hypothesis test using the Normal Distribution I did in a previous post.
2.) And the other is the “risk of ruin” ,which is the application of the risk of ruin formula when it is applicable to prove cheating. The definition of this when is exactly the definition of this second method.

Besides the misconception one might fall (as I did), that made me use the risk of ruin probability where it was not applicable (and got the wrong result of 18.74%), one could also make the below (and I think reverse) misconception:

When one decides to finish taking down the stats at a point where his balance is at the lowest point it was ever observed during the hands of these stats, (e.g. because the balance dropped to zero and he would need to redeposit to continue), then the probability of risk of ruin and of the probability of “ending up that low or below”, are not the same, as one might expect with a first, shallow thought. Why is that?

The probability of “ending up that low or below” presupposes that the number of hands of the sample is not depended on the condition that the player can decide to stop counting his stats when his balance is lower than any other time during the history of these hands. Such an independency is assured when e.g. the number of the hands of the sample is predetermined before the hands start happening, e.g. until meeting a bonus wagering requirement.

Therefore if the player stops counting his stats when his balance is at its lowest point, this creates a bias which makes the probability of “ending up that low or below”, not applicable and false if applied to prove cheating. But in this case, the probability of risk of ruin IS appropriate to use in order to prove cheating! E.g. in the case that one loses all his deposited bankroll, he can claim as a proof of cheating, the very low risk of ruin probability of losing X units of bankroll in Y number of hands (for this I use the calculator

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)

One might claim that the only valid method-probability for proving cheating is the “ending up that low or below”. But I disagree: Suppose one plays 10,000 hands at a game of 0.3% house edge, placing 1$ on each hand. And suppose that the final results do not indicate cheating with more than a 75% certainty, eg. he finally loses only 140$. But before these 10,000 hands were completed, at the 6459th hand his balance had fallen to an amazing -2000$ below the starting balance – initial bankroll (!!!), and after that, it raised back to the point of -140$ below the starting balance, which is not extremely far from expectation. Now the method of “ending up that low or below” ignores that fall of -2000$!!!

Therefore, the risk of ruin probability can also be used for proving cheating, by referring to the lowest point that the account balance (current bankroll) fell below the starting account balace (initial bankroll), or referring to a very large downward swing of the account balance, that it was met somewhere among the history of hands. So, we have 2 weapons to identify cheating by observing the profit/loss data. I think though, that there might be some additional considerations to apply this, and I am still thinking about it. It might have nothing to do with the risk of ruin probability. Oh, yes, that's it: "What is the probability that the bankroll-account balance to have such a large fall from its highest point to its lowest point (a fall which happens in x hands), after playing a total of y hands? (the highest and lowest points observed in y hands)"

You might have ended up close to the expected loss, but still you might have been cheated. How can one investigate this?

 

[ThodorisK]

“Ending up that low or below” is the probability (or method) for proving cheating e.g. Michael Shackleford used:
“...The difference between actual and expected dealer busts is 149.38-89 = 60.38. This is 60.38/8.84=6.83 standard deviations below expectations. The probability of falling this far or more to the left of the bell curve is 1 in 238 billion...”(

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A small comment on Shackleford’s analysis: He and some other analysts used the dealer’s busting rate. But I think that categorizing the possible methods of cheating might miss some other possible methods of cheating (e.g. the dealer getting ten-ten when the player is getting ten-nine) not to mention the method of cheating that small bets win and big bets lose (and that cannot be identified with a flat bet experiment). I am not saying that my experiment of changing the bet between 1$ and 2$ solved this, nor that I did this change for that reason. But I do say that a flat bet experiment observing only the profit/loss made following basic strategy, might be better, as it takes in consideration all possible methods of cheating, except one: the “small bets lose, big bets win” method.

After I wrote the last above paragraph, I read that the return-payoff (profit/loss) results Shackleford had in his sample of 1245 hands, was 95.7%, something which was absolutely “within expectations” and in no case indicated cheating (as the casinobar representative argues and Shackleford agrees), whereas the dealer’s busting rate indicated cheating with an enormous statistical significance (100% minus 1 in 238 billion), by observing a sample as small as of 332 hands, and which sample was a sub-sample of the same 1245 hands sample! So I wonder, we shouldn’t examine the return (profit/loss) but only the busting rate, as this proves cheating much more effectively and revealingly? So, my above arguments are wrong? The dealer’s busting rate is the best indicator, and the return-payoff (profit/loss) stats are relatively useless? But if this the case, I wonder how is it possible that so extremelly low dealer busting rates did not create a statistically significant departure in his return (profit/loss) results from the expected loss. Does the casino have to cheat that much in the busting rates in order to earn that little? Or did he get lucky in all other respects of the game (e.g. he was getting ten-ten when the dealer was getting ten-nine)? If a casino has to cheat that much regarding one variable only, e.g. the busting rates, to generate only a little return, that shows its inability to cheat in all other variables of the game?

I know I am getting more and more difficult to grasp, but I cannot make more understandable what I mean in a short time and in a short text (those unfamiliar with estimation and hypothesis testing of the Normal Distribution will not grasp most of this)

 

[winbig]

I could go play 10,000 hands @ $1 a hand at a B&M casino and be down $2000 easily.

Are they stacking all 8 decks in the shoe against me, and the others at the table?

 

[happygobrokey]

shackleford knew when preparing the experiment that he was looking for this. as you said yourself there are other ways of rigging the cards. and only because the results were astronomically biased did he require such a small sample. if the dealer had been busting closer to the expected rate, then obviously it would take more data to prove a more subtle rig. i mean, when your data shows a 1 in 238 billion already, there's no need to continue because obviously your stats are not all random variance.

and i don't know what you were saying in that post you made with the small typeface. it seemed to me you were having trouble with the expected loss and risk of ruin, so i tried to offer a simple explanation to help out. but i guess your calculations are far beyond my comprehension (15.14=123-107.86 btw, so i was perfectly correct about the expected loss). and in that scenario, the "risk of ruin" taking 123 to be the full bankroll would be equal to the chance of being down that much (albeit if you had more than this 123 then you could keep playing if you had not completed the 5607 hands in the test and get some back). aka's calculator is meant to take the value of the bonus money and predict how much of it on average you stand to lose, and the "risk of ruin" would correspond to losing the whole bonus, but does not factor in the additional money that is the deposit.

i definitely don't try to confuse people or whatever you said, but indeed i try to help those who seem confused. i was genuinely offering my simple, concise take on what i thought the issue between your's and aka's understanding was. and if i'm not mistaken you asked aka what the "sigma" symbol stood for, but considering your skill with the normal distribution, you should know all about sigma being the standard deviaton and sigma squared, the variance. the question then, is how many sigmas down is the event of losing 123 when the mean expectation is to lose 15.14? so sorry i mistook you for being the confused one, apparently it is i who lacks knowledge on the subject and should just shut up so you can complete your calculations. but you did post here on a forum for help and ideas, forgive me for trying to contribute.