Bad Session or Rigged Game?

Looking at risk of ruin probabilities, at what percentage of probability would you consider a loss to be "statistically improbable"? For example, if I estimate a loss in one session of video blackjack has a probability of about 0.3%, or 1 chance in 333, should I be suspicious?

A 0.3% ROR would be something I would be comfortable with. I would say statistically improbable is outside 2 standard deviations, which I believe is somewhere around 97-98%, so a 2-3% chance would be reasonable.

Quote: jackblack21

Looking at risk of ruin probabilities, at what percentage of probability would you consider a loss to be "statistically improbable"? For example, if I estimate a loss in one session of video blackjack has a probability of about 0.3%, or 1 chance in 333, should I be suspicious?

A 1 in 333 chance occurence is unusual, but not nearly enough to warrant suspicion. For example, the dealer getting two blackjacks in a row is a little more than 400 to 1 against, but would that alone cause you to quit the game and never come back?

Quote: teddys

A 0.3% ROR would be something I would be comfortable with. I would say statistically improbable is outside 2 standard deviations, which I believe is somewhere around 97-98%, so a 2-3% chance would be reasonable.

Not sure I made myself clear. I'm not trying to determine if a 0.3% ROR would be acceptable based on my bankroll, bet size, etc before starting a session. I'm saying if I actually sustained a loss in a session that only had a 0.3% probability of occuring, should I be suspicious the game was rigged? If not, what magnitude of loss should arouse suspicion?

Quote: mkl654321

A 1 in 333 chance occurence is unusual, but not nearly enough to warrant suspicion. For example, the dealer getting two blackjacks in a row is a little more than 400 to 1 against, but would that alone cause you to quit the game and never come back?

I'm not doubting your conclusion, but I think your example of two blackjacks in a row is not a good comparison. You're looking at the probability of something happening in 2 consecutive hands - there are many, many sets of 2 consecutive hands in just 1 session of play. We're talking about the probability of something happening over an entire session, and there are many less sessions played than there are 2 consecutive hands played.

Quote: jackblack21

I'm not doubting your conclusion, but I think your example of two blackjacks in a row is not a good comparison. You're looking at the probability of something happening in 2 consecutive hands - there are many, many sets of 2 consecutive hands in just 1 session of play. We're talking about the probability of something happening over an entire session, and there are many less sessions played than there are 2 consecutive hands played.

Obviously, my example was meant to be taken in CONTEXT. If the dealer got two BJs in a row at the very start of your session, that would be one thing. If that happened sometime during a long session, that would be something else altogether. Similarly, you did not give any context for YOUR example. Is that a single, isolated session, or an unusual result in a series of sessions?

That's why I used a simple blackjack-related example to illustrate that a few-hundred-to-one against occurence isn't noteworthy enough to cause suspicion (paranoia, perhaps, but...).

0.3% is less than 3 standard deviations from the norm. Not suspicious enough, especially if this wasn't your first session with this machine. If this was your first session with the device, I would be a little more suspicious, but it's not enough to claim foul play.

My personal limit is around 4 standard deviations. That starts to get improbable...

I don't know what anyone in this thread is really talking about.

Of course it might help if I ever understood just what a standard deviation is.

Anyway, Risk of Ruin is, as I understand it, a figure to be determined BEFORE you start to play and should not be considered after a session.

Most gambling sites seem to discuss a Ten Percent Risk of Ruin or a Five Percent Risk of Ruin though I'm not quite sure what they are talking about.

I know that on the "minus" side people can get suspicious of a rigged game but when its on the "plus" side any unusual result is because they are lucky or skillful gamblers but their good fortune is never attributed to a croupier having a brake on the wheel. The existence of a brake on the roulette wheel is only contemplated at an unusual loss, not an unusual profit.

I think the poker term is Bad Beat ... a very fluid term apparently meaning A Darned Good And Rarely Obtainable Hand Being Beaten By a Darned Better And Even More Rarely Obtainable Better Hand.

Sometimes Lady Luck ....ooops, Lady Variance, holds that Rarely Obtainable Better Hand but quite often players think that Better Hand was originally held by the Dealer's Sleeve.

Is there a mathematical point at which you would be justified in reaching out and yanking the dealer's cuffs? I guess so. Sure wish I understood what a standard deviation was.

Quote: FleaStiff

Is there a mathematical point at which you would be justified in reaching out and yanking the dealer's cuffs? I guess so. Sure wish I understood what a standard deviation was.

I'm willing to yank the dealer on just about any pretext whatsoever.

Standard deviation is the square root of variance. Does that help? Of course not.

Think of the bell curve. Plot "height of adult males in the US". The curve would be pretty tall, and wouldn't taper much on either side. This is an example of low standard deviation. Now plot "income of adult males in the US". This curve would be pretty flat, and would taper pretty far in each direction. This would be an example of a large standard deviation.

In statistical sampling, a result within two standard deviations of the mean is considered to have a "confidence interval" of 95%. This is just a fancy way of saying that 95% of all results are expected to fall within those two standard deviations. So if the mean height of American males was 5 foot 9, and the standard deviation was three inches, then 95% of all males would be between 5 foot 3 and 6 foot 3.

This has applications in the gambling world. The higher the variance, the higher the standard deviation; the higher the standard deviation, the flatter and longer the bell curve. The flatter and longer the bell curve, the wackier your results will be.

Quote: mkl654321

Obviously, my example was meant to be taken in CONTEXT. If the dealer got two BJs in a row at the very start of your session, that would be one thing. If that happened sometime during a long session, that would be something else altogether.

In the spirit of the context of your example I would not be surprised or alarmed to see the dealer get 5 or 6 blackjacks in a row.

Quote: mkl654321

Similarly, you did not give any context for YOUR example. Is that a single, isolated session, or an unusual result in a series of sessions?

In my mind at least, this is difficult to quantify. Here's why. This was the only session I ever played for this long, about 7500 hands. But of course, the only reason I played so long was because I was trying to dig back out of a hole as the dealer drug me to the pits of hell starting from the first hand. Insert random thought - my dealer's name is Bruce. Sure, I've played hundreds of sessions, but the majority of them were for a few hundred hands or less. Should all sessions be compared equally regardless of how long they are? Who knows.