Math confirmation wanted for a casino dispute...

[Justin7]

A player plays 3531 hands of Blackjack, betting a fixed amount on each hand. Assume the house edge is 0.5%, and standard Las Vegas strip rules for everything (I'm slightly overestimating the house edge).

What are the odds that the player suffer a net loss of 250 bets in this period, assuming he plays perfect basic strategy, and there is a shuffle after every hand?

[Matt Rain]

I can't provide the math... but I've (auto)played 100,000s of hands online and 250 bets over 3500 hands seems to be within the realm of possibility.

This might help:

http://wizardofodds.com/blackjack/appendix4.html

According to Shackleford's math, such a bad run is bound to happen once every ~10000 sessions of ~3500 hands.

[UntilTheNDofTimE]

if the deck is reshuffled after every hand wouldnt the same edge Given a 6 deck shoot be different, basically ud be dealing with a unlimited deck, not sure how the logarithym works here

[Justin7]

I can't provide the math... but I've (auto)played 100,000s of hands online and 250 bets over 3500 hands seems to be within the realm of possibility.

This might help:

http://wizardofodds.com/blackjack/appendix4.html

Thanks for the link. This suggests it is about 1 in 10,000. This is a far cry from the 6% chance the book quoted.

I'll give more facts later, but I need to keep exploring this. This one could get interesting.

[UntilTheNDofTimE]

So basically your confirming that online blackjackvprababilities are skewed? As everyone nos, the law of variance has no effect on online softwares because ive spoke with friends of writters and those softwares are written to yield guarenteed % per number of hands, alot higher %'s than the standard

[Justin7]

So basically your confirming that online blackjackvprababilities are skewed? As everyone nos, the law of variance has no effect on online softwares because ive spoke with friends of writters and those softwares are written to yield guarenteed % per number of hands, alot higher %'s than the standard

I've been involved in the development of casino games at an "A" rated book. The game is fair, and the house edge is comperable to a good Las Vegas Strip game.

If you can prove that a good rated book is cheating players - doing what you suggest - it would be news to me. Do you know of a book that does this? I don't think "everyone nos" this.

[betplom]

So basically your confirming that online blackjackvprababilities are skewed? As everyone nos, the law of variance has no effect on online softwares because ive spoke with friends of writters and those softwares are written to yield guarenteed % per number of hands, alot higher %'s than the standard

I agree with you on this, a software programmer will likely do what he's asked by his customer, not wanting to bite the hand that writes the check.

Math is math but programs do what the programmer tells it to do, so you can never be sure of anything, only the person/s that wrote the software know for certain.

[UntilTheNDofTimE]

I wont disclose the 2 books but i will say there not A rated books i play alot of blacjack about 10 hours per week in live casinos, and ive tested it out online and tryed out many softwares but in the end the fact that the deck is reshuffled every hand kind of throws out some elements, and of course the greatest element counting cards,

[tacomax]

A player plays 3531 hands of Blackjack, betting a fixed amount on each hand. Assume the house edge is 0.5%, and standard Las Vegas strip rules for everything (I'm slightly overestimating the house edge).

What are the odds that the player suffer a net loss of 250 bets in this period, assuming he plays perfect basic strategy, and there is a shuffle after every hand?

Most important question with any thread of this type - what software was the guy playing?

[Mac4Lyfe]

A player plays 3531 hands of Blackjack, betting a fixed amount on each hand. Assume the house edge is 0.5%, and standard Las Vegas strip rules for everything (I'm slightly overestimating the house edge).

What are the odds that the player suffer a net loss of 250 bets in this period, assuming he plays perfect basic strategy, and there is a shuffle after every hand?

If the house's edge is 0.5% as you quote than you take away everything else, how many decks, how good/poor is the player, counting of cards, etc...

A 0.5% edge would mean that in 3531 hands you would have a net loss of 3531 * 0.005 = 17.65 hands

If you loss 10% it would be 353.1 hands... 250 hands would mean 7% loss rate which is not out of the ordinary if you take in consideration high and low bets for example.

The net effect of table games isn't the house edge because even a low edge will kill you in the long run. It's the GRIND that eats up your stack... http://vegasclick.com/gambling/houseedge.html

[Matt Rain]

I wont disclose the 2 books but i will say there not A rated books i play alot of blacjack about 10 hours per week in live casinos, and ive tested it out online and tryed out many softwares but in the end the fact that the deck is reshuffled every hand kind of throws out some elements, and of course the greatest element counting cards,

Pretty sure that every online casino reshuffles after each hand. One casino, I forget which, was claiming x amount of deck penetration at one point, but I doubt it's still around.

[betplom]

Pretty sure that every online casino reshuffles after each hand. One casino, I forget which, was claiming x amount of deck penetration at one point, but I doubt it's still around.

They can say whatever they want/believe/were told but unless they allow an independent programmer to look at the source code you cannot be certain about anything.

[Matt Rain]

Like I said, that was their claim.

My own brother coded a blackjack algorithm for a minor player in the online casino biz several years ago and he swears that his mission was to develop a true-to-life blackjack game. Exactly as rigged as the real game sans card-counting.

[UntilTheNDofTimE]

Ill give you a quick example find the true odds of the dealer bustin on a 6 showing, then record the prabability of the dealer busting through 1000 6's , that alone will give you a wild number, about 2-3% gap just there

[Matt Rain]

Ill give you a quick example find the true odds of the dealer bustin on a 6 showing, then record the prabability of the dealer busting through 1000 6's , that alone will give you a wild number, about 2-3% gap just there

No offense, but your posts are nonsensical.

[UntilTheNDofTimE]

Let me find that guys website basically this guy did a test through 3 softwares for different hit stand prababilities and the numbers were all skewed from the true odds from online to live play

[mathdotcom]

A player plays 3531 hands of Blackjack, betting a fixed amount on each hand. Assume the house edge is 0.5%, and standard Las Vegas strip rules for everything (I'm slightly overestimating the house edge).

What are the odds that the player suffer a net loss of 250 bets in this period, assuming he plays perfect basic strategy, and there is a shuffle after every hand?

If you can't answer this question then you shouldn't be helping this A+ book...

[Justin7]

If you can't answer this question then you shouldn't be helping this A+ book...

Wow, is it "Bust Justin's chops night" and no one warned me?

[j0hnnyv]

unreal

[mathdotcom]

Justin, I get a t-statistic of 12,491,667.

ie. impossible that the expected house adv is only 0.5%.

Given he lost 250 bets, the expected house adv was more like ~7%.

[Justin7]

Justin, I get a t-statistic of 12,491,667.

ie. impossible that the expected house adv is only 0.5%.

Given he lost 250 bets, the expected house adv was more like ~7%.

If the unit size average is 1.2, hs is down about 210 bets.

3500 hands. EV at -0.5 is -17.5u. Ignoring short term streaks, he finished 332.5 units below that.

While BJ isn't a perfect 50/50 proposition, it is close enough (after the EV adjustment) that I can use 50/50 for ROR stuff. sqrt(3500) /2 = 29.5 = each 29.5 below the mean is one deviation. So he's about 11 deviations below the mean.

Your T-stat is very close to what mine is (close enough that we're probably doing the same thing). When a book tells me it is a 6% chance, something's definitely wrong. One of us is wrong, and getting a second opinion avoids careless mistakes, and makes for some interesting discussion.

[mathdotcom]

All of this assumes:
1) All bets of same size
2) He did indeed play "perfectly", which would include not splitting/doubling incorrectly, etc.

Book is rogue

[onthewhat]

12 standard deviations?

lol...

[tacomax]

12 standard deviations?

lol...

Nicky's IQ is 12 standard deviations under the mean, and some people still act like he's the Second Coming. Unreal.

[reno cool]

I'd like to know in what capacity they're making this claim. Are they claiming to have a fair game and busting people out at this rate 6% of the time?

[u21c3f6]

If the unit size average is 1.2, hs is down about 210 bets.

3500 hands. EV at -0.5 is -17.5u. Ignoring short term streaks, he finished 332.5 units below that.

While BJ isn't a perfect 50/50 proposition, it is close enough (after the EV adjustment) that I can use 50/50 for ROR stuff. sqrt(3500) /2 = 29.5 = each 29.5 below the mean is one deviation. So he's about 11 deviations below the mean.

Your T-stat is very close to what mine is (close enough that we're probably doing the same thing). When a book tells me it is a 6% chance, something's definitely wrong. One of us is wrong, and getting a second opinion avoids careless mistakes, and makes for some interesting discussion.

Honestly, I try to keep my "math" computations as simple as possible so I don't do nor am I familiar with how to use the "higher" math that is posted here at times. I will post this for what it may be worth which is possibly nothing. I am not exactly sure what you mean by the 50/50 proposition but on average (may not be exact) the dealer wins 48%, player 42% and push 10%. The player draws closer to breakeven because of the 1.5 payoff for BJ (I forget what % of hands are BJs). So in 3889 hands, 3500 hands removing pushes, the dealer would win on average 1867 hands and the player 1633 hands for a difference of 234 hands.

Joe.

[mathdotcom]

Joe

Not all wins are created equal. It's not all about the # of winning hands. You can win a bet and get 1 unit, or for example you can get a blackjack and get 1.5 units. Think of it in terms of flipping coins with a friend, except that Heads has a 50.5% chance of turning up, and you're forced to always choose Tails. If you flip the coin 3531 times, what're the odds you lose $250 betting $1 each coin toss? That is Justin's question.

[Matt Rain]

While I can't back my argument with any kind of significant math, it seems to me that variance in blackjack is quite a bit higher than it is in a series of coin flips. No?

[WileOut]

Matt it is not much variance. A 0.5% edge means that out of every 200 hands, the book is expected to win 1 more hand than the player on average, am I right here?

Guys we all know the online books BJ software is built to take your money at a very high rate. I think most of us have found that out the hard way.

[Matt Rain]

Variance has little to do with the house edge and more to do with the rules of the game. For example, full-pay Jacks or Better (video poker) has a tiny house edge (0.46%) but massive variance. One can easily lose a hundred bets over 500 hands.

House edge and standard deviation table for most common casino games:

http://wizardofodds.com/houseedge

[reno cool]

BJ is surprisingly volatile. Just looking at the example given I would say that such a streak is not ridiculously unusual. not 6% of the time of course. But the luck factor is a bitch.

[donjuan]

Matt it is not much variance. A 0.5% edge means that out of every 200 hands, the book is expected to win 1 more hand than the player on average, am I right here?

That is not variance, but rather expected return. See this for more info: http://en.wikipedia.org/wiki/Central_moment



Justin,

I suck at math but a claim of 6% here is absurd just intuitively. Your conclusion does not surprise me, although perhaps you are slightly underestimating the variance by using 50/50.

[Ganchrow]

Using a house edge of 0.5% and Shackleford's variance figure of 1.1418 and (although I could provide a precise value for the former and an arbitrarily close value for the latter were the exact rules provided) then this would represent a z-score of (250-3531*0.5%)/(1.1418 * √3531) ≈ 3.4245.

This corresponds to a single-tailed p-value of about 0.031%.

Now this analysis of course presupposes perfect basic strategy, which one would expect very few players actually play.

With an effective player disadvantage of 2.61%, for example, p-value jumps to 1%. Certainly not a particularly likely outcome, but hardly outside the realm of possibility.

A p-value of 6%, btw, would necessitate a house edge of about 4.09%. Anecdotally, that doesn't seem unreasonable, although to be sure one would obviously first need to analyze the player's playing decisions.

It should further be noted that were the player doubling and/or splitting more frequently than would be appropriate under basic strategy, then this would serve to even further increase the p-value over and above that which could be attributed to poor play alone.

[tacomax]

While I can't back my argument with any kind of significant math, it seems to me that variance in blackjack is quite a bit higher than it is in a series of coin flips. No?

Huge variance in blackjack. The player can go on a real hot streak and the computer has to call in a virtual cooler to stop him bringing down the house.

[acw]

That Justin7 has no idea what he is talking about is not new to me, but that even Ganchrow misses the main point really starts to worry me.

This corresponds to a single-tailed p-value of about 0.031%.
I am simply assuming that this is right. Not in a mood to double check it all. So on a stretch of 3500 hands there is a 1/3000 chance that one will lose 250 units. So how many online Blackjack players are there out there? 10,000? How many hands may they play a year on average? 10,000? So how many (how often) will bump into a loss of 250 units over 3500 hands? Trust me enough to have at least one now knock on Justin7's door that is playing at a A+++ book.