Quick math question for the Wiz

Mike Shaq,

Can you figure out for me the odds of hitting 3 royals (jorbetter) using perfect strategy in 9000 hands? Also can you give me the odds of hitting 5 royals in 13000 hands?

I would appreciate it if you explained how you came up with your answer.

1. First determine the number you should get n the specified number of hands. Call that m. So in 9,000 hands you should hit 9,000/40,000=0.225.
2. The formula for the event in question happening exactly n times is e^-m*m^x/x!.

In the case of your first question, the odds of exactly 5 royals is e^-0.225*0.225^5/5! =~ 1 in 261,000.

I really wanted the odds of hitting exactly 3 royals in 8862 hands. Can you show your work?

Thanks for your help with this. There is a book (with casino) out there that is trying to call foul on a player who hit 3 royals in 8862 hands. They are claiming that he used a bot and that he manipulated the software to produce the royals as it was mathematically impossible to do what he did. I have been defending the guy and wanted help with the math. I used a calcualter and got P = 0.0014518789445248 of hitting exactly 3 royals which isn't all that impossible.

Oh and this book is stiffing this guy out of $46,000

Quote: kengam77

the odds of hitting 3 royals using perfect strategy in 9000 hands?

While you are all using a calculator and I am removing my shoes, could we determine:
How long does it take to play 9,000 hands of Video Poker.
What are the odds of someone who is skillful at VP being able to actually remain alert and make no mistakes during that time period?

Quote: kengam77

Oh and this book is stiffing this guy out of $46,000

I wonder if they even bothered to determine the odds of it being legitimately accomplished before they decided to stiff him? Since this is an online casino/sports-book somewhere, just what can ever be done about it?

Quote: kengam77

I really wanted the odds of hitting exactly 3 royals in 8862 hands. Can you show your work?

I just showed you how to do it yourself.

Depends on the software. If the softare auto holds winning hands and if they have a fast deal button you can play much faster. The casino in question does both. I am very experienced and I havo no problem playing 18-19 hands per minute. A novice would play at about 12 hands per minute.

Quote: FleaStiff

I wonder if they even bothered to determine the odds of it being legitimately accomplished before they decided to stiff him? Since this is an online casino/sports-book somewhere, just what can ever be done about it?

Honestly the guys running the show are clueless. I don't think they were planning to pay this guy and wanted to use bot play as an excuse. They contend that he didn't even stop to admire his $20k royal and dealt another hand 4 seconds later. The logs actually showed that he hit the Royal, played another hand 4 seconds later and then took a 19 minute break from play. That sounds pretty realistic to me.

I am trying to help this guy get paid, which is not going to be easy. The book will take a public hit especially since they are a "forum book" to begin with.

Name and shame? Or can you direct me to the forum where all action is being discussed? Assuming thats ok with the Wiz?

Another way to get the answer is combin(8862,3)*p^3*(1-p)^(8862-3) = 0.001413192, where p = 493512264/19933230517200 (data from here.) This answer is about 1/708, so if 708 of the book's customers each played 8862 hands of jacks-or-beter, one of the players would be expected to get exactly 3 royals.

That's bullsh*t and shameful. Name the operator, they don't deserve to be anonymous.

Quote: teddys

...they don't deserve to be anonymous.

To find the offending site, search Google for this: 8862 royals stiffs

Quote: WizardofEngland

Name and shame? Or can you direct me to the forum where all action is being discussed? Assuming thats ok with the Wiz?

I wasn't sure about linking the story, but I willl try as it really gives you agood idea about corrupt shops and the forums they are in bed with.

The book is EasyStreet Sports. SBR was originally handling the dispute here: http://forum.sbrforum.com/sportsbooks-industry/988271-easystreet-casino-winner-accused-using-robot-software.html

when EasyStreet didn't like the answers they got from SBR they then went to TheRX where they advertise. The Moderators continue to defend the book there even in light of the evidence against them. Here is the thread there.: http://www.therxforum.com/showthread.php?t=768502

Keep in mind The Rx has post reviewed or banned some of us who have defended the player in question so all the posts didn't go through. Both threads are very long, but also very good reads.

Quote: kengam77

Honestly the guys running the show are clueless. I don't think they were planning to pay this guy and wanted to use bot play as an excuse. They contend that he didn't even stop to admire his $20k royal and dealt another hand 4 seconds later. The logs actually showed that he hit the Royal, played another hand 4 seconds later and then took a 19 minute break from play. That sounds pretty realistic to me.

I am trying to help this guy get paid, which is not going to be easy. The book will take a public hit especially since they are a "forum book" to begin with.

So are there people out there using bots to play quickly and perfectly? didnt know that, but why would you unless it is a positive EV situation?

Quote: odiousgambit

So are there people out there using bots to play quickly and perfectly? didnt know that, but why would you unless it is a positive EV situation?

Yes there are people who use bots. For a long time, I was one of them. If you do a bonus deal where the roll over is big then it can make the task a lot easier. Bots can make mistakes if you program them to. They can also take breaks and pause if you set them up to do that. The bot I used could do just about anything, and was completely undetectable. I used it to play close to 10 million hands of BJ and about 5 million hands of Video Poker among other games.

Quote: kengam77

Yes there are people who use bots. For a long time, I was one of them. If you do a bonus deal where the roll over is big then it can make the task a lot easier. Bots can make mistakes if you program them to. They can also take breaks and pause if you set them up to do that. The bot I used could do just about anything, and was completely undetectable. I used it to play close to 10 million hands of BJ and about 5 million hands of Video Poker among other games.

Amazing. But I was thinking these online casinos always set up the bonuses so that there were rules making it impossible to really profit, at least nowadays.

Quote: odiousgambit

Amazing. But I was thinking these online casinos always set up the bonuses so that there were rules making it impossible to really profit, at least nowadays.

some casinos have and some haven't. It is clearly not as lucrative as it once were, hence my retirement from chasing the bonuses. The casino in question had a 25x rollover in the casino on 100% bonuses. Playing a 99.54% payback machine gives a clear advantage to the player even considering the rollover.

I just looked over the thread about this at forum.sbrforum.com. Briefly, it seems that easystreetsports.com doesn't want to pay a winner because:

1. He hit 3 Royals in 5848 hands. The probability of that is 1 in 2,200. Certainly no reason not to play a player.
2. He played too fast, indicating bot use. The allegation is he played 5848 hands in 326 minutes. That is 1,076 hands per hour. The best of VP players can play that fast on a real machine. I'd have to give the player the benefit of the doubt there too.
3. Something about a charge-back at a sister casino. I don't know about that, but if they don't like it, they shouldn't have opened an account for him in the first place.
4. Something about refusing to take a lie detector test in Costa Rica. That is just bizarre.

Of course most of the information seems to be from the player's point of view. If anybody knows the player he is welcome to contact me directly if he would like me to investigate, for possible addition to my blacklist.

Interesting and thought provoking.

Quote: kengam77

Honestly the guys running the show are clueless. I don't think they were planning to pay this guy and wanted to use bot play as an excuse. They contend that he didn't even stop to admire his $20k royal and dealt another hand 4 seconds later. The logs actually showed that he hit the Royal, played another hand 4 seconds later and then took a 19 minute break from play. That sounds pretty realistic to me.

I am trying to help this guy get paid, which is not going to be easy. The book will take a public hit especially since they are a "forum book" to begin with.

Yet another example of why it's truly insane to play with real money in an internet casino. You win, they refuse to pay you, what can you do about it? Zippo, zilch, nada. You can try to trash them on the internet, but that won't get you your money back.

Here is a link to Easystreet's "expert's" report as the basis of their refusal to pay the player:

http://www.therxforum.com/showthread.php?t=838354&p=8601418&viewfull=1#post8601418.

I'm giving easystreet a chance to respond before I add them to my blacklist.

Never having signed up for an on line casino, I would assume that there is a page of small print that delineates the resolution of dispute process. Unless it says that 'you must fly to Costa Rica at our expense and take a polygraph test' I would say they must pay the player. I hope EZstreet responds to the Wiz's request.

Quote: Wizard

1. First determine the number you should get n the specified number of hands. Call that m. So in 9,000 hands you should hit 9,000/40,000=0.225.
2. The formula for the event in question happening exactly n times is e^-m*m^x/x!.

In the case of your first question, the odds of exactly 5 royals is e^-0.225*0.225^5/5! =~ 1 in 261,000.

So you used a Poisson distribution here? This seems like a straight forward binomial distribution problem, what's the relation between the two? I understand the EV variance of a Poisson are m, but are the distribution interchangeable like that?

Quote: Wizard

Here is a link to Easystreet's "expert's" report as the basis of their refusal to pay the player:

http://www.therxforum.com/showthread.php?t=838354&p=8601418&viewfull=1#post8601418.

I'm giving easystreet a chance to respond before I add them to my blacklist.

My vote would be add them to the blacklist immediately based on the following aspects of their message:

1) Players accused of impropriety are deemed guilty until proven innocent.
2) The bar for proof of innocence is a ridiculous threshold, including use of a polygraph (which is almost universally regarded as illegitimate, except by the practitioners of polygraphy).
3) It is statistically impossible to hit 3 royal flushes in less than 9000 hands of VP.
4) Playing fast enough can "overwhelm the RNG" and provide favorable odds to the player.

Perhaps if they rescind those policies, and make an effort to understand the math better, you could remove them from the blacklist. But the Expert's conclusions, especially about the math and EV, are patently ridiculous *unless the software is broken* -- in which case, the player did nothing wrong.

Proper use of expert testimony requires that both sides be able to examine the expert's opinion. That certainly didn't happen here. In this case, if the casino's expert were properly cross-examined, he'd be forced to retract several of his statements, leaving his credibility in tatters.

Typical case of RNG fatigue syndrome. The computer gets tired from being run too fast, and starts dealing royal flashes in hopes, that the player will just go away. Happens all the time.

Of course, but everyone knows that when RNGs get tired they only output zeros instead of both zeros and ones, and all-zeros means the deck doesn't actually get reshuffled between hands.¹ If you ever see a long streak of exactly the same VP hand over and over and over, slow down. You're playing too fast.


¹This is true if you use a standard RNG with the Fisher-Yates shuffle algorithm -- just walk through the steps to shuffle if you always draw zero as the RNG value. This assumes you're iterating from 0 .. n-1 rather than from n-1 to 0; in the latter case the deck would actually be reversed every hand. However, the rest of this message is very much tongue-in-cheek...

Quote: MathExtremist

Of course, but everyone knows that when RNGs get tired they only output zeros instead of both zeros and ones, and all-zeros means the deck doesn't actually get reshuffled between hands.¹ If you ever see a long streak of exactly the same VP hand over and over and over, slow down. You're playing too fast.


¹This is true if you use a standard RNG with the Fisher-Yates shuffle algorithm -- just walk through the steps to shuffle if you always draw zero as the RNG value. This assumes you're iterating from 0 .. n-1 rather than from n-1 to 0; in the latter case the deck would actually be reversed every hand. However, the rest of this message is very much tongue-in-cheek...

Is this less efficient than the Knuth-Fisher-Yates shuffle ?

Quote: buzzpaff

Is this less efficient than the Knuth-Fisher-Yates shuffle ?

Same thing.

My mistake, they are one and the same. Confused K-F-Y with Sattolo's algorithm.

I In a nutshell, the shuffle will be as random as the particular RNG used to implement the algorithm.
An intuitive explanation is that for an array with m element, even though as n, the decreasing control variable of the loop goes down towards 1, the possible cells where the cell at position n may be swapped with diminishes, the probability that this very cell has readily been moved increases in the exact same proportion. In other words, the last element of the array could end-up anywhere in the array, but it has only one chance to be moved (upon the very first iteration). The second to last element to be moved has one less place to go but there is a probability of 1/m that it may readily have been been moved during the very first iteration. etc.

Quote: weaselman

Typical case of RNG fatigue syndrome. The computer gets tired from being run too fast, and starts dealing royal flashes in hopes, that the player will just go away. Happens all the time.

*applause*

Quote: MathExtremist

3) It is statistically impossible to hit 3 royal flushes in less than 9000 hands of VP.

I thought this statement was laughable as just this weekend I ran some sims for someone and got 2 Royals in around 2,000 hands at one point, and I wasn't looking very hard (100 runs when tracking Royals).

Either that or my RNG is broken from over used.

Here is a preview of my official position on this matter, at the moment. I know there is challenge fatigue on this site, so forgive me for issuing one of my own.

Any comments or corrections before I make this public tomorrow?

Quote: Wizard

... Any comments or corrections before I make this public tomorrow?

Typo (repeated word) in the last sentence.

Quote: Wizard

Here is a preview of my official position on this matter, at the moment. I know there is challenge fatigue on this site, so forgive me for issuing one of my own.

Any comments or corrections before I make this public tomorrow?

You can also arrive at 1 in 710.839 by doing the direct (binomial) calculation instead of the poisson approximation. p^3*q^8759*c(8762,3) = 0.140679% (1 in 710.839), where p=1/40000.

You may also want to address the fact that their expert is unrebuttable (i.e. cannot be cross-examined) as well as the fact that a bot on a negative game should be *welcomed* by the casino rather than disallowed. (What was the EV of the actual paytable he was playing?)

Finally, I have a big problem with the idea of a gaming operator lying in wait for a player to experience a big win before invoking some rule like "no bots". Except in situations where bot play can be demonstrated to give an advantage over another party (e.g. poker or bonus abuse), I fail to see the legitimacy of an anti-bot policy. If I were a well-funded gaming operator with limits set appropriate to my bankroll (e.g. no $10,000/hand slot games), I'd love the extra handle. But if "no bots" is strict, there should be a universal policy to bot-scan all play, not just conditionally scan the big winners. (This is why regulation is important, folks.)

This isn't the first time I've heard of an online casino freaking out over a >25k cashout. I dealt with such an issue a few years ago; to my knowledge, the software vendor stepped in and paid the player -- and then revoked the operator's software license.

Then there's the issue of the player being an alleged gaming cheat, and whether the casino can retroactively keep his winnings based on past transgressions against a third party. Can someone answer this question: In Nevada, if a known gaming felon (but not someone who's banned) makes a legal bet in a casino, does that casino have to honor the results win or lose? In other words, can they wait until the player wins and then confiscate the funds, but keep the losses as if the bet was legitimate?

I totally agree that casinos should openly allow bot play, except in live poker. A reason I think many don't is to have an excuse to not pay any winner they wish. Don't want to pay -- just accuse them of using a bot. I will add that point to my page, thanks.

If the basis for the charge that there is bot play, is the speed of the play, then why don't they check that while they are playing and cut that person off. It would seem to be the easiest thing to check. Just send out a warning to vary their speed. Of course, it should be very easy to program a bot to vary it's speed.

It seems like they are confusing two things here. One is that he has a bot, and two that he cheated somehow and got lucky with the royal flushes. As we discussed earlier, the world of craps jumped right from 119 rolls of the dice to 154 rolls of the dice (after a 20 year period). That's a jump from 31 million to 1 to 5.9 billion to 1. When you are that far out on the tail, then there are some big jumps. The probability of three royal flushes in that many hands is extraordinary, but not on the level of the 154 rolls in a row in craps. The term "statistically impossible" is just an attempt to add pseudo science to word impossible.

A public transcript of the play (with times) should be released. Otherwise the company loses credibility.

Quote: kengam77

They contend that he didn't even stop to admire his $20k royal and dealt another hand 4 seconds later. The logs actually showed that he hit the Royal, played another hand 4 seconds later and then took a 19 minute break from play. That sounds pretty realistic to me.

If you're saying another hand was completed 4 seconds after the royal hit,and then there was a break, then this makes sense. I have hit a few royals and already hit the deal button before I realized it hit. This tends to happen when you draw to three or two to a royal because you aren't expecting it, plus you are trying to play as fast as possible and there is no time for processing your winning hands.

Also, their claim that the hands were played too fast is pure rubbish. I've started using a touchsmart computer which makes playing 1100-1200 hands/hr pretty normal.

Quote: MathExtremist

4) Playing fast enough can "overwhelm the RNG" and provide favorable odds to the player.

They were just about to hire a better Random Number Generator, but Google already got him for Search Autocompleter.

Quote: clarkacal

Also, their claim that the hands were played too fast is pure rubbish. I've started using a touchsmart computer which makes playing 1100-1200 hands/hr pretty normal.

Excellent point. If the casino assumed the player's UI was mouse-based when it wasn't, their estimate would be off.

Quote: MathExtremist

Excellent point. If the casino assumed the player's UI was mouse-based when it wasn't, their estimate would be off.

Why would they care how fast you played? In a negative expectation game that would normally mean more money per hour.

Quote: pacomartin

Why would they care how fast you played? In a negative expectation game that would normally mean more money per hour.

They were attempting to infer that the player was using a bot, which is against the ToS of most online casinos. I agree with you, and if I had an online casino I'd welcome bot play in my -EV games...

Just to clarify, EZ Street later admitted the player actually played these hands over a nearly 9 hour period with over 3 hours of breaks throughout, meaning, rather than the rate of 3.3 seconds a hand over about 5.5 hours, it was a rate of about 5.5 seconds a hand for the session. EZ Street used the 3.3 second rate to state as only a bot could keep that pace, but their admission makes the premise simply wrong.

Also beware, EZ Street has a highly misleading promo offer, "Here's $100 to try us out" or similar wording. The $100 can never be cashed, period, and you are required to match the winnings up to $1000 with a cash deposit, THEN, a 10x rollover. So that "free" $100 is pretty much worthless.

i know most of the pts have already been addressed by both sides but this dog-n-pony show that EZ street is putting seems like a desperate scam to me, all this over a measly 50k in liabilities. when this type of deadbeating happens at a corporation they're like 3 steps from a chapter nine exit (which in cr amounts hauling off the servers in the middle of the night and bar locking the rental office doors in the morning)

hoever, just for fun let's revisit some of this fiasco:

1.) the claim that if player cannot remember his royal he must not be on the up and up. Uh, if the player did not stop until a hand or two AFTER the royal was dealt (entirely possible if he was playing fast and his brain did not register the event yet), then it is even more likely he will be as inattentive to the details of the royal hand since his brain did not have the time to register the event as significant until next hands were dealt, especially if you questioning him a week after!

2.) the "CR Challenge" was an even bigger LOL,

a.) the polygraph testing issue: for those that don't know, CR is an absolute haven for obtaining faulsified documentation. You pay the priest (who don't make any siginificant income) sufficient dinero and he'll offcially certify you as the second coming of jesus. that's even assuming the part of getting the player into polygraph is on the up and up, they could/and have the taxi stopped in the middle of carrying the guy from the air port san jose, and go for a little personal catchup time.

but let's even assume for the minute that they're willing carry this dog-and-pony show to the end and go through the steps of a polygraph certification. It would cost them less than 500usd to have the CR polygrapher to doctor the results and reveal that evn saint mary herself has been shtting her britches.

this whole farce is equivalent of agreeing to be arbitrated by a CR monk who will meditate and then translate god's decision on this matter.

b.) the 1k+/hr hand thing w/ perfect strategy. another laughable ploy, EZ street has never conclusively PROVEN the player was using PERFECT PLAY, in fact the only thing that they have proven is that they don't even understand what perfect play is on vp since they are stating it's an "opinion", would then the player have to play up to the standards of that "opinion" in his demonstration? (ie: does he have to hit 3 more royals in order for him to pass?)

so how could they request the standard when they don't even know what the benchmark is? no perfect play has been proven, only that the player could play 1000+ hands for 3 straight hours, give this is their entire case: then it should be obvious that the only thing the player have to prove in this matter is that he can manually play 3000+ hands in 3hours given the ability to auto-hold and fast deal. which is a pretty insignificant feat b/c it just involves hitting two buttons over and over..

@ the Wizard - since this thread has been bumped above but not updated, I assume the casino hasn't made things right. Does that mean you will be adding them to your blacklist?

I thought they had already been added to the blacklist.
I imagine one payment dispute might not be grounds, but persistent behavior during that one dispute surely should be.

Oh, and by the way, a "Mystery Expert" is a person who is an expert in either the writing of mystery stories or in the solving of a mystery. A person who claims expertise in a certain field but foolishly attempts to lurk in the shadows of anonymity so as to remain unaccountable for his errors is either not an expert or is simply a coward. Most likely he is both. Be careful when shaking hands with him, his palms are likely to still be greasy.

And instead of a "lie detector" or polygraph, always insist on a reading of tea leaves instead. That way you get the benefit of a nice refreshing beverage and the results of the tea leaves are just as valid as the results of a polygraph examination.