Simple Math Question

[olds442jetaway]

I have now gone about 200k hands without a Royal. Mostly job or deuces wild games. Would the probability of this be about the same as flipping a coin and getting heads or tails 10 consecutive times? I divided 40k into 200k and got 5. Since on a coin, heads should show up every other flip or once every 2 flips and 2 times 5 is 10, I figured my odds of missing the Royal in 200k hands to be about the same as getting 10 consecutive heads, 10 straight reds on the Roulette table ( discounting 0 or double 0), or 10 consecutive passes in a craps game. I think this is a record for me in missing a Royal. Also just curious on the probability of this happening. I came up with about a 3 percent chance in round numbers of missing a Royal in 200k hands.

[Minn. Fatz]

That's some serious negative variance but not quite as bad as missing ten even chances in a row.

Assuming you're playing JB 9/6 and full pay DW about evenly, you should be hitting that RF on average once in every about 41,958 hands. Your probability of catching a Royal on any given hand then is:

1 / 41958 ~ .0000238

So, your probability of not hitting a Royal on any given hand is:

1 - .0000238 = .9999762

Call this probability x. Then, your probability of not hitting a royal in n hands is:

x ^ n

or x times itself n times. Since x < 1 this gets closer to 0 as n increases.

Recall you should hit that RF about every 42,000 hands, on average. Using the above formula (and slightly more accurate estimates of your RF probability), your probability of not hitting any RFs in:

40,000 hands is 38.54 percent, or once in 2.59 trials
80,000 hands is 14.86 percent, or once in 6.73 trials
120,000 hands is 5.73 percent, or once in 17.5 trials
160,000 hands is 2.21 percent, or once in 45.3 trials
200,000 hands is 0.85 percent, or once in 117 trials

To find the equivalent for a coin flip or other even chance, we need to take the logarithm to the base 2 of 117 (actually, 117.53+):

log2(117) ~ 6.88

So it's more like missing a coin flip or other even chance a little less than seven times.

But that probably doesn't feel any better. Fortunately, there's a slightly better than even chance that you will get two RFs in your next 42,000 hands.

Thanks for the question. Better mathematics.

[DaBurglar]

dear olds442jetaway: First off, that sucks eggs that you are on such a dry spell, I totally feel you on that! Where have you been playing?  That's what I'd love to know..... In my experiences, Vegas and Reno never had me in a NON-Royal dry spell for longer than 90k to 100k hands before hitting a royal, so your dry spell is twice as bad as I ever had in those markets.   There is another casino market, however, that I have experienced such horrific "dryness" in,,,,,,however, I am on a self imposed hiatus from mentioning this casino market locale in any of my posts in a negative manner, so I cannot elaborate.   I will just mention it rhymes with "Gigantic Kitty"..... Here's hoping you end your drought pronto!

[olds442jetaway]

Thanks for the great math refersher. By the way, all of the play was at Mohegan. I don't think DaBurglar will be surprised since I have read his other posts about both Ct casinos. I have no proof of course of any tampering, but can't believe some of the negative streaks in Ct. I am still waiting for the long hot streaks, but 20 years is a but much to take. My lifetime average on Royals is still over 120,000 in Ct. Pretty good sample too. About 5 to 6 million hands played. Which reminds me DaBurglar, speaking of Gigantic Kitty, I am really enjoying the Boardwalk Empire series on HBO. Since I don't get that channel at home, I of course have to watch it in the room at the casino lol. At least that saves me a hundred bucks or so for that hour I am watching the show!

[Minn. Fatz]

Since the Blockbuster stores closed Mrs. Minn and I have subscribed to HBO for Boardwalk Empire, The Newsroom and Real Time with Bill Maher. If I had to tell my late father how much we spend to watch TV -- with commercials yet -- he wouldn't know whether to or go blind.

[DaBurglar]

dear olds442getaway: Yes, the connecticut casinos are just as abysmal as "Frantic Ditty"'s casinos, but since they are Indian lands and have their own special rules worked out between them and the state, and since their business is in the crapper even worse than "Pedantic Twitty's" economy, it doesnt surprise me they have horrible VP, and just like CET, they have stopped giving comps on VP too.... I appreciate very much your Boardwalk Empire Reference!   Maybe someone else on this forum who thinks I am the only one who changes direction of threads (i.e. HIJACK) will see that is not the case, and further will notice your skillful execution of said "hijacking" will serve as an example that it is NOT a bad thing to happen.    Boardwalk Empire is a Great show and actually has helped the city ots based on gain a few new visitors, much more so than the idiotic campaign of "DO AC"!    If only they'd just stick to straightforward ADVERTISING in diverse markets on TV! Boardwalk Empire is radically different than other HBO epic success stories, like THE WIRE and THE SOPRANOS, and yet it is also eerily similar!    For instance, in the Wire Series, resident lone badd-ass "Omar" is played by the same actor who now plays Chalky WHite, Michael K Williams.    And in the series Boardwalk Empire, we now have a new resident lone badd-ass, Richard Harrow, played by Jack Huston..... BTW, my favorite Boardwalk character is Mr. Harrow, the guy steals EVERY scene he is in despite his character's speech impediment and lack of actual dialogue....his ability to merely express himself via body language and eye/facial gestures is amazing. Who else is everyone's favorite Boardwalk Empire persona???   FYI -  Boardwalk Empire is yet one more reason I still go to "Semantic Bitty" despite lousy VP....when I am on the Boardwalk I can transport myself back in time to the 1920s and imagine the bootleggers offloading Cuban Rum on the beach .... the city actualy has a lot of history if you know where to look and use your imagination!

[olds442jetaway]

Michael Shannon playing George Mueller, then Stephen Graham playing Capone, Paul Sparks playing that idiot Mickey Doyle. However, this is a hard choice and I think they all play their parts extremely well. I am sure these guys would have a ball with the vp machines and certainly find a way to play with the RNGs. I'd be curious to know how the booze they have coming into Florida compares to what is on the market today. They sure seem to like it! I wasn't able to work in much vp talk here, but what the heck. We all need a little diversion once in awhile.

[Vman96]

Thanks for the great math refersher. By the way, all of the play was at Mohegan. I don't think DaBurglar will be surprised since I have read his other posts about both Ct casinos. I have no proof of course of any tampering, but can't believe some of the negative streaks in Ct. I am still waiting for the long hot streaks, but 20 years is a but much to take. My lifetime average on Royals is still over 120,000 in Ct. Pretty good sample too. About 5 to 6 million hands played. Which reminds me DaBurglar, speaking of Gigantic Kitty, I am really enjoying the Boardwalk Empire series on HBO. Since I don't get that channel at home, I of course have to watch it in the room at the casino lol. At least that saves me a hundred bucks or so for that hour I am watching the show!

It's definitely rigged if those are your statistics. Having 42 royals or less in 5 million hands of single play deuces is a 1 in 245 trillion occurrence. To compare to a "normal bad luck" scenario, less than 100 royals in 5 million hands of single play deuces is about 7% likely.

Start a crusade in exposing illegal activity like I have suggested to DaBurglar perhaps? Mohegan and Foxwoods are supposed to be Class III gaming of course.

Edit: If you are mixing in significant Double Down Stud hands in with this, then this could make a lot more sense. The odds of getting the royal there is 1 in 649,740 hands (i.e. a "dealt royal"). But you pretty much need to have half of your sample be of Double Down Stud before your results would be "normal bad luck".

[Minn. Fatz]

Michael Stuhlbarg as Arnold Rothstein. The ultimate advantage player, even though he does come to a Bad End.

[olds442jetaway]

The sample I got my statistics from is strictly from draw poker play. No double down stud was included and no multi line games where the Royal came in on other lines were included. I have been dealt 3 Royals in Double Down Stud in about 2 million hands so that one is right on average. I am also starting a sample and keeping records on getting 4 deuces. That is still my favorite game and I used to hit them once a trip on average of 5,000 hands played. That would be about right. Now since late in 2010, and especially this year, even the 4 deuces aren't hitting like they should. I have now gone 30k hands without quad deuces. The time before that was similar. Before 2010, I would sometimes hit quad deuces 2 or 3 times in a 10 hour session of about 6,000 hands. Then a trip or two would go by without the deuces hitting. That would make sense, but nothing like this. Funny, you mentioning about class 3 machines. Two different slot managers up there told me they were class 2, but the gaming comission told me class 3. I couldn't find the little bingo symbol the class 2 is supposed to have so who knows. What few die hard vp players that are left playing in Ct all have similar stories. Another funny thing I have noticed is the regular players not hitting big hands and the one timers or irregular players hitting some very big hands. Really makes you wonder.