Looking for Royal
February 18th, 2012 at 8:36:52 PM
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OK Folks,
My wife and I play video poker together, but we've yet to hit a royal flush. Maybe this next trip. 8-)
My question is how many trips will it take before we have a 90% chance to hit at least one Royal Flush.
Here is some more data. My wife and I take 1 trip per year to Las Vegas and we play 9/6 Jacks or better video poker. Let's assume that we stay 5 days and play 2 hours per day. Let's say we can play 400 hands in an hour and play perfect standard strategy without deviating to attempt to get a royal flush.
So here's my calculation:
400 hands per hour * 2 people * 2 hours per day * 5 day trip = 8000 hands per trip
Chance of a royal flush: 493512264/19933230517200
Chance of no royal flush: 1 - 493512264/19933230517200
Chance of no royal flush in N trips: (1 - 493512264/19933230517200)^(8000*N)
So a 90% chance at at least one royal is a 10% chance of no royals.
0.1 = (1 - 493512264/19933230517200)^(8000*N)
Solving for N: log(0.1)/(log((1 - 493512264/19933230517200)*8000) = 11.625 trips
So somewhere on our 12th trip will my wife and I have a 90% chance to have at least 1 royal flush. How does my calculation look?
--helpmespock
My wife and I play video poker together, but we've yet to hit a royal flush. Maybe this next trip. 8-)
My question is how many trips will it take before we have a 90% chance to hit at least one Royal Flush.
Here is some more data. My wife and I take 1 trip per year to Las Vegas and we play 9/6 Jacks or better video poker. Let's assume that we stay 5 days and play 2 hours per day. Let's say we can play 400 hands in an hour and play perfect standard strategy without deviating to attempt to get a royal flush.
So here's my calculation:
400 hands per hour * 2 people * 2 hours per day * 5 day trip = 8000 hands per trip
Chance of a royal flush: 493512264/19933230517200
Chance of no royal flush: 1 - 493512264/19933230517200
Chance of no royal flush in N trips: (1 - 493512264/19933230517200)^(8000*N)
So a 90% chance at at least one royal is a 10% chance of no royals.
0.1 = (1 - 493512264/19933230517200)^(8000*N)
Solving for N: log(0.1)/(log((1 - 493512264/19933230517200)*8000) = 11.625 trips
So somewhere on our 12th trip will my wife and I have a 90% chance to have at least 1 royal flush. How does my calculation look?
--helpmespock
February 18th, 2012 at 9:48:36 PM
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It doesnt quite work the way the math hints it should work.
On any given hand you have about a one in 42,000 chance of hitting a royal.
On any given hand you have about a 1 in 629,740 chance of being dealt a royal.
Missing royals in the past does not increase or decrease your chance of hitting a royal in the future.
Hitting royals in the past does not increase or decrease your chance of hitting a royal in the future.
The machine has no memory. It does not know if you are due to hit a royal, or if you should be deprived of another royal.
I hit my last royal after about 170,000 hands. Then about seven years ago I hit two royals about 8 hours apart, and got the second royal after playing only three hands during the second session, which was actually four hands after the first royal.
On any given hand you have about a one in 42,000 chance of hitting a royal.
On any given hand you have about a 1 in 629,740 chance of being dealt a royal.
Missing royals in the past does not increase or decrease your chance of hitting a royal in the future.
Hitting royals in the past does not increase or decrease your chance of hitting a royal in the future.
The machine has no memory. It does not know if you are due to hit a royal, or if you should be deprived of another royal.
I hit my last royal after about 170,000 hands. Then about seven years ago I hit two royals about 8 hours apart, and got the second royal after playing only three hands during the second session, which was actually four hands after the first royal.
February 18th, 2012 at 9:51:01 PM
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DUHHIIIIIIIII HEARD THAT!
February 19th, 2012 at 12:07:32 AM
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Quote: IbeatyouracesGood luck. I've gotten 3 more this past week. Once you get that 1st one, then they come with a fury. At least they have for me.
Pics or it didn't happen...
In a bet, there is a fool and a thief.
- Proverb.
February 19th, 2012 at 1:31:32 AM
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Personally, I've become quite unimpressed with big royal flush counts because many of these players are on penny and nickel 50-play and 100-play machines and "force the royals" by putting emphasis on royal draw cards.
What impresses me are reports of multiple royals on single line machines, and being dealt royals on multi play machines.
It happened to me once: I was dealt a royal on a 50-play machine at Mandalay Bay. It was a nickel machine. A $12.50 push of the button got me ten grand. I would like to tell you that there's a picture of a smiling me in front of the screen -- but there isn't. You see, the shock of it happening made me immediately vomit.
What impresses me are reports of multiple royals on single line machines, and being dealt royals on multi play machines.
It happened to me once: I was dealt a royal on a 50-play machine at Mandalay Bay. It was a nickel machine. A $12.50 push of the button got me ten grand. I would like to tell you that there's a picture of a smiling me in front of the screen -- but there isn't. You see, the shock of it happening made me immediately vomit.
February 19th, 2012 at 6:56:26 AM
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Quote: WongBoPics or it didn't happen...
Different poster here, but when I was in Vegas in Feb. 2010, I hit a royal flush at Casino Royale on a .25 BP machine. I was actually trying to hit four-of-a-kind for the old bonus promotion. As soon as I hit the four-of-a-kind I was going to get up, but hit the Royal first. I eventually got 4 sevens, then left after that, up over $1000.
About 36 hours later, I walked from Rio to Palms and played 9-6 JoB in quarters. I had ordered a drink, was up about $50, and was going to leave, but the drink took forever to get there. I ended up losing the $50, plus my initial $100, down to my last $5. I had four to the royal, hit deal, and got the fifth card. I cashed out with $1005. I DID take pictures, but they are on an old phone...
"One out of every four people are [morons]"- Kyle, South Park
February 19th, 2012 at 7:42:55 AM
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Quote: AlanMendelsonIt doesnt quite work the way the math hints it should work.
Hmmm...have I made a mistake in my calculations somewhere? Wait...I think my number was correct, but I missed a bracket in formula so it should be:
LOG(0.1)/(LOG((1-493512264/19933230517200))*8000)
Quote: AlanMendelsonMissing royals in the past does not increase or decrease your chance of hitting a royal in the future.
Hitting royals in the past does not increase or decrease your chance of hitting a royal in the future.
Oh I understand that. I could have gotten two royal flushes on my first two hands I ever played, but that would have been highly unlikely.
What I wanted to get a handle on is my expectation of how many royals I should be seeing given our play, and according to my calculation it'll be our 12th trip before we have even a 90% chance for at least one royal flush. The flip side of that is that I have a 10% chance of not hitting any royals by my 12th trip. That's 1 in 10 which is still within the realm of possibility.
I just wanted to confirm what I suspected -- given our play it would be likely for my wife and I to not have any royal flushes to this point.
--helpmespock
February 19th, 2012 at 7:44:05 AM
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Using Alan's number for chances of hitting a royal, if you play a single hand of JoB, there is a .9997619047619.. chance that you will NOT get a royal. Let's call that P. To find out how many hands it would take to give you a 10% chance of NOT getting a royal ( 90% of actually getting it ), you take the probability of not getting the royal, P, and calculate the exponent that gets you to .10
P^x = .10
WolframAlpha.com tells me that this number is 96,707.4
Now divide by the number of hands that you play per trip (8000) and you get 12.088425 trips. Keep in mind that if you have an equal likelihood of hitting it on the first hand as you do of hitting it on the second hand or the 96,707th hand so good luck!
Of the flip side, there is still a 10% chance that you will not experience a royal in the intervening 12+ trips.
P^x = .10
WolframAlpha.com tells me that this number is 96,707.4
Now divide by the number of hands that you play per trip (8000) and you get 12.088425 trips. Keep in mind that if you have an equal likelihood of hitting it on the first hand as you do of hitting it on the second hand or the 96,707th hand so good luck!
Of the flip side, there is still a 10% chance that you will not experience a royal in the intervening 12+ trips.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
February 19th, 2012 at 7:53:06 AM
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Quote: WongBoPics or it didn't happen...
My wife and I don't typically carry a camera of any type in the casino. Our cell phone is pay-as-you-go in Canada so we'd have to jump through hoops to get it to work in the US and as a result we don't bring it.
If we were lucky enough to hit a royal flush would the casino take our picture for us? Also I assume that the machine starts up the alarm and red light so that an attendant would have to come over to pay us. Who and how much should you tip in a situation like this? Typically we play $0.25 machines.
--helpmespock
February 19th, 2012 at 8:02:58 AM
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Quote: helpmespock
If we were lucky enough to hit a royal flush would the casino take our picture for us? Also I assume that the machine starts up the alarm and red light so that an attendant would have to come over to pay us. Who and how much should you tip in a situation like this? Typically we play $0.25 machines.
The casino might take a picture for you. However, I've only had one hand pay on a .25 Royal. All the rest, the machine didn't lock up, as the payout is under the threshold of $1200 required by the US. I've hit about 10 Royals at the .25 level, so my guess is unless Canada has a different threshold, you'll probably just continue to play without needing assistance.
"One out of every four people are [morons]"- Kyle, South Park
February 19th, 2012 at 8:15:21 AM
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Quote: TiltpoulThe casino might take a picture for you. However, I've only had one hand pay on a .25 Royal. All the rest, the machine didn't lock up, as the payout is under the threshold of $1200 required by the US. I've hit about 10 Royals at the .25 level, so my guess is unless Canada has a different threshold, you'll probably just continue to play without needing assistance.
Typically we only gamble in Las Vegas. It's just not as fun anywhere else. 8-)
I've been to Canadian casinos twice and the best Jacks or better video poker they have for $0.25 is 6/5. I might as well play a slot machine with that kind of pay table.
Interesting that it's typically no hand pay for a $0.25 machine. I'm assuming that the $1200 threshold is for the W2G thing right? Can I take the $1000 ticket to the ticket cashing machine or must I go to the cashier?
February 19th, 2012 at 8:16:23 AM
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DUHHIIIIIIIII HEARD THAT!
February 19th, 2012 at 8:26:34 AM
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Quote: helpmespockI've been to Canadian casinos twice and the best Jacks or better video poker they have for $0.25 is 6/5. I might as well play a slot machine with that kind of pay table.
Yeah isn't that the truth? I think I remember my one trip to Casino Windsor that they had lousy VP tables.
Quote: helpmespockInteresting that it's typically no hand pay for a $0.25 machine. I'm assuming that the $1200 threshold is for the W2G thing right? Can I take the $1000 ticket to the ticket cashing machine or must I go to the cashier?
Depends on the casino. Most require high dollar amounts to go to the cage, but I think about half of mine I cashed out at a machine.
"One out of every four people are [morons]"- Kyle, South Park
February 19th, 2012 at 2:06:29 PM
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I get about seven a year. I can't tell if that's normal or I'm just really lucky. I do play a lot. I mostly play single-line. I've hit one $4,000 (dollar) and three $2,000 ($.50) jackpots. The rest are all $0.25, which I prefer because I don't like getting W2-Gs.
This last trip to Vegas I hit three royals which was incredibly lucky, I think. Needed it!
This last trip to Vegas I hit three royals which was incredibly lucky, I think. Needed it!
"Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe." -Rig Veda 10.34.4
February 19th, 2012 at 9:18:03 PM
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Quote:Can I take the $1000 ticket to the ticket cashing machine or must I go to the cashier?
Depends on the casino. When I hit a quarter royal at the Palms the machine locked up and it was a hand pay. That was when they had the FPDW progressive but it was only at like $1003 (no, I am certainly not complaining). While I was waiting I recorded the music and made a ringtone. :)
When I hit at Red Rock, it just gives 4000 credits. The ticket changing machine is perfectly happy to pay out the $1000.
February 19th, 2012 at 10:01:22 PM
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I've hit a Royal twice in my life on non-multiplay machines. On the 50 plays, I've hit it numerous times.
I hit it for $1,000 at the Bellagio (I posted the pictures when I hit it). Then on my stupid $.02 multistrike poker machine, I was dealt it on line 1 (there are four lines, 1x, 2x, 4x, 8x) for wow, $320.00 (16000 x .02).
I hit it for $1,000 at the Bellagio (I posted the pictures when I hit it). Then on my stupid $.02 multistrike poker machine, I was dealt it on line 1 (there are four lines, 1x, 2x, 4x, 8x) for wow, $320.00 (16000 x .02).
-----
You want the truth! You can't handle the truth!
February 27th, 2012 at 1:16:38 PM
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Quote: AlanMendelsonbut there isn't. You see, the shock of it happening made me immediately vomit.
NICE! When I win big money I would immediately projectile vomit also...fortunately (or unfortunately) it hasn't happened to me yet..biggest I've hit is $1500 off of a Slot Tournament and $1209 off of a Progressive Royal.
Gambling calls to me...like this ~> http://www.youtube.com/watch?v=4Nap37mNSmQ
February 27th, 2012 at 1:27:57 PM
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My wife and I played approximately 2500 hands of video poker full pay deuces wild and full pay double double bonus this weekend. We did hit a few natural four of kinds playing deuces (paying 25 credits), but not 4 deuces and didn't hit any four of a kinds playing double double. We ended up down $300 playing quarters. I believe that equates to about an average return of 90%. Approximately, $3,125 in total play for a return of $2,825. Considering the fact that we were playing full pay machines and I had my smart phone with the wizard of odds optimal deuces wild strategy open for any questions I believe this to be a pretty bad run on the machines.
We always play a hundred dollars through the machine, 80 hands, then determine whether to keep playing or not. Not for sure if this is the best strategy, but it is the one we are working with currently.
We always play a hundred dollars through the machine, 80 hands, then determine whether to keep playing or not. Not for sure if this is the best strategy, but it is the one we are working with currently.
February 27th, 2012 at 1:31:14 PM
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" but not 4 deuces and didn't hit any four of a kinds playing double double." And you expected what percentage hold ??
February 27th, 2012 at 1:42:47 PM
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Quote: buzzpaff" but not 4 deuces and didn't hit any four of a kinds playing double double." And you expected what percentage hold ??
I don't know what to expect. I guess by playing 2500 hands I was counting on hitting at least one four of kind to help the overall return. Is 2500 hands not enough to expect a natural four of a kind?
February 27th, 2012 at 2:00:32 PM
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Nah. That is exceedingly average. 90% is a common result in the short term. I've had anywhere from 75%-85% too, and that was on JoB. You should hit the deuces every 5,000 hands or so. I'm in the middle of a three cycle deuces drought (15,000+ hands), and before that another three cycle drought. (But hit three Royals in Vegas!). I heard some guy was in the middle of six cycles without the Deuces. And that is on DW; DDB has mega-variance. I heard one person call it the "devil's game." I would tend to agree with that. You should get a natural quad every 420 hands or so, but that is not guaranteed of course and you can trend downward VERY quickly with the low two pair payouts.Quote: SONBP2My wife and I played approximately 2500 hands of video poker full pay deuces wild and full pay double double bonus this weekend. We did hit a few natural four of kinds playing deuces (paying 25 credits), but not 4 deuces and didn't hit any four of a kinds playing double double. We ended up down $300 playing quarters. I believe that equates to about an average return of 90%. Approximately, $3,125 in total play for a return of $2,825. Considering the fact that we were playing full pay machines and I had my smart phone with the wizard of odds optimal deuces wild strategy open for any questions I believe this to be a pretty bad run on the machines.
"Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe." -Rig Veda 10.34.4
February 27th, 2012 at 2:36:24 PM
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Quote: helpmespockInteresting that it's typically no hand pay for a $0.25 machine. I'm assuming that the $1200 threshold is for the W2G thing right? Can I take the $1000 ticket to the ticket cashing machine or must I go to the cashier?
Several years ago I was at the Wynn with my wife, my brother and his wife, and their just-turned-21 daughter. My brother's family and I were seeing "Spamalot" and we left my wife loose in the casino (she wasn't interested in seeing the show). During the show, she hit a Royal on a $0.25 JOB machine and had to walk around for over an hour with the $1,000 TITO, just waiting to wave it at us after we got out of the show. The funny part was that she wanted to make a big deal out of cashing the ticket and none of the staff seemed to be as excited as she was. It was just another $1,000 changing hands to them - granted, it was the Wynn, after all.
Another interesting observation happened at Potawatomi casino in Milwaukee. This was a few years ago, when you had to go to the cashier to collect on your slot card offers. So, I'm standing in line to get my $10 free play and the couple in front of me had a TITO worth $1,700. They nonchalantly handed it to the cashier and she promptly scanned the ticket and paid out the $1,700, no questions asked. I'm next, and I handed the cashier my $10 slot play coupon. I then had to produce my player's club card AND my drivers license (picture ID), AND sign a receipt before the cashier would give me the $10! Go figure...
February 27th, 2012 at 2:36:32 PM
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Quote: helpmespockInteresting that it's typically no hand pay for a $0.25 machine. I'm assuming that the $1200 threshold is for the W2G thing right? Can I take the $1000 ticket to the ticket cashing machine or must I go to the cashier?
Several years ago I was at the Wynn with my wife, my brother and his wife, and their just-turned-21 daughter. My brother's family and I were seeing "Spamalot" and we left my wife loose in the casino (she wasn't interested in seeing the show). During the show, she hit a Royal on a $0.25 JOB machine and had to walk around for over an hour with the $1,000 TITO, just waiting to wave it at us after we got out of the show. The funny part was that she wanted to make a big deal out of cashing the ticket and none of the staff seemed to be as excited as she was. It was just another $1,000 changing hands to them - granted, it was the Wynn, after all.
Another interesting observation happened at Potawatomi casino in Milwaukee. This was a few years ago, when you had to go to the cashier to collect on your slot card offers. So, I'm standing in line to get my $10 free play and the couple in front of me had a TITO worth $1,700. They nonchalantly handed it to the cashier and she promptly scanned the ticket and paid out the $1,700, no questions asked. I'm next, and I handed the cashier my $10 slot play coupon. I then had to produce my player's club card AND my drivers license (picture ID), AND sign a receipt before the cashier would give me the $10! Go figure...
June 20th, 2012 at 1:53:31 PM
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I understand what the original poster is asking: about how many trips at the given rate of play should it take before it is 90% likely to have seen a Royal? He is not asking what the chances are in any given hand. If I'm not mistaken, there is some way to quantify the likelihood of an event happening or not within X number of independent trials. A simple answer would be that a Royal appears on AVERAGE every 40,000 hands. But I don't think 40,000 hands represents a 90% likelihood of seeing one, but probably the midpoint of a 50% likelihood of seeing one. I wish I had the math expertise to give the answer, but I'm sure you would need many more hands than 40,000 to reach a 90% likelihood.
June 20th, 2012 at 2:32:26 PM
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" I'm sure you would need many more hands than 40,000 to reach a 90% likelihood. "
93,654 hands approximately plus or minus 1/56th
93,654 hands approximately plus or minus 1/56th
July 1st, 2012 at 7:28:45 PM
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Not sure how long it will take, but the first one is the hardest one. The day I hit my first I also hit my second. I have a total of 5 now.
Good luck.
Good luck.
July 2nd, 2012 at 6:39:43 AM
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Quote: 4andaKickerI wish I had the math expertise to give the answer, but I'm sure you would need many more hands than 40,000 to reach a 90% likelihood.
Quick hit of math:
The 90% likelihood of getting at least one Royal in N hands = the 10% likelihood of getting zero Royals in N hands
If you assume the probability of getting a Royal = 1/40,000 (is it really that high? I thought it was closer to something like 1/25,000), then the probability of not getting a Royal = 39,999/40,000, and the probability of not getting a Royal in N hands is (39,999/40,000)N.
For this to be 0.1, you have
(39,999/40,000)N = 0.1
Since log (XY) = Y log X, take the logarithm of both sides:
N log (39,999/40,000) = log 0.1
N = log 0.1 / log (39,999/40,000) = 92,102.25
July 2nd, 2012 at 6:29:25 PM
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Quote: ThatDonGuyQuick hit of math:
The 90% likelihood of getting at least one Royal in N hands = the 10% likelihood of getting zero Royals in N hands
If you assume the probability of getting a Royal = 1/40,000 (is it really that high? I thought it was closer to something like 1/25,000), then the probability of not getting a Royal = 39,999/40,000, and the probability of not getting a Royal in N hands is (39,999/40,000)N.
For this to be 0.1, you have
(39,999/40,000)N = 0.1
Since log (XY) = Y log X, take the logarithm of both sides:
N log (39,999/40,000) = log 0.1
N = log 0.1 / log (39,999/40,000) = 92,102.25
Yes it is that high, and actually it approaches 43,000 hands for some games but the 40,000 figure is a generally accepted average. Thanks so much for showing how this probability is calculated.
