5 Royals - Video Poker

Bear with me, this is my first post.
$1 Single line, 9-6, Double Bonus, progressive. Unbelievably, a royal each Saturday (the only day I play) for the past 5 Saturdays on the same bank of 10 machines. Total hours played during this run: 50; total hands played during this run: approximately 25000; lifetime total hands played on these machines: approximately 200,000. Any idea what the odds are for this run? Is more info needed to calculate? Understandably most think this run is made up -- until I show them the W-2Gs. Thanks.

Update: hit #6 this past Saturday.

Why did you say you had 5 then put an update during the same typing to say you got your 6th?

Doing this quick so double check it:

Probability of hitting a royal: 0.000024
Probability of not hitting a royal after 25,000 * 5 hands: 4.97%
Probability of at least 1 royal: 95.03%
Probability of at least 2 royals: 80.08%
Probability of at least 3 royals: 57.68%
Probability of at least 4 royals: 35.27%
Probability of at least 5 royals: 18.47%

Summation of k=x to 125000 (125000 choose k)*0.000024^k*(1-0.000024)^(125000-k)

Quote: DiscreteMaths2

Doing this quick so double check it:

Probability of hitting a royal: 0.000024
Probability of not hitting a royal after 25,000 * 5 hands: 4.97%
Probability of at least 1 royal: 95.03%
Probability of at least 2 royals: 80.08%
Probability of at least 3 royals: 57.68%
Probability of at least 4 royals: 35.27%
Probability of at least 5 royals: 18.47%

Summation of k=x to 125000 (125000 choose k)*0.000024^k*(1-0.000024)^(125000-k)

Why did you do 25,000 * 5?

Quote: RS

Why did you do 25,000 * 5?

Maybe I am misunderstanding but I thought he was doing 25,000 hands a session and did 5 of these sessions.

He played 25k hands total (5k/Saturday).

Quote: RS

He played 25k hands total (5k/Saturday).

Oh ok. So for only 25000 hands it would be:

at least 1 royal: 0.451192
at least 2 royal: 0.1219
at least 3 royal: 0.0231136
at least 4 royal: 0.0033575
at least 5 royal: 0.000394365

edit: also if you want to know chances of getting a royal playing 5k hands its about 11.3%

My last three royals were all on the same machine, two weeks apart and about 20 total hours of play.

Figuring out the odds after the fact makes little sense. You need to figure out the odds beforehand. For example, the odds of hitting one royal a week five weeks in a row in the NEXT five weeks is quite a bit different than EVER having a five-week stretch like that. Hitting five royals in 25000 hands is also, probably, hitting five royals in 100,000 hands. We just don’t talk about that 75,000-hand “dry spell” because it isn’t as interesting.

The two things we can agree on is that when you hit a very-unusual combination --- whatever it is --- you always want to know “what are the odds?” Presumably if you figured out they were 500 million to one that would make it more special than if they were "only" 50 million to one. It's typical to add extra stuff after-the-fact to make the number higher. In this case, it was "they were all on the same bank of machines." Had they all been on the exact same machine, that would have been added because that makes it seem even more special. Had they all been in hearts (or even all red), that would have been part of the story. Sometimes you take pictures and afterwards compare the pictures and notice that all five of them had an ace in the second position --- or whatever.

The other thing we can agree on is this poster will now have a story starting out with “let me tell you of a 5-week stretch back in 2016” that he will share for as long he is alive.

Personally I can’t blame him for doing this. After my biggest run, I wrote book about it!

Quote: rickbow

Bear with me, this is my first post.
$1 Single line, 9-6, Double Bonus, progressive. Unbelievably, a royal each Saturday (the only day I play) for the past 5 Saturdays on the same bank of 10 machines. Total hours played during this run: 50; total hands played during this run: approximately 25000; lifetime total hands played on these machines: approximately 200,000. Any idea what the odds are for this run? Is more info needed to calculate? Understandably most think this run is made up -- until I show them the W-2Gs. Thanks.

So, bottom line is you've played 200,000 hands of 9-6 Double Bonus, never hit a royal, and you want to know the odds?

From my Double Bonus page, we see the the probability of a royal with optimal strategy is 487789056/19933230517200 = 0.0000244711.

The probability of going 200,000 hands without a royal is thus (1-0.0000244711)^200000 = 0.007489227 = 1 in 133.5. I know it's no consolation, but stranger things have happened. The sad thing about video poker, and all games of independent trials, is no matter how long you go without a royal, you're still no closer to one than when you started.

Quote: BobDancer

Figuring out the odds after the fact makes little sense...

I agree. However, maybe it makes the pain a little easier to take. I must admit to having calculated the odds of four safties in in the last seven Super Bowls after Super Bowl 49. The answer, by the way, is about 1 in 5,300. Of course I never bother to calculate the odds on bets I do well with.

More importantly, welcome to the forum!

I might remind everybody that Dancer bashing is now against forum rules, as personal insults are prohibited against all forum members.

Glad to see mr. Dancer has graced us with his appearance.

How do we know this is the real bob dancer?

Quote: RS

How do we know this is the real bob dancer?

His first post is very similar, some parts verbatim, to what BD said on GWAE recently. On the other hand, he didn't tell us to go out and hit lots of royal flushes at the end of his post.

Quote: RS

How do we know this is the real bob dancer?

Trust me, it is.

Quote: Wizard

Trust me, it is.

Welcome Bob!

I figured it was 98.01% chance it was the real BD.


Regardless, I think it can be important or at least beneficial to be able to determine odds after-the-fact as well as going into a play. After-the-fact, not really necessary, but can be helpful in determining if you're doing something wrong or making costly errors, especially if you're playing stuff like 100-play and putting in the hours, where you'll get closer to N0 quicker.

But most importantly -- going into a play, you may definitely want to figure out how good or bad you can run (and yeah, sometimes running good is a BAD THING because whatever it is that you're attacking would get ended quicker than normal). Ya can't just go into a play thinking, "I have X value, let's go!" If all the value comes from hitting a royal flush in diamonds.....or hitting 2 royals within 24 hours....or whatever it may be, you're going to want to know (IMO) how frequently you'll win about X or lose about Y. Given the variance, especially in VP, oftentimes it's something like, "75% chance I'll lose $3k, but 25% chance I'll win $15K...or thereabouts". In this case, the value makes sense for the risk (IMO), but for other plays or players with differing risk factors would be more likely or less likely to play such a promotion. Another example is if you give someone a free-roll on something. If you give someone a free-roll on the 75% chance to lose $3k or 25% to win $15k....well, now you're looking at a -$375 value (for yourself), whereas the guy getting free-rolled is looking at a value of +$3,750.

Yes, we spoke about that on yesterday’s show.

I’ve addressed more than 100 “what are the odds” emails through the years after someone hits aces-with-a-kicker three times in 10 minutes or some other unusual series of events. From return emails, I understand that my “you can’t determine odds from one carefully chosen set of parameters, starting with the first good event and ending with the last, and then generalizing that” answer is NOT what people want to hear.

I assume that if I’ve answered that type of email 100 times, Shack has answered very similar emails 10,000 times. And he then built a website based on those answers. And then he sold that website for big bucks.

Hmm. Maybe I should rethink my answer!

50/50 it either happens or it doesn't. but i wouldn't book an even money bet on it happening most times.

Quote: RS

If you give someone a free-roll on the 75% chance to lose $3k or 25% to win $15k....well, now you're looking at a -$375 value (for yourself), whereas the guy getting free-rolled is looking at a value of +$3,750.

Freeroll deals are hard to figure out but it's valuable information to have.

Speaking of free rolls. I have seen notable poker players taking advantage of backers I have seen where the backer puts up 100% of the money, the player gets 50% of the profits and none of the losses on a per day basis.

Quote: RS

If you give someone a free-roll on the 75% chance to lose $3k or 25% to win $15k....well, now you're looking at a -$375 value (for yourself), whereas the guy getting free-rolled is looking at a value of +$3,750.

Freeroll deals are hard to figure out but it's valuable information to have.

Speaking of free rolls. I have seen notable poker players taking advantage of backers I have seen where the backer puts up 100% of the money, the player gets 50% of the profits and none of the losses on a per day basis.

Quote: AxelWolf

.nnSpeaking of free rolls. I have seen notable poker players taking advantage of backers I have seen where the backer puts up 100% of the money, the player gets 50% of the profits and none of the losses on a per day basis.

Hellmuth, Negreanu, etc.

Quote: AxelWolf

Freeroll deals are hard to figure out but it's valuable information to have.

Speaking of free rolls. I have seen notable poker players taking advantage of backers I have seen where the backer puts up 100% of the money, the player gets 50% of the profits and none of the losses on a per day basis.

From my experience both personally and with friends those deals involve make up with terms like that.

Quote: PokerGrinder

From my experience both personally and with friends those deals involve make up with terms like that.

Sure many "fair" deals do have make up or include stipulations like 200++ hours before any profits are taken out. I'm talking weekend deals where some guy has been watching poker after dark and he's willing to make a short term deal with someone notable. I guess if someone is begging you to give them action and they are fully aware of variance then that's on them.

I have known a few people who didn't really understand poker (they assumed a pro would always win every session). One guy was given an opportunity to back an aggressive pro where he could take 100% of the risk and receive 60% of the profits for the weekend with about 20 hours of play. I told them they were crazy and talked him out of it. Someone made a similar deal for 70% of the profit. I balked at that, however he was determined and it was a week's worth of play. He wanted to learn poker better I suggested that he make that part of the deal and sit behind. It turned out well for him.