Royal at all costs strategy
Poll
 | 5 votes (41.66%) | ||
| | 3 votes (25%) | ||
| | 4 votes (33.33%) |
12 members have voted
I have never gotten a royal flush — either in a real casino or at home. (I think I got a royal on my Palm Pilot once, but the memory is fuzzy.)
The question for the poll is: how many hands do you think it'll take me to get a royal?
Big Poppa pump can demonstrate the math.
Quote: smoothgrh...The question for the poll is: how many hands do you think it'll take me to get a royal?
My guess is 15,999.
But the answer with the highest probability of being right is one!
Cash in $400
Bet 5x$0.10=$0.50
Cash out $369
Lost $31
31/101 31% win pct
61.38% payback
Future updates will be more like every thousand hands if I can remember.
Can you elaborate more, perhaps I missed something?Quote: smoothgrhSomewhat in the "Stupid things to do during lockdown" category, in an attempt to re-create the infamous "video poker bug" on my home machine
I assume you're talking about the infamous Nestor and Kane double up bug? If so, do you have this version of the machine with double up enabled?
What does hitting a royal have to do with the double up bug?
Quote: smoothgrhSomewhat in the "Stupid things to do during lockdown" category, in an attempt to re-create the infamous "video poker bug" on my home machine, I'm going to try the "royal at all costs" strategy, which the Wizard says would produce a royal once every 23,081 hands.
I have never gotten a royal flush — either in a real casino or at home. (I think I got a royal on my Palm Pilot once, but the memory is fuzzy.)
The question for the poll is: how many hands do you think it'll take me to get a royal?
Using combination math, I have independently calculated the probability of a Royal Flush using the "royal at all costs" strategy as 0.000043326 or 1/ 23080.7473. This agrees with the Wizard - no surprise!
I found this to be a fairly tough calculation. On the Royal Seeker Return Table from the link above, the Wizard also reports the probability of getting all the other various poker hands on the payout table (Jacks or Better up to a straight flush). I can see how to do that, but I must tell you that, in my opinion, the Royal Seeker Return Table was really an impressive combination math calculation by Wizard!
The WOO site has these seemingly trivial little things on it, hidden away, but in reality some of them are pretty magnificent calculations.
Quote: smoothgrhSomewhat in the "Stupid things to do during lockdown" category, in an attempt to re-create the infamous "video poker bug" on my home machine, I'm going to try the "royal at all costs" strategy, which the Wizard says would produce a royal once every 23,081 hands.
I have never gotten a royal flush — either in a real casino or at home.?
How much time have you spent playing VP in a casino. Can’t believe you’ve never hit one. Last Royal I hit was a dealt Royal, That has happened to me twice since I moved to Reno.
From a probability point of view if you get multiple choices then pick one but the odds of then making a Royal are the same. i.e. you may have 2 of the 5, but still need the other 3, so it makes no difference whether you keep AK or QJ. However in practice you'd play QJ from AsKsQhJh7d as you have more outs.
Catch | 1st Perms | 2nd Perms | Contribution |
|---|---|---|---|
5 | 4 | 1 533 939 | 6 135 756 |
4 | 940 | 163 185 | 153 393 900 |
3 | 43 240 | 14 190 | 613 575 600 |
2 2 | 25 200 | 946 | 23 839 200 |
2 | 597 000 | 946 | 564 762 000 |
1 1 1 1 | 20 000 | 43 | 860 000 |
1 1 1 | 248 000 | 43 | 10 664 000 |
1 1 | 744 000 | 43 | 31 992 000 |
1 | 719 200 | 43 | 30 925 600 |
0 | 201 376 | 4 | 805 504 |
2 598 960 | 0 | 1 436 953 560 | |
2 774.374 |
NOTE: Corrected figures posted later, these assumed you could have five cards on the re-draw!!
Quote: AxelWolf
I assume you're talking about the infamous Nestor and Kane double up bug? If so, do you have this version of the machine with double up enabled?
What does hitting a royal have to do with the double up bug?
Yes, and OMG thanks for reminding me to turn on the Double Up feature. I mistakenly assumed it was on by default. And yes, I have one of the affected chip sets.
Regarding royal flush, the bug is supposedly present with any win (such as quads), but I figured if I’m going to re-create this, why not do it with some style?
Quote: Vegasrider
How much time have you spent playing VP in a casino. Can’t believe you’ve never hit one. Last Royal I hit was a dealt Royal, That has happened to me twice since I moved to Reno.
Very little time. It wasn’t until 100-hand video poker came out did I really get interested in learning strategy, and not until I bought my own machine in 2015 did I regularly start playing VP in a casino. And I usually quit when I hit quads.
Quote: charliepatrickA quick look (it's well past wine o'clock here!) I get a different answer, so I'm wondering whether I've got some wrong assumptions. For instance I am assuming that you only hold cards that could make a Royal Flush. So from AsAhAcAdKd you only hold AdKd.
From a probability point of view if you get multiple choices then pick one but the odds of then making a Royal are the same. i.e. you may have 2 of the 5, but still need the other 3, so it makes no difference whether you keep AK or QJ. However in practice you'd play QJ from AsKsQhJh7d as you have more outs.
Charlie, I am in perfect agreement with your 2nd column that is labeled "1st perms."
Its your third column and fourth columns that I don't agree with. Example: for all the initial hands in which you are drawing 4 cards to a Royal Flush, the probability of making the Royal on the draw is 1/combin(47,4). For the hands in which you are drawing 3 cards to a royal, the probability of the royal is 1/combin(47,3).
When summing cases with different numbers of cards being drawn, I found it was easier to convert to probabilities before summing.
Catch | Perms | 1st Prob | 2nd Prob | Contribution |
|---|---|---|---|---|
5 | 4 | .000 001 539 | 1.000 000 000 | .000 001 539 |
4 | 940 | .000 361 683 | .021 276 596 | .000 007 695 |
3 | 43 240 | .016 637 424 | .000 925 069 | .000 015 391 |
2 2 | 25 200 | .009 696 186 | .000 061 671 | .000 000 598 |
2 | 597 000 | .229 707 268 | .000 061 671 | .000 014 166 |
1 1 1 1 | 20 000 | .007 695 386 | .000 005 606 | .000 000 043 |
1 1 1 | 248 000 | .095 422 784 | .000 005 606 | .000 000 535 |
1 1 | 744 000 | .286 268 353 | .000 005 606 | .000 001 605 |
1 | 719 200 | .276 726 075 | .000 005 606 | .000 001 551 |
0 | 201 376 | .077 483 301 | .000 002 608 | .000 000 202 |
2 598 960 | 1.000 000 000 | .000 043 326 | ||
23 080.747 |
5h 10c Js Qd Kh
Are we assuming there's other pays and they actually matter? If not, would it really matter? The king. If there are other paybacks that matter, I assume that Jack would be the proper hold.Quote: michael99000What would be the Royal at All Costs play with this hand. ?
5h 10c Js Qd Kh
Quote: AxelWolfAre we assuming there's other pays and they actually matter? If not, would it really matter? The king. If there are other paybacks that matter, I assume that Jack would be the proper hold.
I would assume the jack.
I would go with the J as well for more straight possibilities.
Quote: DRichOn this Royal at all cost strategy would you hold the ten in this dealt scenarios 10h 9c 9s 9d 9h?
I would hold my nose and the 10.
I’ve thrown away several dealt trips.
Quote: michael99000What would be the Royal at All Costs play with this hand. ?
5h 10c Js Qd Kh
I have been keeping the J.
Playing 5x$0.10
Starting amount: $400
Current: $269.50
Lost $130.50
165 won/500 games 33% win
47.8% payback
Quote: smoothgrhI have been keeping the J.
Regarding 5h 10c Js Qd Kh in 9-6 Jacks or Better, the Wizard's hand analyzer gives these returns:
0.456121 jack
0.293337 ten
https://wizardofodds.com/games/video-poker/hand-analyzer/
Imagine you find a video poker machine that has a paytable with only one line:
Royal Flush___ 3000
and it says that you may draw twice. That is, you get an initial deal, discard cards, and draw. Then discard cards a second time, and draw a second time. What is the house edge on this unusual video poker game?
Well, I've performed a calculation of the combinations and probabilities associated with that, assuming the player uses a perfect Royal Seeker strategy.
To use an example, on the initial deal let's assume that the player gets two cards that are 10 or higher: a Jack of hearts and a Ten of spades. Now let's assume, the player holds the Jack of hearts, discards the four other cards including the 10 of spades, and draws 4 cards and gets 'AdKd + two other cards that are less than 10.' The calculation assumes that the player will then draw 3 cards to the AdKd on the second draw. If however, on that first draw, the player gets Ace of spades and King of spades, my calculation understands that the spades suit was 'killed' by discarding the 10 of spades on the first draw, and so continues to draw to the Jack of hearts.
Results
After the initial deal, you will have a Royal Flush with a probability of 1.539 E-06, or 1 in 649,740 (approx).
After the first draw, you will have a Royal Flush with a probability of 0.0000433326, or 1 in 23,080.7 (approx).
And, after the 2nd draw, you will have a Royal Flush with a probability of 0.0003326, or 1 in 3,006.375 (approx).
You can see that the 1st draw increases the likelihood of having a Royal Flush by about 28.15X. However the 2nd draw only increases the likelihood of a Royal Flush by a factor of 7.677X.
The first draw involves drawing an average of 3.804 cards; on the 2nd draw an average of 3.364 cards are drawn.
To answer the original question about this hypothetical VP paytable, here is the return table:
| Outcome | Payout | Probability | Return |
|---|---|---|---|
| Royal Flush | 3,000 | 0.000332626 | 0.997879436 |
| Lose | -1 | 0.999667374 | -0.999667374 |
| Total | 1 | -0.001787938 |
So the house edge on this unusual double-draw Royal Flush-only VP game would be about 0.179%.
Quote: gordonm888Royal Flush After 2 Draws with Royal Seeker Strategy
Imagine you find a video poker machine that has a paytable with only one line:
Royal Flush___ 3000
and it says that you may draw twice. That is, you get an initial deal, discard cards, and draw. Then discard cards a second time, and draw a second time. What is the house edge on this unusual video poker game?
Well, I've performed a calculation of the combinations and probabilities associated with that, assuming the player uses a perfect Royal Seeker strategy.
To use an example, on the initial deal let's assume that the player gets two cards that are 10 or higher: a Jack of hearts and a Ten of spades. Now let's assume, the player holds the Jack of hearts, discards the four other cards including the 10 of spades, and draws 4 cards and gets 'AdKd + two other cards that are less than 10.' The calculation assumes that the player will then draw 3 cards to the AdKd on the second draw. If however, on that first draw, the player gets Ace of spades and King of spades, my calculation understands that the spades suit was 'killed' by discarding the 10 of spades on the first draw, and so continues to draw to the Jack of hearts.
Results
After the initial deal, you will have a Royal Flush with a probability of 1.539 E-06, or 1 in 649,740 (approx).
After the first draw, you will have a Royal Flush with a probability of 0.0000433326, or 1 in 23,080.7 (approx).
And, after the 2nd draw, you will have a Royal Flush with a probability of 0.0003326, or 1 in 3,006.375 (approx).
You can see that the 1st draw increases the likelihood of having a Royal Flush by about 28.15X. However the 2nd draw only increases the likelihood of a Royal Flush by a factor of 7.677X.
The first draw involves drawing an average of 3.804 cards; on the 2nd draw an average of 3.364 cards are drawn.
To answer the original question about this hypothetical VP paytable, here is the return table:
Outcome Royal Flush Lose Total
So the house edge on this unusual double-draw Royal Flush-only VP game would be about 0.179%.
Very interesting, no way I would have thought a 3000 coin payout would be close to 100% return in a game like this.
But in every VP game I'm aware of, prizes are paid out on a "for 1" basis. So if a game like this pays 3000 for a royal flush, it's really 3000 for 1, or 2999 to 1. And a losing hand is 0 for 1 or -1 to 1. Your chart actually shows the payout for 3000 to 1 basis.
So for the "for one" basis the loss column should be 0 instead and the royal flush at 3000 for 1 would return 0.997879436 to the game, yielding a "house edge" of about 0.212%.
Started with $400
Playing 5x$0.10
Now at $132.50
314 wins/1000 hands (31.4%)
46.5% payback
Drew four to a royal on one hand.
Missed holding the ten with a high card about three times early on, but now keeping watch for that.
Am thinking “what have I gotten myself into?”
The prospect of possibly doing this 22 more times (or more) makes me think of the name: Sisyphus.
2,308 games played
723 games won
31.32% win
5x$0.10=$0.50/play
$1154 played
$535.50 won
46.40% yield (“payback %”)
Lost $618.50
Highlights:
One 4-to-a-Royal after the draw.
One quads drawn after one card held.
Approximately 230 minutes of my life that could have been spent doing something else. But it’s all in the name of science and entertainment!
A few statistics/observations:
—1,425 “winning” hands of 4,700 total hands—about 30.3%
— Payback percentage of 44.76%
— Three “true” 4 to a royal hands, either on the draw, or with drawn cards—the last card not completing the royal
— Three “fake” 4 to a royal hands, in which I finished 4 to a royal, but a non-royal card was drawn before the final card.
— At some point, I felt like this was a “joyless” way to play, wherein the only excitement was to get an occasional full house (I got quads once).
— But later, I realized that even being able to do something as inane as this experiment in my home was a blessing that many others don’t have the time/means/health to do.
— I still think it’s stupid, but it takes only about 10 minutes to play 100 hands, and it’s something I do during my morning coffee or to wind down the day.
Quote: smoothgrhUpdate: I'm at 20% of the 23,081 hands that take on average to get a royal flush using the "Royal or Nothing" strategy. I have not gotten a royal flush.
A few statistics/observations:
—1,425 “winning” hands of 4,700 total hands—about 30.3%
— Payback percentage of 44.76%
— Three “true” 4 to a royal hands, either on the draw, or with drawn cards—the last card not completing the royal
— Three “fake” 4 to a royal hands, in which I finished 4 to a royal, but a non-royal card was drawn before the final card.
— At some point, I felt like this was a “joyless” way to play, wherein the only excitement was to get an occasional full house (I got quads once).
— But later, I realized that even being able to do something as inane as this experiment in my home was a blessing that many others don’t have the time/means/health to do.
— I still think it’s stupid, but it takes only about 10 minutes to play 100 hands, and it’s something I do during my morning coffee or to wind down the day.
44% return sounds high if this is a true royal at all costs strategy.
Quote: DRich44% return sounds high if this is a true royal at all costs strategy.
Click on the link in the OP, you'll see it's 48.02% for 9/6 Jacks. He's about right on pace for NOT hitting a royal.
You back into Jacks, 2 pair, and trips: 22.85%, 4.64%, and 2.04% of the time respectively. That adds up. The bigger categories other than quads and SF give back more than 1% return each.
Quote: billryan17,611
Okay, I am NOT accepting this figure. Let just say I am not disputing it at the present time. I would like to know how long would it take to play that number
of real games?
Quote: FleaStiffOkay, I am NOT accepting this figure. Let just say I am not disputing it at the present time. I would like to know how long would it take to play that number
of real games?
A 1000 hands an hour is a very realstic number for a videopoker player.
Quote: DRichA 1000 hands an hour is a very realstic number for a videopoker player.
Especially when you get used to playing the Royal only strategy.
Quote: tringlomaneEspecially when you get used to playing the Royal only strategy.
Do real people actually play that strategy and stick to it?
I can't imagine someone being dealt four aces with a kicker and throwing it away to go for the royal.
Quote: DRich44% return sounds high if this is a true royal at all costs strategy.
Whoa! Sudden interest in this topic!
In the original post, I linked to the Ask the Wizard newsletter in which he says:
Quote: WizardI assumed that given two plays of equal royal probability the player will choose the play which maximizes the return on the other hands. The house edge of this strategy on a 9/6 jacks or better game is 51.98%
So if HE is 51.98%, then payback would be 48.02% which is about what I’d have if I get a royal at about 23,000 hands.
Quote: DRichDo real people actually play that strategy and stick to it?
I can't imagine someone being dealt four aces with a kicker and throwing it away to go for the royal.
I can imagine it’s a real strategy for many players until they start making pat hands.
I'm up to 5,900 hands on my home video poker machine. Are the odds of getting a royal flush relative to me, not just the machine I'm playing?
In other words, what if I indeed got a royal flush on my Palm Pilot in the early 2000s (and it was a fair game)? Does that mean I need to factor in all those game that I played? Maybe I got lucky and it took me only 6,000 hands on my Palm Pilot, so now I've already gotten a royal flush in about 18,000 hands: 6,000 at home + 6,000 on Palm Pilot + 6,000 at actual casinos?
So maybe I'm not "due" for another royal flush until another 28,162 hands: (23,081*2)-18,000?
But then, do I actually need to play those hands? If it could be on any device, what about if I just happen to walk past a video poker machine and observe a person playing a hand? Does that count as a hand played for me as well?
Does one even need to observe it? Can you say that in the old days, a "change girl" strolling the floor on her shift is observing hundreds or thousands of hands or spins each shift, and tallies the same amount of plays and will observe a jackpot according to the true odds?
Am I drunk?
Quote: DRichDo real people actually play that strategy and stick to it?
I can't imagine someone being dealt four aces with a kicker and throwing it away to go for the royal.
Missed this.
No I don't think so, but some people have suggested it might be a good idea for tournaments. I'm not convinced on that though.
And the probability of making a royal on any given hand varies by the strategy played, smoothgrh. Like rsactuary said, every hand is independent and you're never "due".
When you get two RFs in a row, what will be the odds off getting another the next hand- 1 in 40,000.
My pondering is about what constitutes a hand. I observe hands when I play. I also observe hands when I watch other people play. Do all these observations of hands make the statistics relative to me move closer to the long-term statistical average of royal flush frequency?
If you want to say that you on average you got a royal every 40000 hands, you can't include the royals you see watching other people play. If you want to say you see a royal every 40,000 hands, then by all means include the hands you see other people play. This also gets complicated because people are playing different games with different strategies and not even the correct strategy. Then there's multi-hand play, how would you account for that if you were counting "seeing" hands?
Quote: billryanDo the odds change if you are observing the hand rather than playing it yourself?
I know when it comes to sports betting, baccarat, stock trading , the win rate is much higher on internet message board posts than anywhere else.
A phenomenon worth studying
there are just some people who get off on making up grandiose crap. I'm not sure if they're delusional and believe that people believe them or they just don't care as long as there's a chance someone believes them.Quote: michael99000I know when it comes to sports betting, baccarat, stock trading , the win rate is much higher on internet message board posts than anywhere else.
A phenomenon worth studying
I'm now at 7,000 hands, with 2,125 wins so win rate is at 30.3%, but still no royal. Yield is 45.18%.
I was thinking: who pays out jackpots at a mom & pop store? Is a slot distributor that places the machines at the store on the hook when several jackpots hit at once? I wouldn't want Frankie's Tiki Room to go under because a bunch of people get royals.
I assume the store pays to have the machines placed there to drive customer traffic. Does the store get any share of slot revenue?
Quote: smoothgrh
I was thinking: who pays out jackpots at a mom & pop store? Is a slot distributor that places the machines at the store on the hook when several jackpots hit at once? I wouldn't want Frankie's Tiki Room to go under because a bunch of people get royals.
I assume the store pays to have the machines placed there to drive customer traffic. Does the store get any share of slot revenue?
OMG! I hope you are not playing at a retail establishment or the airport for that matter. Very low paybacks.
Quote: smoothgrhI took a break from playing, but am now back at it (not that anyone cares).
I'm now at 7,000 hands, with 2,125 wins so win rate is at 30.3%, but still no royal. Yield is 45.18%.
I was thinking: who pays out jackpots at a mom & pop store? Is a slot distributor that places the machines at the store on the hook when several jackpots hit at once? I wouldn't want Frankie's Tiki Room to go under because a bunch of people get royals.
I assume the store pays to have the machines placed there to drive customer traffic. Does the store get any share of slot revenue?
Almost every bar, restaurant, or store has a slot route operator that runs the machines. Generally the stores get a percentage of the win and shares the win wih the slot operator. Most bars for example get about 85% of the weekly win.
Quote: kewljOMG! I hope you are not playing at a retail establishment or the airport for that matter. Very low paybacks.
i'm playing in my garage! And the payback pct is so low because i dump winning hands in favor ot cards that would improve my hand to a royal.
Quote: DRichAlmost every bar, restaurant, or store has a slot route operator that runs the machines. Generally the stores get a percentage of the win and shares the win wih the slot operator. Most bars for example get about 85% of the weekly win.
Thanks for the info! But don't establishments also pay to lease the machines? I had heard that Debbie Reynolds's casino was losing money every day from leasing slots. Or was that situation different because she was likely on the hook for paying out jackpots?
