Expected vs Actual Royal Flushes

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Even though I love thinking about gaming math, particularly video poker, I have been a horrible record keeper in my gambling exploits, so I can't give a good answer to this. In my case, if you count my dealt penny royal as individual royals (only 6 lines :(), I have to be above average. Otherwise, I would guess I am below average, 3 royals total (dealt Royal counted once). As for number of total hands, oh god, I dunno, hopefully not above 200,000 at this point.

Two years ago I went through about 180,000 hands without a royal and the number 180,000 came by figuring my tier score with Total Rewards. This year I have had 8 royals but because Total Rewards changed to offer 5,000 tier score point bonuses and smaller bonuses for certain sessions, I have no idea if I am above or below the expected number of royals.

duplicate

VP is a very up and down scenario.

I keep detailed records (assuming the points generated while playing are accurate). In the past 2 1/2 years I have played 630K hands of mostly 9/6 Jacks (Occasionally play 9/6 Bonus Poker Deluxe). I have had 14 royals which is about a 45K per royal average. This wouldn't seem too bad except for the banks I play. One (JOB) bank has a progressive royal, straight flush and 4 of a kind. The other bank (multi-games) has a progressive royal. The casino is not next door to me, so I don't always get to choose whether to play or not after driving to it. I do get to choose which bank I play which is normally the JOB bank since it is normally the higher overall game. I have many strategy charts for the various pay amounts and change play accordingly. The average incidence of royal over this time should be about every 36.5K hands. Therefore I am still down a little more than 3 royals.

I did not have my first royal doing this for about 160K hands. I have never been closer than within about 1 royal of expectations. When I got this close I thought things were finally going my way, but then I hit another bad streak

It does make you a tad paranoid when you do not seem to get your share. I have tracked different things at different times and the banks appear to be on the up and up.

As an oddity 3 of my 14 royals have been dealt to me.

This should be in the VP forum.

Because of the progression in the royal amounts (40K hands = $1000) I do get to see occasionally how long it can take to have a royal hit. I have seen the banks in the 7-8K range a few times. I had to leave once when a bank was at 7600 and found out later that the bank was over 9K when the royal was finally hit. As many different times as I have seen the banks in the 5-6K range, it does give you some idea of how often it can take a lot more than 40K hands to have a royal hit. This kind of info would be hard to obtain from a non-progressive bank.

I have heard of people going 10 royal cycles On $ DW.

I'm very luckily overroyaled. I don't keep detailed records but I don't think I've ever been down more than one royal cycle. (Thank the gambling gods).

I don't keep detailed records but I do have a good estimate of how many hands I've played based on the number of points I have at the casino - points that are 1 point per dollar for vp. I've hit one royal in about 120,000 hands. I keep hoping that it will start to catch up to normal range soon. I also rarely hit a straight flush but I'm not quite sure how often I should expect them. I don't know for sure but I think I've hit 4 or 5 in those 120,000 hands.

Quote: PBguy

I don't keep detailed records but I do have a good estimate of how many hands I've played based on the number of points I have at the casino - points that are 1 point per dollar for vp. I've hit one royal in about 120,000 hands. I keep hoping that it will start to catch up to normal range soon. I also rarely hit a straight flush but I'm not quite sure how often I should expect them. I don't know for sure but I think I've hit 4 or 5 in those 120,000 hands.

For ~120,000 hands, you should be closer to 12 for the average. :-\

Fwiw, I wouldn't doubt I am behind on SF either. But I really don't recall how many I have had. I know I got the steel wheel dealt once...lol

Quote: tringlomane

For ~120,000 hands, you should be closer to 12 for the average. :-\

Fwiw, I wouldn't doubt I am behind on SF either. But I really don't recall how many I have had. I know I got the steel wheel dealt once...lol

Probably pushed myself closer to average on SF's today...

Hmmm.....I didn't realize you could bet only 1 hand with the bonus bet as well. I knew you could bet all 3 lines with no bonus bet. Can you play 2 lines with a bonus bet but not the 3rd? can you do that on all STP ?

Quote: AxelWolf

Hmmm.....I didn't realize you could bet only 1 hand with the bonus bet as well. I knew you could bet all 3 lines with no bonus bet. Can you play 2 lines with a bonus bet but not the 3rd? can you do that on all STP ?

Yessir, you can bet any amount of lines you wish for max bet as long as you use the touch screen. Partly why I like STP so much. Last time I was at that casino (Blue Chip in Indiana), I hit this. Of course, all 10 lines would have been nicer here...doh



I played 10-line because 3/5 line was 9/5 JoB, but 10-line was 9/6 JoB. Unfortunately, they downgraded 10-line quarters to 9/5 JoB now, so I said screw it and moved to nickels only today to cut down my expected loss. I looked around the casino and 9/5 JoB w/STP (98.72%) was still the 2nd best game. Best game was 98.91% DW44 in multiple places. Quarter spin poker, quarter 3-play, or dollar 1-play :-\

Quote: tringlomane

For ~120,000 hands, you should be closer to 12 for the average. :-\

Fwiw, I wouldn't doubt I am behind on SF either. But I really don't recall how many I have had. I know I got the steel wheel dealt once...lol

I did have one royal flush draw where I was dealt suited 10 thru K and on the draw I got the suited 9 for the straight flush. Not nearly as good as the rf but a nice consolation prize.

You can count how many RF's I've had in my life on zero hands.

In terms of actually playing for money, I'm probably near one Royal cycle on JoB, don't know for sure, but it's close. In terms of Play For Fun games on-line, including videopoker.com and the Free JoB on WoO, I've probably played through three or more cycles (if you include my cycle on real money games) and haven't seen one. I play close to Optimally. I am down to approximately one mistake per 500 hands on Wizard's JoB game, I always treat going for the five-high straight incorrectly. ALWAYS.

If I gave myself a minute to think about it, I'd make the right play, but I get into my rhythm and just naturally make the wrong play.

I haven't kept detailed stats over the last 20 years of playing video poker, but i would guess my royal flush numbers are pretty close to where they should be. Sadly, on my current bad luck streak I am about three standard deviations out since hitting my last royal flush.

My biggest "so close to a jackpot" moment came when I was dealt 4 to a RF playing 5c 100 play VP. If I had been dealt the RF it would have paid 20 grand. Instead I hit one RF out of the 100 hands for a total win of $231.75. Big difference for not being dealt that Jack of Spades!

Quote: larwiz1

VP is a very up and down scenario.

I keep detailed records (assuming the points generated while playing are accurate). In the past 2 1/2 years I have played 630K hands of mostly 9/6 Jacks (Occasionally play 9/6 Bonus Poker Deluxe). I have had 14 royals which is about a 45K per royal average. This wouldn't seem too bad except for the banks I play. One (JOB) bank has a progressive royal, straight flush and 4 of a kind. The other bank (multi-games) has a progressive royal. The casino is not next door to me, so I don't always get to choose whether to play or not after driving to it. I do get to choose which bank I play which is normally the JOB bank since it is normally the higher overall game. I have many strategy charts for the various pay amounts and change play accordingly. The average incidence of royal over this time should be about every 36.5K hands. Therefore I am still down a little more than 3 royals.

I did not have my first royal doing this for about 160K hands. I have never been closer than within about 1 royal of expectations. When I got this close I thought things were finally going my way, but then I hit another bad streak

It does make you a tad paranoid when you do not seem to get your share. I have tracked different things at different times and the banks appear to be on the up and up.

As an oddity 3 of my 14 royals have been dealt to me.

Just an update. If I think about it I will do it ever so often.

I have now played 672K hands and have 17 royals. Still about 1 short of the expected for the machines I play, but getting closer. My three royals came from a 4 card royal, 3 card royal and a 2 card royal. So a little bit of everything. They changed their amount to get a point from $12 to $20 a couple of months ago, so I will have to play 200K hands every 6 months to keep highest card level. By this time next year I should be approaching 1.1 million hands of single line. Hell of a lot of hands for an old man's hands.

Quote: larwiz1

Just an update. If I think about it I will do it ever so often.

I have now played 672K hands and have 17 royals. Still about 1 short of the expected for the machines I play, but getting closer. My three royals came from a 4 card royal, 3 card royal and a 2 card royal. So a little bit of everything. They changed their amount to get a point from $12 to $20 a couple of months ago, so I will have to play 200K hands every 6 months to keep highest card level. By this time next year I should be approaching 1.1 million hands of single line. Hell of a lot of hands for an old man's hands.

What casino or casino group is this? Been hearing about VP cutbacks at more places now.

I don't put names of casinos on the web. I don't know that casino personnel monitor the web, but I just don't believe in stoking any fires one way or another. Casino in the boondocks. If you were an avid VP player and lived anywhere close you would use VPfree to look at the place.

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silly


I want pizza

Quote: mustangsally

It looks like the number of actual Royals one gets is still a random variable, even following perfect play and picking the better games to play by the best pay table.

And n the case of playing the best paytable for Double Bonus and Triple Double Bonus, your chances for a Royal goes down significantly thanks to the 7 for 1 payout for a standard flush.

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I am not playing the normal 9/6 Jacks. The game has a progressive royal, progressive SF and progressive 4 of a kind. The average incidence of royal for the times I play is about 36500. So I should have 18+ royals after 672K hands on average. I am just rounding it down to 18

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silly

Sally

I understand what you are saying. I am quite familiar with the binomial calculations. I am looking at the game as a long run (what ever number of hands that is) project. I decided to use the average incidence of royal as my marker of whether or not I am getting my share of royals. If I am to the left of this marker I am down and to the right I am up on my share. This is my method of allaying my paranoid on whether or not the machines have a legitimate RNG. However, royals are such an infrequent event that I have tracked some other things.

It would be too laborious to track all types of starting hands, but I did track starting 3 of kinds for about 100K hands and that was within a couple of the expected. I still track 4 of kinds (I don't know why, just habit) and that is within 10 of the long term expected number over about 600K hands. These are at least indicators to me that the machines have a legitimate RNG. Out of curiosity I started tracking starting 4 card royals this year. This is sort of out of whack (but statistically possible) since I should over many 350K sessions have about 127 per session and have only had 102.

I have 36 machines to pick from to play. However, I have relegated myself to playing the vast majority of my hands to only 8 of them. Machines are not equal in speed of play. The ones I generally play let me play about 950 hands an hour. This is fast enough to suit me. Some of the machines still have the old programming which makes them print a ticket for your last hand if your credits go over 400. This is just an irritation.

By the way, the 36500 figure I use for average incidence of royal is too high. It should be down in the 34k-35k hand range. This is because I am not weighting the data. If the overall long time percentage is above 100.5 I will probably play 6K-8K hands. About all I can physically play for a day. When the long run is closer to 100% I will play a lot fewer hands.

Mustangsally, you make my head explode.

I said I would update this occasionally.

I have played at least 1,087,580 at the casino. This is based on the number of points I have generated over almost 4 years. Based on an incidence of royal of 36000, this would be about 30 royals expected. I have actually had 29 so very close to the long run average. I have been down close to 5 royals below the expected long run amount, but I have had streaks and sort of caught up. Never been ahead of the long run average. Even though I use 36000 as the incidence of royal, I started weighting the data (I play more hands when the royal is higher) the data and the incidence of royal has averaged about 34900. The highest royal amount that I played at was about 8800 (roughly 190000 hands without a hit). The royal was hit sometime in the early morning so I don't know how high it got to.

My longest bad streaks were 155K and 180K hands without a royal. My royals have averaged 5250 (25 of them) at the $1 level and 3478 (4 of them) at the 50 cent level. I don't play the 50 cent game very often (around 8% of the time), but it does occasionally get up that I force myself to play it.

I've convinced myself I've played 125000-140000 hands of full pay DW, DB, DDB without a royal this year. I hardly played at all 1st half of the year, and have pounded it daily for 2-3 months for anything from 1-6 hour sessions. As well as a few sessions July-Aug.

I better see that 3 royals in a month soon or I'm gonna break something!