I believe that one of the biggest problems for video poker players, even many very skilled ones, is understanding bankroll requirements. This has become an even bigger problem in recent years because of the decline of really good VP plays. Most of us are having to play with a much smaller edge than we were several years, and too many are not recalculating the bankroll needs for their current plays. Thus in my personal e-mail and conversations with players and reading Internet chatter on video poker forums, I am seeing severe disillusionment that is giving rise to doubts that financial successful advantage VP play can really be achieved.
First, players are forgetting or straying away from the basic building block: playing ONLY when you have an advantage. You need to change your goals – and rename your hobby – if you decide to play – for whatever the reason – when you do not have the advantage. I’m not saying that is a bad thing IF you are doing this with your eyes wide open and you can afford purely recreational play. But don’t try to fool yourself in thinking that you are still an advantage player.
But even those who are sticking with that basic advantage-player premise, some seem to be forgetting another basic truth: you must look at the LONG TERM and not be discouraged at the inevitable short-term losing streaks. And I believe the cause for this anguish among even skilled VP players is that the lower the edge you have on the casino, the longer the long-term will be AND the bigger the bankroll you will need to survive.
I’m going to talk about this subject more in future blog writings as there are many facets to these issues. Today I want to share a good article on this subject that zeros in on the role of the royal flush and how it impacts your short-term results. This was written by my good friend and fellow gaming writer, Henry Tamburin, the author of five books on casino gambling, featured blackjack writer for dozens of magazines and web sites, and editor of the Blackjack Insider Newsletter. He is also an avid video poker player.
UNDERSTANDING ROYAL FLUSH CYCLES IN VIDEO POKER
by Henry Tamburin
One of the most misunderstood concepts in video poker is “the royal flush cycle.” It’s important if you want to be successful at video poker that you understand what this is, and how it can affect your bankroll.
A royal flush cycle is the mathematically calculated average number of hands it takes to hit a royal flush using perfect strategy. The number of hands in a royal flush cycle varies slightly from game to game. For Jacks or Better, the royal flush cycle is 40,391 hands, whereas a Full Pay Deuces Wild game it’s 45,282 hands (See Table 1). Why is there a difference in the number of hands? Because in some games, the playing strategy calls for holding more two- or three-card royal flushes (than other games); therefore, you will get more royal flushes.
Table 1
Royal Flush Cycles
| Game | Cycle |
| Jacks-or-Better | 40,391 |
| Double Bonus | 48,048 |
| Double Double Bonus | 40,782 |
| Deuces Wild-Full Pay | 45,282 |
| Deuces Wild-NSU | 43,456 |
| Joker Wild-Kings-or-Better | 46,214 |
Most players expect to hit one royal flush after playing roughly 40,000 hands. That is not necessarily the case. The math says on average you will hit a royal flush once in every 40,000 hands, which means for a whole bunch of sets of 40,000 hands, you’ll average one royal. In other words, in any given one set of 40,000 hands, you could wind up with more than royal or, heaven forbid, possibly no royals. (Would you care to guess what the chances of the latter catastrophe occurring? Keep reading for the answer.)
There is a mathematical formula that you can use to calculate the probability of hitting any number of royal flushes in any number of cycles (the formula is called the Poisson Distribution after the French mathematician Simèon Poisson, who developed the formula in the 19th century to calculate the probability of rare events). Don’t worry …you (or I) don’t have to take out our calculators because my friend and fellow video poker author Dan Paymar (creator of Optimum Video Poker software trainer) has done the work for us. The calculations yield the following results for one cycle of 40,000 hands (Jacks or Better):
Table 2
Probability of Hitting a
Royal in One Cycle
| # of Royals | Probability |
| None | 36.8% |
| 1 | 36.8% |
| 2 | 18.4% |
| 3 | 6.1% |
| 4 | 1.5% |
| 5 | 0.3% |
| 6 or more | 0.1% |
Wow! If you look at the data in Table 2, it says that you have the same 36.8% chance of getting one royal or no royals after playing one cycle of 40,000 hands. Since the royal flush contributes 1.98% toward the overall 99.5% ER for jacks-or-better, your return between royals is only 97.5% (meaning that your bankroll will more than likely head south from one royal flush to the next one). This, dear readers, is why you must have enough bankroll to play video poker … to cover those times when you play many hands without hitting a royal.
Have I ever played one cycle and not hit a royal? You bettcha and it was painful. I keep records of all my playing sessions and the worse streak I ever had was about 135,000 hands without a royal flush. Even though that was painful (for my bankroll and me), I have friends who play video poker that have gone way more than 135,000 hands between royals (ouch!).
However, let’s be optimistic and look at the other side of the curve. I recently played roughly 40,000 hands of 9/6 Jacks or Better (one cycle) in Las Vegas and I hit three royal flushes. Was I lucky? According to Table 2, the chance of hitting three royals in one cycle of Jacks or Better is a paltry 6.1%. So yes, I would consider myself very lucky to have hit three royal flushes during this trip.
The data in the above table also leads to this conclusion: You have about a 63% chance of hitting one or more royal flushes in one cycle and only a 36.8% chance of hitting no royals (does that make you feel any better?).
Do you think it’s impossible to play 200,000 hands of Jacks or Better (five cycles), which many video poker aficionados consider to be the “long term,” without hitting one measly royal flush? I hate to be the bearer of bad news but according to the data in Table 3, you have a 1 chance in 140 (0.7%) of not hitting a royal flush even after playing 200,000 hands (or roughly 400 hours of play).
Table 3
Probability of No Royals after X Cycles
|
# Cycles |
Probability of No Royals |
|
1 |
36.8% |
|
2 |
13.5% |
|
3 |
5.0% |
|
4 |
1.8% |
|
5 |
0.7% |
|
6 |
0.3% |
|
7 |
0.09% |
|
8 |
0.03% |
The percentages in Table 3 are scary. You have a 5% chance of getting no royals after 120,000 hands (3 cycles), and 1.8% chance after 160,000 hands (5 cycles). Even though the chance of winding up without a single royal flush are slim, if it were to occur, it could be financially catastrophic (especially if you don’t have enough bankroll to weather this remote, but still possible, outcome).
The reality for video poker players is this: In any one royal flush cycle of roughly 40,000 hands, there are no guarantees that you will hit exactly one royal flush. If you are lucky, you could get more than one royal flush, and if unlucky, you could wind up without any royals (this is why having enough bankroll to play video poker is very important).
what are the odds of having a royal delt to you?
Also if you get one in six cards, 7or 8 or 9 or 10 cards
Just answering some of the questions posed:
You know how many hands you have played by recording or remembering the balance of your slot club points when you begin play, then calculating the coin-in and dividing by the appropriate number based on denomination and what the slot club $-per-point number is. For instance, if you’re playing dollar denoms ($5 per play) at a casino that awards one point for every $2 played, every 100 hands would award 250 points–so 2,000 points would mean you’d played 800 hands.
There is no “optimum” bankroll level–as your bankroll increases, your risk of ruin decreases, so “optimum” would be whatever amount gives you a risk of ruin you can live with. Obviously, we’d all like infinite bankrolls. The reason to look at RoR is that below a certain level of bankroll, you will probably bust out, i.e., your RoR is above 50%, even if you are playing a +EV game. Volatility also enters into RoR and thus, bankroll requirements.
If you wish to calculate strategy changes for progressive royal games, simply use any one of the many video poker software programs out there, change the royal payout to the actual number of coins represented by the progressive, and then compare the resulting strategy chart with the one for the “base” game. Also note: on 9/6 JOB, you don’t even reach breakeven until the progressive is about 5,300 units, so playing when it reaches 5,000 units is still a losing game.
Great article! I play JOB at an OK casino where there is very little cash back offered. However, the progressive often gets over 5000 units for a royal. Where do I find out how to adjust my strategy when the progressive puts me in “advantage realm?” Thanks for info!
Kevin raises a good question. Should my bankroll be at the optimum level every time I being play?
Don
Like Jim and Bev’s comment, how do you know how many hands you have played in any given session?
Jean, as usual you are right on point! My wife and I have been Royal…less since last February when we hit, while playing on machines next to each other, within 10 minutes. Seven days later I hit a progressive royal at a different casino! We are recretional players only, visiting casinos about 2 to 3 times a month, in the So. California area.
During a 6 hours play yesterday we could not hit much of anything and found ourselves depressed going home on a down-streak. Your article comes at a very good time to put our perpective back on track. We will regroup and refigure our bank roll as we plan a Vegas trip next month. To good fortune and good health!
Thanks as always.
Playing seriously since 1995, I have had a 200,000-hand royal drought at least six times (my records aren’t complete for the entire last eighteen years). My worst sustained losses have never exceeded $5,000 (4000 hands) at .25 denomination (the vast majority of my play). I therefore view $5,000 as a minimum bankroll for quarters. However, I have one question that I’ve never seen adequately answered. Given that your bankroll is constantly being depleted while you wait for your next royal, if you have what you consider an adequate bankroll when you start playing, that bankroll will drop below that threshold as you wait for the royals to show up–it’s the nature of the beast. If my 5K bankroll dropped to 2K, I might consider myself functionally unable to play, as my risk of ruin would now be unacceptably high. I’m sure that the reason many good players go broke is that they are undercapitalized: they have an adequate bankroll, but only barely so. If they hit a rough patch, they don’t either a) stop playing, b) move down in denomination, or c) play higher EV games; rather, they just keep playing even though their bankrolls are no longer sufficient. The smaller your bankroll, the less short-term bad luck you can withstand. And we all know how in video poker, things can go to pot in a hurry–and stay there, for many sessions in a row. You have to be able to weather the storm–so my stated 5K .25 play bankroll would really have to be, say, 7K for me to be comfortable.
Great article. Would you happen to know how many hours of play it might take someone to complete one cycle?
I think one factor that is almost always ignored in these discussions is the tax implications of being a recreational player and trying to get an advantage. If you only gamble a few times a year it is very hard to reach the “long term” in one year. My recent statistics showed 3 losing years punctuated by 1 very profitable year but after paying taxes on my “winnings” it was obvious that I was not going to have an advantage unless I played much more frequently. Not many of us are able to file as professional gamblers.