Odds Of A Royal Flush In Video Poker

The Royal Flush is the pinnacle of success and luck for a video poker player - the best and highest paying hand in the game. Many readers have sent us questions about how often they should expect royals, and how many hands it should take to hit a royal flush. This article is going to discuss 'Royal Flush Cycles', which are measurements of how long it should take to hit royals in different types of video poker games.

The bottom line is as long as the pay schedule is the same for a particular video poker game, the odds of getting a royal flush will be the same no matter where the machine is located (assuming a random deal). Playing with a slot card changes the odds of winning; Video poker machines have hot and cold cycles; The odds of winning are better on multi-hand machines: A Royal Flush MUST Hit Every 40,400 Hands False. While the average number of hands between royal flush wins might be 40,400 there is nothing in the machines that make this happen. Thus the probability that you will not get a royal flush, for example, in three hands is approximately 1 to 20. Fortunately, in video poker you win only with the highest possible hand. Otherwise you would need a huge bankroll.

What is a Royal Flush Cycle?

The first thing you should know is that a royal flush cycle is the average amount of hands it takes to hit a royal flush for a specific game while playing with perfect strategy. If a cycle is 40,000 hands, that is the long run average of how many hands it will take to hit a royal.

However, because of variation you could easily hit a royal flush on your first hand, or not hit one until your 120,000th hand. The more you play, the closer you'll get to averaging one royal flush per one royal cycle worth of hands played.

Cycles for Different Games

The next thing you should know about royal flush cycles is that they vary from game to game. This has nothing to do with the machine or it's odds of hitting a royal flush - it's all about the strategy you use. Some games call for holding more two and three card royals, while other games say you should discard them to attempt other draws.

Jacks or Better Royal Flush Cycle

In Jacks or Better you can expect a royal flush every 40,391 hands. This is based on playing with perfect Jacks or Better strategy and playing a full pay game.

Deuces Wild Royal Flush Cycle

In full pay Deuces Wild you can expect a royal flush every 45,282 hands. In 15/10 Loose Deuces you can expect a royal flush every 45,236 hands. The difference between the two cycles comes from the strategy changes for the different pay tables.

Double Bonus Royal Flush Cycle

In 10/7/50 Double Bonus you can expect a royal flush every 48,048 hands. In 10/7/80 Double Bonus you can expect a royal flush every 46,727 hands. How many casinos are in michigan. The difference comes from the strategy changes for the different pay tables.

Joker Wild Royal Flush Cycle

In 20/7/5 Joker Wild with a 4,000 royal flush, you can expect royals every 41,214 hands. In 20/7/5 Joker Wild with a 4,700 royal, you can expect one every 38,614. The difference comes from the strategy changes for the different pay tables.

Why do Pay Tables Effect Royal Cycles?

After you saw the odds above, you probably were wondering why the pay tables would effect the royal flush cycles. Well, in all actuality, the pay tables don't effect the machines' odds whatsoever. However, they do effect how you play the game.

For example, if you're playing a 20/7/5 Joker Wild game with a 4,700 coin royal, you're going to chase the royal more often than a game with a 4,000 coin royal. Since you're chasing the royal more often you'll hit it more often, and thus the shorter cycle.

Royal Flush Poker Game Free

Quite often, people use the well-known normal distribution toestimate the kind of results that you should expect whenplaying video poker. But, this estimate is off by quite abit unless you are talking about a very largenumber of hands (around 4,000,000 should do). For a smallernumber of hands, we need to be more careful. On this page,I will examine four popular video poker games with quitedifferent characteritics. Note that variance is measuredin units of bets squared.

Video poker games tend to have high variance, and most of that varianceis carried in the high payoff hands (typically Royal flush and specialbonus hands such as Four Deuces).Although these hands have a majoreffect on the EV, for short term play, the probabilities of the common hands are more important. The followingchart shows the probability distribution of ending bankrolls afterplaying 1000 hands of the four games specified.

Although the area under each curve is the same (they all integrateto give 1.0), they have different shapes. The Jacks or Bettercurve is sharpest because JB does not have a second high payinghand besides the Royal. On the other hand, Deuces Wild hasa distinct 'knee' at around 200 units, which corresponds to the200 unit payout of the 'mini-jacpot' of four deuces.Also notice the little 'blips' at around 800 units on each curve.All of the games pay 800 for a Royal, and those blips representthe chance of getting a Royal in 1000 hands.

Looking at these curves alone, it is hard to see that Deuces Wildhas the highest EV and Jacks or Better the worst.In fact, for such a short session, you are more likely to benear even, and to avoid a large loss, play JB rather than the othergames, even though it has the worst EV.So, what happens if we look at a larger session?

Probabilities - 10,000 Hands

After 10,000 hands, things start to smooth out quite a bit.It is apparent that the lower EV of JB is starting to dragit downward -- the long term expectation is to lose yourbankroll playing any negative expectation game. Also noticethat the 'four deuces' knee has been completely absorbed inthe Deuces curve, and the Royal kneeis starting to merge for Jacks (itwill take about 30,000 more hands before the Jacks kneeis no longer apparent). Also, Deuces is starting to looka good bit better than Double Bonus (especially on theleft hand side, where the losses are!).

But, 10,000 hands may be a bit long for a session for mostplayers. I picked 5,000 hands as a good intermediate valuethat is close to what I expect most players would plan fora short trip.

After 5000 hands, the left hand Jacks peak is almost perfectlynormal --- but it matches a normal curve with a variance (and expecation) corresponding to subtracting out the Royal.Because cases where a Royal does occur (represented by theright hand peak) are well-separated from the first case, here we can get a good approximation of the distributionby combining two normal curves. But that is not truefor Deuces or Double Bonus (Pickem is quite close to normalby this point because the very high paying hands are sorare). Notice that both Deuces and DB are not symmetric-- the right hand side of the curve has 'lifted its foot'considerably.

So, what does this mean to the player? I'm glad you asked.We can redraw the same curves to give the cumulative probabilitiesand read off what to expect on a session of 5000 hands.

Cumulative Probabilities - 5000 Hands

Odds Of A Royal Flush In Video Poker Tournaments

For any given ending bankroll (starting from zero, remember), thecurves indicate the percentage of the time that you will end upat or below the indicated point after 5000 hands of the chosengame. Looking at the vertical line at zero ending bankroll, we cansee that you should expect to lose at Jacks or Betterabout 72% of the time, but only about 55-56% of the time at theother games.From the other angle, the 50% horizontal line show that halfthe time we should lose 102 units or more when playing JBfor 5000 hands, but only 32-51 (or more) for the other games.

From a trip bankroll perspective, the 5% and 10% lines maybe the most interesting.For a 5000 hand session, Double bonus can be cruel -- youwill end up losing over 400 units one trip in 10, and 488or more 1 in 20. The other games aren't quite so bad, butyou must be prepared for the variance.

Be careful of one thing --- the curves assume you play thefull 5000 hands. So, you might dip below the ending bankrollon the way to getting there. You really need a bit more thanthe curves indicate (ballpark estimate: 10%) to be sure you don'tend up with playing more before the end of your trip morefrequently than you had planned for.

I hope these curves will help you to understand the cruelyet enticing game of video poker. We can't get rid of thevariance, but we can understand and prepare for it.

Odds Of Hitting Royal Flush

Odds Of A Royal Flush In Video Poker Tournament

--jazbo