Much like the myths that abound about slot machines, video poker is also the cause of many myths and misconceptions. In this article we uncover some of the most common myths and show you why they are false. Below is a list of some of the myths and fallacies that we discuss.
The numbers you quote are for drawing to a Royal Flush. The ability to draw cards to improve you hand has a significant effect on your chances to hit winning hands. There are 2,598,960 possible five-card hands you can be dealt. Of those hands, only four are Royal Flushes. So, 1 out of about 42,000 hands result in a Royal Flush after the draw. It means that after about 50,000 hands, the odds dictate that you will have hit every possible hand combination, including the coveted royal flush. Cyber bingo com. Surely, that sounds like a lot of hands, but this game can go very quickly, especially for experienced players. What are the odds of getting a Royal Flush on a video poker game by holding two cards and drawing three to make the royal flush? From Laguna Niguel, California The number of ways to draw 3. X change game online. 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. Math videos by Subject (Poker Probability is in Precalculus). College Math - 7E.9 - Probability of being dealt a Royal Flush - Duration: 2:07. Farrington Math 38 views.
- A royal MUST hit within the average 40,400 hands
- You will always win if you find a machine with a 100%+ payback
- Another player got my royal flush!
- Each possible hand combination is programmed into the machine
- 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
Last changed 1/9/99
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.
Game | Expected Value | Variance |
---|---|---|
9/6 Jacks or Better | 99.544% | 19.51 |
Pickem Poker | 99.9536% | 15.01 |
Deuces Wild | 100.762% | 25.84 |
10/7 Double Bonus | 100.172% | 28.26 |
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.
Odds Of A Royal Flush In Video Poker Game
Cumulative Probabilities - 5000 Hands
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. Popular casino table 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.
Odds Of A Royal Flush In Video Poker Machine
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.
Royal Flush Odds Texas Holdem
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What Is A Straight Flush
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