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I've been visiting your site for almost a year and want to take this opportunity to thank you.
Thank you not only creating the site, but for constantly updating it with new and informative material.
I can only imagine the amount of time your must put into it.
I have a number of questions.
The first is about the banners.
I'd like to know how we could optimize your income by clicking on the banners.
Do you get paid on the basis of hits, unique hits or a flat fee or some other formula?
Currently I only click on a banner if it's something new, but I'd be happy to click on a few just click for source every time I visit, if that would help generate income.
The next questions I have are about your perfect strategy for Jacks or Better table, and the practice Jacks or Better game.
I hate to seem dense, but that's never stopped me from asking questions before.
Where on the table do you find the rank of a hand with 1 high card A,K,Q,J and no penalty cards?
My second question is somewhat related to the first.
According to the practice game, the optimum play for a hand with unsuited A,Q,K and no penalty cards is to hold the K,Q and discard the A with the low cards.
Intuitively, I would have thought that keeping the Ace is the better play.
What is the advantage of dropping the Ace, and how would I determine the optimum play on this hand from the table?
Thanks Denis for your kind words and your interest to help keep the site financially healthy.
When you first wrote just clicking my banners helped.
However, as I update my answer in 2013, it is acquisitions that put rice on my table.
It doesn't do much good to click on the banner if you don't at least sign up for an account, and preferably make a deposit.
You can see from mythat there is a single line for "one high card.
You have the optimum strategy for jacks or better video poker for a particular pay table.
I'm afraid to learn this strategy if Casino Niagara doesn't have the same pay table.
Do you have an optimum strategy for "all" pay tables?
I assume there is a significant difference.
Does your play-for-fun simulate the "real world"?
Why do you assume the maximum coins bet?
Does the pay table change?
I doubt that Casino Niagara would have the "full pay" pay table that my Java game is based on.
With little competition they can be stingy and people will still play.
I'm afraid I don't have any strategies available for other pay tables.
Assuming perfect strategy, this has a return of 97.
Using perfect strategy for full pay video poker, as found on my site, on this game the return would be 97.
The two strategies are almost the same and you are only giving up 0.
Also, I assume maximum coins bet because that is what the player should do.
If you play less than maximum coins you will only get 250 per coin on a royal flush, causing a reduction in the rate of return of 1.
InterCasino Double Bonus has the following pay table for 5 coins bet.
What is the return of this game?
I have a couple of questions for you.
I have noticed in your tables of probabilities and expected returns for video poker, that the probabilities and corresponding number of hands for each hand vary for the same type jacks or better, for example from one pay out chart to another.
For example, on the first jacks or better chart, the probability of forming a three-of-a-kind is 0.
Why would this discrepancy exist?
It seems that the only possibility is that the game is being played with a different strategy.
Otherwise, the probability of forming any hand should be the same in that type of game, no matter what the pay outs are.
If you have indeed devised a unique playing strategy for each pay out schedule, would you mind sharing that info with us?
Secondly, I am wondering which, if any, online casinos currently advise the player of a shuffle in blackjack multi-deck, of course.
Also, do you know, among the majority who do not, which shuffle after each hand and which just do not advise of a shuffle although it actually occurs after many hands?
It would be great to have this knowledge.
A follow up question would be, if they do indeed shuffle best video poker vegas strip regular casino intervals, can a player assume that if he enters a private table that he beings with a full shoe?
Thanks again for your great web site, and I look forward to your response to my questions.
Thanks for the kind words.
Yes, the probability of a three of a kind depends on the pay table, which affects player strategy.
My video poker program always makes the optimal play for every hand by looping through all the possible cards on the draw.
However, creating a strategy in writing is very time consuming.
Am I better off playing 1 coin in the dollar game or 5 coins in the quarter game?
As my shows, the return for that game, with five coins bet, is 100.
Just put in 250 per coin bet for a royal flush.
The calculator defaults to 4,000, so change it to 1,250.
Press "analyze" and you'll see the return is 99.
So, you're much better off playing five quarters in 9-6 Jacks or Better.
Any info would be appreciated.
I really appreciate all the information on blackjack on you site.
I wonder, in jacks or better video poker how is the 99.
For example how do you know what is the best play with an unsuited jack and king?
Personally I break them down into 191659 different kinds and weight each one with the number of similar hands.
For example the odds are the same with four aces and a king singleton regardless of the suit of the king.
I analyze each way and take the play with the greatest expected value.
To determine the expected value of a play you have to analyze all the ways the replacement cards can fall and score each hand.
Just reducing the initial hands to 191659 we still have 498,114,074,640 hands to analyze.
Clearly more short cuts are in order.
It would take a desktop computer several hours at least to work through this many hands.
For example with any pair and 3 singletons the probability of improving the hand to a two pair is always the same.
Things get more complicated with straights and flushes but still manageable.
My program can calculate the expected return for a game of jacks or better in about one minute.
I hope this answers your question.
It seems counter to my experience playing the game.
You can then use this information to determine what is the probability of winning or losing more than a specified number of units.
For example the winning or losing within two standard deviations, or 88.
There is more to it than this.
Please see my part on the standard deviation in my section on the.
With more volatility the probability of ruin is greater, but so is the probability of a big win.
Thanks for the answer about risk of ruin on power poker vs.
Now for a follow up.
From my we can see the standard deviation for 1-play jacks or better is 4.
The standard deviation for 4-play jacks or better is 5.
Keep in mind these figures are per hand and relative to the betting unit.
So you are better off betting the smaller total amount in 1-play.
Interestingly you can double the total amount bet in 4-play and the standard deviation only goes up see more 14.
It seems that online casino free no deposit required both should be the same.
I was playing jacks or better on your site.
I had the following: 2 spades ,5 clubs ,J clubs ,10 diamonds ,7 clubs.
The optimal play is keeping the Jack only and your program stated the expected value was 2.
Which one of us has the rounding error?
Leave it to a couple math geeks to argue over the eighth decimal place.
I checked the exact combinations of each hand and you are right.
Whatever you are using obviously carries floating point arithmetic to more decimal places than the internal Java calculator.
The return from the royal is 0.
So the return from the other hands must be 0.
Although the probability of a royal is shown as 0.
So the breakeven point is a meter of 977.
Understanding that optimal play yields 99.
I were to play 1000 hands of 10-play poker or 10,000 hands of single-play poker, assuming the same pay tables and denomination, I know the strategy and expected value are the same, but is there any difference in variability?
However, standard deviation is what I think we should be talking about, which is the square root of the variance.
The standard deviation of 10,000 hands of 10-play is 372,122 0.
The standard deviation of 10,000 hands of 1-play is 195.
As long as the total final hands are the same, 10-play will always be 38.
For more information visit my section on the.
Since I started the number of times I have had four to a royal after the draw is 170, while my number of royals is zero.
What are the odds of this?
For every royal you see, you will be one card away 88.
Of the four to a royal hands, 50.
Here are the exact numbers.
Hand Combinations Probability Four to royal + straight flush 299529168 0.
The probability of seeing zero with a mean of 1.
When the frequency of a Straight Flush is about four times that of A Royal Flush, how come it pays so low, about 16 times less?
I concede that it is impractical.
In the probability of a royal flush is 22.
Overall the straight flush only contributes 0.
The straight flush is the Rodney Dangerfield of most forms of video poker, it best video poker vegas strip no respect.
I can only speculate that game makers wanted a big top prize.
I've been to Vegas six times in the past year, and each time I go I find it more difficult to find a "full pay" Jacks or Better machine.
In fact, this last visit, I couldn't find any!
Are full pay machines a thing of the past, or do the casinos just rotate machines?
I suggest for the latest video poker offerings.
There are a lot of free online video poker games available.
However, I am looking for a version I can run without being connected to the Internet.
Do you know of a free downloadable version of Jacks or Better that does not use the Internet while running?
Just a nice basic, realistic functionally version would be great.
If one plays a Jacks or Better video poker machine, at 40,00 hands per session with perfect strategy, I assume that a royal would appear about every 10 sessions.
What are https://chicago-lawyer.info/best/best-casino-slot-payouts-in-vegas.html odds of not hitting a royal for an entire year about 50 sessions playing once a week?
I assume that you assume the probability of a royal is 1 in 40,000.
Playing 4,000 hands per session the expected number of royals per session is 0.
A very close appoximation for the probbility of zero royals per session is e -0.
The reason it is not 90% is because sometimes you will get more than one royal per session.
The expected number of royals in 50 sessions is 0.
If you were playing single line it would be easy.
The probability of no royals can be closely approximated as e -3.
The math gets messier with mutli-line games.
I think the easiest way to answer the question is by random simulation.
So you would have played 3,200 initial hands.
The expected number of hands with a royal in 3,200 hands is 3.
By the same method of approximation, the probability of getting zero royals is e -3.
The exact answer, based on the simulation results, is 1-0.
However, the machine that you showed was a short pay 9-6 machine because two pair only paid 1 instead of the normal 2 giving the house an extra 5% advantage.
Changing the value of two pair from 1 to 2 is a common trick by the casinos to increase the house edge.
I knew somebody would eventually write about that.
An embarrassing moment for me, much like the many incorrect edits I had no control over, in my old Casino Player articles.
Sir, thank you so much for such a wonderfully informative site.
The variance would be the same as the base game played.
Lines Covariance 2 1.
The variance of the base game is 19.
The covariance is 33.
So the total variance is best casino near maryland />The standard deviation is 52.
I went to Vegas in June '07, utilizing your video poker jacks or better strategy.
The results were quite satisfying.
Do they exist any longer?
I feel speaking, best offline poker app ios remarkable pain.
For information about current video poker offerings in Las Vegas, I highly recommend.
Any chance of publishing an updated strategy for these odds?
That is an error rate of only 0.
The frequent video poker players out there will know why I was playing 26 lines.
Why play 26 lines?
However, I feel with 59 hands a three of a kind on the deal turns into a hand pay too often.
For the benefit of other readers, the coefficient of skewness skew for any random variable is a measure of which direction has the longer tail.
A negative skew means the most likely outcomes are on the high side of the distribution, offset by the extremes tending to be on the low side.
A positive skew is the opposite, where the most likely outcomes are the low side, but with the extremes tending to be on the high side.
The mean is less than the median with a negative skew, and greater with a positive skew.
An exact formula can be found ator lots of statistics books.
Loosely stated, skewness is going to correlate with how often you get a win in a session.
In Jacks or Better, for the most part, you are not going to get a winning session over a few hours if you do not hit a royal.
You can sit down at Double Double Bonus and be a winner after a few hours more often because of the big quad payouts.
Because most people are subject to cognitive biases, the pain from a loss is twice the pleasure from a win.
People do not really play Double Double Bonus because they like the variance, they play because they have a greater shot at winning.
The following table shows some key statistics for four common video poker games.
It is interesting to note that skew is greatest best video poker vegas strip Jacks or Better.
I suppose one could say that a game with a large skew has a greater chance of a loss check this out a session of a few hours.
However in a game like Deuces Wild or Double Double Bonus, the second highest wins can pull you out of the hole over a session.
In other words, the skew keeps you from winning when you are not hitting royals.
My thanks to Jeff B.
I was offered a 10% rebate on losses in video poker.
Under your assumptions, you should quit after being up at least one unit, or down 17 units.
Usingwe can find the the expected best video poker vegas strip of plays to achieve either marker is https://chicago-lawyer.info/best/best-solo-poker-game-for-android.html />The probability that the marker achieved is the 17 unit loss is 17.
So, the expected refund is 0.
The expected loss of playing 19.
So, the expected profit is 3.
The other video poker player is right.
Hand Pays Combinations Probability Return Royal Flush 800 493512264 0.
Hand Pays Combinations Probability Return Royal Flush 800 493512264 0.
The following table shows the probability of each kind of royal, according to the number of cards held, given that there was a royal.
It shows that 3.
The probability of a royal to begin with is 1 best video poker vegas strip 40,391, so the unconditional probability of a royal holding one card is 1 in 1,186,106.
Cards Held Combinations Probability 0 1,426,800 0.
I was wondering why there are so many more than 52 choose 5, and how to compute them.
The reason my video poker return tables have almost 20 trillion combinations is you also have to consider what could happen on the draw.
Here are the number of combinations according to how many cards the player discards.
Regardless of how many cards the player discards, the return combinations should be weighted so that the total comes to 7,669,695.
For more on how to program video poker returns yourself, please see my page on.
This question was raised and discussed in the forum of my companion site.
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