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Reason #4 why the Wizard likes Bodog:
One-stop shopping
Bodog offers the triple crown of gambling: casino, poker, and sports. Many other casinos have tacked on poker as an afterthought, and many poker rooms have tacked on a casino as an afterthought, and the lack of attention shows, sometimes painfully. And very few of these sites let you make sports wagers. But Bodog doesn't just offer all three, they do each one well, and everything's integrated. It's easy to play all three off one deposit, off just one account. Another nice thing about Bodog is that you don't need a separate account to play casino games with fake money. In fact you do not even need an account for that at all, you can just click over there and play. Finally, Bodog usernames are only six or seven characters long making them possible to remember. By contrast some competitors' usernames are extremely long and cumbersome. (Visit Bodog) Jacks or Better game. One click and you're in:
No popups, no download, no registration, no B.S., just the game. See important note about Bodog payouts & deposits. |
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Home • What's New • Advice & Strategy • Ask the Wizard • Gambling online • Play for Fun |
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A fellow employee swears his mom is on a 25-year video poker winning
streak. She makes four trips a year to Vegas and always wins at least a $1000 with a $400 buy-in. He says she usually wins $10,000. He is upset at my lack of faith in her luck. He wants to bet me his mother will be ahead after a four-hour session. Should I take this even-money bet?
— John from Upland
As long as she is flat betting at a steady rate, yes, by all means take the bet. Either she is using some kind of worthless progression, or this is second-hand exaggeration. This got me to thinking, what would be the optimal number of hands for your friend’s side. Assuming 9/6 Jacks or Better, and optimal strategy, the probability of being ahead is maximized at 136 hands, with a probability of 39.2782%. May 13, 2008
The video poker machines at the casino all say "This machine pays 80% of the time or better." This seems inconsistent with your percentage of about 53% throwaway hands. Is this to make the game more fun, but then adjusted to have lower payouts or something like that? — Diana from Albuquerque
It is probably not a real video poker machine, but a "pull tab." In jurisdictions with heavy regulation, like New Mexico, players should be careful that they understand what they are playing. With a pull tab the win is predestined. The cards are just for show.
December 14, 2007
Went to Vegas in June '07 utilizing your video poker jacks or better
strategy. The results were quite satisfying; however, after scouring six casinos on the Strip, and all the downtown casinos, I was unable to find a 9/6 video poker Jacks or better machine. Do they exist any longer? — Geng from Palm Bay
I feel your pain. 9/6 Jacks or Better is getting harder to find, even at the locals casinos, but they definitely still exist. Some of the MGM/Mirage properties have 9/6 Jacks in their high limit rooms. The Wynn is king of 9/6 Jacks; they have them all over the place. For information about current video poker offerings in Las Vegas, I highly recommend VP Free.
December 14, 2007
I have looked at many video poker strategy charts, and many are different. Are they, or should they be, the same based only on probabilities and nothing else? I asked one author and he said that he "tweaked" the charts, but gave no method. — Jack from Georgetown
Video Poker strategy charts are not an exact science. There is always a tradeoff between brevity and accuracy. There are also issues about the best way to express a rule. Unless there was a huge emphasis on simplicity, it is unlikely two writers would come up with the same strategy.
November 23, 2007
Sir, thank you so much for such a wonderfully informative site. Could you comment on the variance and covariance in Spin Poker — J.B. from Las Vegas
You're welcome. I ran some random simulations in 9/6 Jacks or Better, to get at the answer to your question. The following table shows the covariance for 2 to 9 lines played, in 9/6 Jacks or Better. The variance would be the same as the base game played.
Let's look at an example of 9-line 9/6 Jacks or Better. The variance of the base game is 19.52. The covariance is 33.46. So the total variance is 19.52 + 33.46 = 52.98. The standard deviation is 52.981/2 = 7.28. November 23, 2007
On the 'Vegas FAQ' show on the Travel Channel, you recommend the 9-6 Jacks or Better machines. 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. It wasn't I who showed that machine. The producers didn't understand I was referring to 9/6 Jacks or Better. Later in the editing room they showed somebody pointing to a 9/6 Double Double Bonus Poker game, which has a return of 98.98%. That is much worse than 9/6 Jacks or Better, at 99.54%. An embarrassing moment for me, much like the many incorrect edits I had no control over, in my old Casino Player articles. November 4, 2007
I submit to you that the advantage video poker player should sometimes deviate from optimal strategy, if following the Kelly Criterion. In borderline hands, I think Kelly may favor going for the less volatile play, even at a lower return, although I can’t think of a particular example. What are your thoughts? — Scott E. from New York I agree! As discussed in my section on the Kelly Criterion, there is an optimal bet size for any given bet with a player advantage, for purposes of balancing both risk and reward. Betting the exact Kelly amount will result in the greatest bankroll growth for the player with average luck. For example, in full pay deuces wild, with a return of 100.76%, the optimal amount to bet every hand is 0.03419% of bankroll. These days if you can find full pay deuces wild it will probably be only at the 25-cent denomination, but if you could bet anything, 0.03419% of your total bankroll would be the optimal amount for long-term bankroll growth. For a player with a bankroll of $3,656, a quarter denomination game would be the perfect Kelly bet size. As I discuss in my section on Kelly, the optimal bet amount is the one that maximizes the expected log of the bankroll after the bet, which I will call the Kelly Utility. Usually the Kelly Utility is maximized by making the optimal strategy play. However, one exception would be a five 3s to 9s, with three deuces. In particular, let's look at 22266. The expected value of keeping the deuces only is 15.057354, and keeping the five of a kind is always worth 15 exactly. The following table shows both the conventional expected value and the Kelly Utility holding the three deuces. The Kelly Utility for any given hand on the draw is p*log(1+0.0003419*w), where p is the probability, and w is the win.
The next table shows the same figures for holding the five of a kind.
You can see that the Kelly Utility is higher keeping the pat five of a kind, at 0.002222 vs. 0.002193. For this particular hand, keeping the five of a kind will be the correct play under the Kelly Criterion for bankrolls up to 13,290 units, or for quarter players up to $16,613.
As I said, the optimal Kelly bet size for the optimal strategy player is 0.03419% of bankroll. The optimal bet size for the player playing optimal strategy, except keeping a dealt 22233 to 22299 is 0.03434% of bankroll. The bankroll growth of the optimal strategy player will be 0.0002605% per bet made. For the Kelly player it will be 0.0002615% per bet made. Every 40,000 hands the player following optimal straegy, and Kelly bet sizing, can expect bankroll growth of 10.98%. The conservative player keeping a dealt 22233 to 22299, and Kelly bet sizing based on that strategy, can expect growth of 11.03% per 40,000 hands. So, I maintain that in some situations, indeed, you should go against optimal strategy and go for the more conservative play. I just hope Rob Singer doesn’t hear about this. September 20, 2007
I really enjoy your site, and thank you for the pertinent information! Reading and learning has erased my bad habits and made me a better player, I am certain! Here is my question. I read about games you write about and really think that some of them would be fun to try, like the World Series of Poker (Final Table Bonus) video poker game. Not knowing, however, where to find it, and others, I usually wind up writing to the maker of the game at their website and asking where I can find their game outside of Nevada, since I am in the Midwest. I NEVER get an answer! Besides being just bad customer service, I still have the question of finding the game to be answered. Do you know of a site, or a way, to find which specific games are at which casinos? You would think the game's manufacturer would list where to find it to assist in letting players find the game. – Larry S. from Columbus, OH
Thanks for the kind words. I think the gaming manufacturers should take this as a good suggestion. I get requested for this information by players all the time, but it is simply too much for one person to keep on top of. A noteworthy exception is Masque Publishing, the owners of Spanish 21. They keep an online list of where the liberal Spanish 21 rules can be found. September 11, 2007
I played 50-line 9/6 Jacks or Better $1 machine over the weekend and got killed. Any idea what the odds are of putting $800,000 coin in on 50-line $1 and not hitting a single royal? Just curious. – Dave from Las Vegas
If you were playing single line it would be easy. $800,000 is 160,000 $5 hands. That is 3.9616 royal cycles. The probability of no royals can be closely approximated as e-3.9616 = 1.9%.
The math gets messier with mutli-line games. I think the easiest way to answer the question is by random simulation. My video poker appendix 6 shows the probability of getting at least one royal per hand in 50-play 9/6 Jacks or Better is 0.00099893. Each hand of $1 50-play costs $250. So you would have played 3,200 initial hands. The expected number of hands with a royal in 3,200 hands is 3.1966. By the same method of approximation, the probability of getting zero royals is e-3.1966 = 4.09%. The exact answer, based on the simulation results, is (1-0.00099893)^3200 = 0.04083732, or 4.08%.September 1, 2007
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 the odds of not hitting a royal for an entire year (about 50 sessions playing once a week)? Thank You. – Dave S. from New Haven
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 0.1. A very close appoximation for the probability of zero royals per session is e-0.1 = 90.48%. 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 0.1 × 50 = 5. The probability of zero royals in 50 sessions can be closely approximated at e-5 = 0.67%. The exact probability is (39,999/40,000)^(200,000) = 0.67%, as well. June 19, 2007
I've been to Vegas 6 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? - John G from Bellingham, WA
9/6 Jacks or Better can still be found at most casinos, although often limited to the high limit room. I suggest VP Free for the latest video poker offerings. January 18, 2007
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. Yet, wouldn't it be fair to set the payoffs of each hand in the inverse proportion to its frequency? – Krisha from Bel Air, MD
Good question. In 9/6 jacks or better the probability of a royal flush is 22.65% of that of a straight flush, but a royal pays 16 times more. Overall the straight flush only contributes 0.55% to the return of the game. The straight flush is the Rodney Dangerfield of most forms of video poker, it gets no respect. I can only speculate that game makers wanted a big top prize. Nobody likes to come in second, so perhaps that is why the original game makers didn’t pay the straight flush much by comparison.
December 13, 2006
I started to play $5 single-line Jacks or Better recently. 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? – Steve from Oxnard In 9/6 Jacks or Better with perfect strategy you will see a royal on the draw once every 40,601 hands, but four to a royal once every 460 hands. For every royal you see, you will be one card away 88.33 times. Of the four to a royal hands, 50.37% will pay nothing, 24.89% will pay as a pair, 7.89% as a straight, 16.16% as a flush, and 0.69% as a straight flush. Here are the exact numbers.
The expected number of royals for 170 four to a royals is 170/88.33 = 1.92. The probability of seeing zero with a mean of 1.92 is e-1.92 = 14.59%. July 31, 2006
A casino has a promotion where you get a bonus for getting each of the different 4-of-a-kinds in video poker. For simplicity, I assume each 4 of a kind occurs with equal probability. How does one calculate the average number of 4-of-a-kinds one must get before one can expect to have received each of the 13 different kinds at least once? Thanks very much, I really appreciate all of the information on your site! - Jon from Lafayette, CO Let's examine the general case first. Define p as the probability that the next four of a kind will be one that you need for the promotion. Define q as 1 - p. Define m as the expected number of four of a kinds to get one that you need. The sum of probabilities is 1. Thus, (1) p + p*q1 + p*q2 + p*q3 + p*q4 + ... = 1 The following is the formula for m in terms of p and q. (2) m = 1*p + 2*q*p1 + 3*q2*p + 4*q3*p + 5*q4*p + ... Multiply both sides of (2) by q. (3) mq = 1*pq + 2*p*q2 + 3*p*q3 + 4*p*q4 + 5*p*q5 Subtract (3) from (2) (4) m - mq = p + pq + pq2 + pq3 + pq4 + ... The right side of (4) equals 1 from (1). (5) m - mq = 1 (6) m*(1-q) = 1 (7) m = 1/(1-q) = 1/p. So, if the probability of an event is p, then on average it will take 1/p trials to occur. To get back to the problem at hand, it will obviously only take one four of a kind to cross the first one off the list. The probability the next four of a kind will be one that you need is 12/13. So, on average, it will take 13/12=1.0833 trials to get it. Once you have two crossed off the list, the probability the next one will be one that you need is 11/13, so that will take 13/11=1.1818 more trials to get the third one. Following this pattern the total expected number of four of a kinds to get at least one of each kind is 1 + (13/12) + (13/11) + (13/10) + ... + (13/1) = 41.34173882. April 19, 2006
Understanding that optimal Jacks or Better play yields 99.54% return on a 9/6 machine, I have a quick question: If there were no such thing as a Royal Flush, but everything else remained exactly the same, what would the return be on the same machine? Thank you. -- Michael from Seattle
If a royal flush paid the same as a straight flush then 9/6 Jacks or Better would have a return of 98.03%.
March 5, 2006
At Bally's in Atlantic City there's 1$ 9/6 JoB [Jacks or Better] video poker with a progressive royal flush payout beginning at 4k. Since non progressive 9/6 JoB have a return of 99.54% with perfect play, at which point would the progressive payout raise the return above 100%?
My Jacks or Better section shows the return of a 940/9/6 game to be 0.999030. The return from the royal is 0.024686. So the return from the other hands must be 0.999030-0.024686 = 0.97434. Although the probability of a royal is shown as 0.000026, that is only to two significant digits. Let's use the return divided by the win, or 0.024686/940 as the probability. If j is the jackpot amount solve for j in the following equation:
1=0.97434 + j*(0.024686/940) So the breakeven point is a meter of 977.33 bet units or $4886.66. This assumes perfect 940/9/6 strategy. However few people know 940/9/6 strategy. If using 800/9/6 strategy then we would use the 800/9/6 table:
1 = (0.99543904-0.01980661) + j*(0.01980661/800) So if using 800/9/6 strategy the jackpot would need to reach 984.22 bet units or $4921.10. Jan. 3, 2006When playing video poker will it decrease my odds of winning if I put a $50 bill in, instead of $5 or $10 increments? - Karen from Eastchester, New York No. Neither the amount you put in nor the denomination affects the odds. The same is true of slots. Nov. 9, 2005I do my best to make only "smart bets" and to avoid machines with lousy pay tables. I must admit I just don't have the time to memorize the ever increasing number of different configurations out there. I do know that casinos ban photo equipment, but is it ok to bring in, say, a pad and paper so you can record the pay tables of certain machines and look them up at home? Or better yet, bring "cheat sheets" right into the casino? Right now I'm afraid to do so because I don't see anyone else doing it and would be afraid that they'd nullify my payout if I were to hit a jackpot based on some rule that I wasn't aware of. Any insight? Thanks! Yes, I take notes in the casino all the time. The only time I have had trouble was when the Suncoast prohibited me from playing slots and writing at the same time when I was taking notes for my Las Vegas slot machine survey. Camera usage seems to be much more tolerated lately, so lately I have been taking pictures of rule screens and pay tables when I have my camera available. I also usually have cheat sheets in my possession when playing video poker, in case I run across a hand I don't know how to play, which is rare. I keep the cheat sheets hidden but have never had a problem whipping them out in a pinch. The reason you don't see other players with cheat sheets is about 99.44% of video poker players don't know what they are doing and the rest have the strategy memorized. Sept. 4, 2005 I was curious. How do the odds change in video poker if a person always shoots for a natural royal flush? (In other words always holding the most beneficial hadn to obtain a natural royal flush.... disregarding all other possible hands.) A strategy of going for a royal at all costs, as if all the other hands paid zero, would result in a return of 47.85% on a 9/6 Jacks or Better game. The expected frequency of a royal would increase form once every 40388 hands to once every 23081. April 3, 2005 Due to table-game tips to dealers being "highly recommended", each hand/play costs or "loses" the player a little bit (as little as ~$0.50-$1.00 just to be considered 'live' by dealers) each time. With games of low bankrolls and minimum bids (i.e. ~$1000 in pocket and ~$2 per play), the tip & house-edge would often make games like video-poker more worth while as far as returns and (possibly) comps are concerned. You make a good point. Tipping definitely does add to house advantage in table games. If one were to tip one bet until every 100 hands that would add 1% to the house edge. Slot and video poker players also get comped and in general treated much better. These are things to consider when deciding which game to devote your time to. Jan. 16, 2005 If you were playing $50 per play, what would you personally chose between these two games of video poker (assuming both games have the same pay schedules and you bet the maximum of 5 coins for each hand): single-play at $10 or ten-play at $1 per hand? Thanks for your time and consideration. Mathematically they of course have the same expected return. However I would play the 10-play because the volatility is less and I think it is more fun. Dec. 13, 2004 Many Oklahoma Indian casinos can only use "class 2" poker machines, where "skill" is not allowed to be a factor -- does this mean the hands are somehow predetermined? And would the next hand be the same no matter who played it? Let me explain what a class 2 machine for the benefit of others. It is a slot machine in which the outcome is determined by the draw of bingo balls. If done well (and it often isn't) the game will play just like a regular slot machine. I have been to two casinos in Tulsa and the closest thing I found to video poker were not class 2 slots but rather "pull tabs." With pull tabs the player makes his bet, presses a button, 5 cards appear on the screen, and a voucher drops if you won anything. You may take that to the cashier. Although there is a pay table for the 5-card stud hand I do not think the cards are dealt randomly. Rather it is just a visual aid to show you how much you won. Sept. 23, 2004 I know that in video poker, the cards are selected at random -- but are they selected at the instant the button is pushed for both deal and draw? I think different video poker makers do it different ways. On all at least the draw cards are determined when the player presses the button. I think some also determine the draw cards at this time. Others keep shuffling the remaining 47 cards until the player presses the button to draw the replacement cards. Sept. 23, 2004 I saw a video poker game in which all wins are tripled for next 9 hands following any three of a kind in threes. The three threes count in a full house but not a four of a kind. How could I estimate the effect of this rule? The probability of any three of a kind or full house, based on "9/6" jacks or better is 0.085961. To make things easy I'll divide by 13 to get the probability that the rank of the three of a kind is threes. This is obviously overstating the probability because you will see more in jacks through aces because correct strategy is to hold those cards more often. 0.085961/13 = 0.006612. Tripling the wins for 9 games is like getting 18 free games. 18* 0.006612= 0.119023. To this I would apply some kind of fudge factor to account for the disproportionately fewer three of a kinds in threes, perhaps 75%. 0.119023*0.75 = 0.089267. So whatever your normal return is multiply it by 1.089. Aug. 23, 2004 Any advice to us folks in Connecticut, with the absolute worst video poker machines in the world? Is there an accepted way to pressure a casino to improve their selection when the market doesn't necessarily require it? That is what happens in an environment with almost no competition. Asking the casino for better machines won't help. If players will play games with lousy pay tables why should the casinos change anything? Your only hope is to write to the lawmakers in Connecticut and ask them to end the two-casino monopoly on gaming in that state and allow others to compete. July 28, 2004 How does the RNG logic interact with the "hold %"? I believe that most machine are set to hold X% and that over time that number will be reached. It would seem that that "hold" number must have some influence on the odds a machine will pay or not. I realize that a newly installed machine that has never been played can hit the royal on the first play, however, it is my belief that over time, the hold % will met by that machine. I have also heard the term "cycle". I slot tech at a casino told me that a machine was on a 365-day cycle. What does that mean? First lets clear up what the term "hold" means. For purposes of electronic games it is the theoretical return the game is set to. In both video poker and slots each play is random and independent of all past plays. The laws of mathematics dictate that even with independent trials the as the sample size gets larger the actual return will tend to get closer to the theoretical mean, or the hold. So contrary to popular belief a machine never goes hot or cold to get back in balance. Never mind the term "cycle." It is a poorly named industry term for the number of possible outcomes of the random number generators inside the machine. Unfortunately the term has trickled down only to confuse low level employees and players alike. Contrary to popular myth there are no cycles and again each play is equally random and independent of all other plays. July 28, 2004 Do you have a book on various versions of video poker, or can you recommend a book where can I get strategies for Bonus Poker, Double Bonus, Tripple Bonus, Double Double Bonus, and Tripple Double Bonus? Video poker does not suit itself well to books. There are so many different games and pay tables, and they add new ones so quickly, that a book would be dry and quickly outdated. I recommend getting video poker software that can produce a strategy for almost any game. Two examples of such software are Video Poker Strategy Master and Frugal Video Poker. May 30, 2004 If I put a $100 bill in a 98% return video poker machine and play until I go broke then how much on average will I bet in total? There is a simple formula for this answer. It the initial investment divided by the house edge. In this case the answer is $100/0.02 = $5000. However due to the volatility of video poker, most of the time the $100 won't last this long. May 5, 2004 I think I read somewhere that if someone could come up with a system that had even only 1% player edge, you could easily turn 1000$ into 1000000$. But some video pokers have an 0.77% player edge, why aren't you turning it into like $770,000 or something? Is it because you can't bet more than 5$ at a time and it would take WAY too much time? Thx. And oh, I said it before, and I'll say it again, LOVE your site!! Thanks! Yes, I said before that if I had a betting system that had just a 1% advantage I could turn $1000 into $1,000,000 by simply grinding out that edge. This would also be possible in video poker but it would take much longer because the 0.77% advantage game (full pay deuces wild) can only be found in the quarter level. Assuming you can play 1000 hands per hour (a speed few can attain) and played perfectly that would result in an average income of $9.63 per hour. To reach $1,000,000 would require working 11.86 years non-stop. $1000 would also be very undercapitalized to play quarter video poker, so the risk of ruin would be quite high. It would be faster to reach the $1,000,000 with the same edge in a table game because the player can bet more. April 11, 2004 The Fremont in downtown Vegas offers a video poker game called Treasure Chest. It's basically Jacks or Better with the full pay table with one change - if you bet max coins and get four of a kind, you are taken to a bonus screen where you can choose one of five treasure chests. The chests contain 120, 160, 320, 640, or 1,000 coins. How does this affect the theoretical return and does it change the optimum strategy? From playing, I can say most of the time you get 120 coins, and sometimes 160. Higher values seem rarer. I suspect the chest value depends on how fast you select the chest after getting to that screen. I've seen this game. As I understand gaming regulations it is permissible to have the lower prizes more likely than the higher prizes. The best you can do is to estimate the average win of a four of a kind and then run that through a program like this one to get at the optimal return. To get a strategy you can use Video Poker Strategy Master or Frugal Video Poker by entering any pay table. April 11, 2004 Hi, I read almost everything on your site and all I can say is WOW and THANKS so much for all the help you bring to everyone. I have however a question which I think is interesting and should be added in your FAQ section. You say there is no betting system that can beat a game of luck. I am 100% on your side with that as I have tried dozens of them and with no results. You just can't beat the casino in the long run. HOWEVER, how come there are professional players? I mean, there are some people that are called 'Professional blackjack players' who make their living by gambling. Everyone sees them on television in tournaments and things like that where they bet thousands and thousands. How come they make a living out of it if there is no possible way to win in the long run, it's their job, so it's necessarily in the long that they are winning. How come? You're welcome. It must have taken all day to read my entire site. You are confusing betting systems, which are worthless, to legitimate strategies that give the player an advantage. Two games that can be proven beatable with good rules and proper strategy are blackjack and video poker. So I call a system a worthless method of following trends in games with a house advantage, and a strategy something like card counting in blackjack that is mathematically proven to work. Video poker can be beaten by hunting down the best pay tables and then following a reliable strategy on which cards to keep and which to discard. March 6, 2004 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 2.3662715, but I calculated it myself and got 2.3662714. 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. The exact value is 5*(84412/178365), or 2.36627140974967 to 15 decimal places. Whatever you are using obviously carries floating point arithmetic to more decimal places than the internal Java calculator. Feb. 27, 2004 If you had to pick one video poker game to practice on line,(so you knew how to play when in Vegas), what would it be? You put me in a difficult spot with that question. I'm familiar with three programs and am friendly with the owners of all three. So I'll try to go over the features of the three and let you decide. Do you think the Jacks or Better strategy on your site would work well in live poker? No! Absolutely not! Jan. 31, 2004 You have developed an excellent website for information concerning gambling, and I have found it very useful. Thank you for all the work. I have just a couple of quick questions. On your video poker tables you use the figure of 19,933,230,517,200 possible results. How did you determine that this is the number of total possible results? Secondly, I understand how the RNG function works on slot machines. Is there a RNG for video poker, (which means all the results are mapped), or does the program run differently than this? To answer your first question, there are 2598960 ways to choose 5 cards out of 52 for the initial hand. On the draw there are 1, 47, 1081, 16215, 178365, or 1533939 ways to draw the replacement cards, depending on how many card the player holds. The least common denominator for these numbers is 7669695. The actual combinations are weighted to get a total of 7669695. So the total number of combinations is 2,596,960*7,669,695=19,933,230,517,200. To answer your second question video poker machines simply pick numbers at random from 1 to 52 and assign them to a card. The random number generators themselves are very complicated but the object is simple. Aug. 7, 2003 Please help me understand the logic in Jacks or better, why off suit A-J it's better to hold K-J @$2.4172063 expected return and A-K is $2.3382688. It seems that they both should be the same. Thanks - Larry from Fishers, USA There are two spreads for forming a straight with K/J (AKQJT and KQJT9) and only one spread with A/J (AKQJT). Feb. 20, 2003 Your internet newspaper column has not been updated since June. Are you OK? I hope so. I have a Black Jack basic strategy card and it is very beneficial. Are there basic strategy cards for electronic poker games? Thanks for your time. - Charlie Lowrey from Schaumburg, Illinois I'm not sure what Internet newspaper column you are referring to. However I'm okay. As a matter of fact you can get my own video poker strategies in a handy dandy strategy card at Custom Strategy Cards. The video poker cards may not be listed yet but I know the proprietor has them so just ask. Sept. 24, 2002 Hi Wizard. In your opinion, which sites offer the best payouts regarding video poker? Also, which software do you prefer for video poker? Thank you kindly for always being there with your indispensable wealth of knowledge. - Barry Levy from Brooklyn, New York Two questions from Brooklyn in a row, what are the odds of that? The best video poker odds are with Microgaming and Real Time Gaming. It depends on your specific game of choice. Of these two I prefer the Real Time Gaming interface better. Aug. 31, 2002 Hi, have you ever heard any complaints about "SLOTLAND casino" because I am a bit suspicious about their space jack game. Playing the perfect strategy the expected return is 101.7%. But after playing many and many hands I have not made any profit. So, I would like to have your opinion! - LEGRAND Stephanie from Les Clayes Sous Bois, France Actually I get a player return of 101.62%. Buried within their rules is this statement, "Please note that all games share the same mechanism which determines the jackpot win. Thus, with card games, the probability of hitting the jackpot combination is not natural but controlled by this shared random mechanism in the same way as slot machines' wins." It is my understanding that they offered this game for quite a while before posting this warning. I just don't trust any casino that would rig a card game, even if they admit it in the fine print. Aug. 4, 2002 Thanks for the answer about risk of ruin on power poker vs. single play. Now for a follow up... which has more volatility, $1 jacks or better, or $.50 4-play jacks or better (betting $10 per play instead of $5 per play)? - Ray McNamee from Maple Glen, Pennsylvania From my video poker appendix 3 we can see the standard deviation for 1-play jacks or better is 4.417542. The standard deviation for 4-play jacks or better is 5.041215. Keep in mind these figures are per hand and relative to the betting unit. Adjusting for bet size and number of hands the standard deviation of $5 bet in 1-play jacks or better is 11/2*5*4.417542 = 22.08771. The standard deviation of 4 bets of $2.50 in 4-play jacks or better is 41/2*$2.50*5.041215 = 25.20608. 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 by 14.12%. Aug. 4, 2002 You give a standard deviation for a 9/6 Jacks or Better VP is 4.417542. I'm trying to figure out what that means. If I have played 100 hands, does that mean that 2/3 of the time my result would be within 441 Wagers? It seems counter to my experience playing the game. - Ray McNamee from Maple Glen, Pennsylvania The standard deviation of 100 hands of 9/6 Jacks or Better is 1001/2*4.416 = 44.16. 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 88.31 units, is 4.55%. There is more to it than this. Please see my part on the standard deviation in my section on the house edge. April 15, 2002 Great site. I was playing video poker this weekend when the conversation turned to whether it is better to play one machine or try several machines looking for the one that is paying. After much discussion, the only thing I could really offer was that we were no more or less likely to hit the Royal Flush on any given machine at any given time. (You've told us enough times about the independence of trials that I almost understand.) Ok, with that said, here's the question. If the Wizard had $200 and walked in to a bank of 10 full-pay machines, how would he play this bankroll? Would he put $200 in one machine? Or would he split the bankroll and play $50 in four machines? Or would he play $20 in each one? I think the mathematical answer is, that it doesn't matter, but how would the wizard play it? - Gil Loeser from Saint Petersburg You're right, the mathematical answer is that it doesn't matter. I would choose the machine either randomly or based on environmental factors. My highest priority is that if there were any smokers in the vicinity I would sit as far from them as possible. Otherwise I would distance myself from any loud noises, including other players. If the machines were crowded I would pick an aisle machine, giving me a little more elbow room and one less neighbor. June 29, 2001 If I know the variance on a game of video poker, how do I figure out the bankroll I would need to have a 90%-95% probability of avoiding ruin? Great site! Thanks in advance for your answer! - Dave Trapp from Mulvane, USA I hope you're happy, I spent all day on this question. Please visit my new video poker appendix 1 for the answer to your question. There is no easy way to get a risk of ruin figure with just the variance. It depends on exactly what the returns are for each hand and their probability. June 6, 2001 At the Turning Stone Casino in NY, they offer $1 10/7 and 25 cent 9/6 jacks or better video poker. Being a low roller, I'm not prepared to bet $5 per hand. Am I better off playing 1 coin in the dollar game or 5 coins in the quarter game ? - Stuart A. Schlissel from Lake Katrine, U.S. I assume by "10/7" you mean double bonus. You can quickly find the return for many common pay tables by using my video poker expected return tables. There you will see that 10/7 double bonus has an expected return of 100.17%. 9/6 jacks or better has a return of 99.54%. So the 10/7 is obviously the better game. I'm surprised they would have that at all in a non-competitive location. June 6, 2001 You have the optimum strategy for jacks or better video poker for a particular pay table. I practiced for a few hours on your play for fun program - I'm ready to try the real thing - got a royal flush after about 500 hands (down about $350). I'm afraid to learn this strategy if Casino Niagara doesn't have the same paytable. 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 paytable change? - George W. Bordner from Clarence, USA I doubt that Casino Niagara would have the "full pay" pay table that my Java game is based on. With no competition they can be stingy and people will still play. I'm afraid I don't have any strategies available for other pay tables. I suspect Casino Niagara offers 8/5 jacks or better, which pays 8 for a full house and 5 for a flush. Assuming perfect strategy this has a return of 97.30%. Using perfect strategy for full pay video poker, as found on my site, on this game the return would be 97.29%. The two strategies are almost the same and you are only giving up 0.01% by using my strategy on an 8/5 machine. 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 1.36%. Oct. 5, 2000 Does a video poker game whether it be jacks or better or any wild version play like an actual deck of real cards? In other words, the payoff schedule on the front of the machine determines what exact payback this machine has or can this be tinkered with inside with computer chips making the payoff schedule meaningless? I always thought this would be dishonest until I read an article in Strictly Slots magazine that it has and can be done. If this is true you could have two identical VP machines side by side that have different house edges like. I know casinos can and in regular slot machines. If this is so then all this VP payback% on payoff schedules that I have been reading for years in magazines, software and books is useless. -- Ray from ? I am very confident that any respectable maker of video poker machines makes them fair and accurate. Is it possible there are dishonest machines or chips out there? Sure. I would be interested to read the article you refer to. Q: Is there a way casinos can change the odds of a standard video poker. For example can the game be programmed to allow certain cards be duplicated to create a lower probability outcome or are the odds the same for every poker game and casinos just change the payout table to lower the payout. -- James from the U.S. A: The casinos just change the payout table to lower or raise the odds. The cards are dealt fairly. Aug. 27, 2000 Q: Hello Mr. Wizard. 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 banners 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? -- Denis from Rochester, New York A: Thank Denis for your kind words and your interest to help keep the site financially healthy. Banners are sold on a monthly basis. However the advertisers expect results for their advertising dollar. Results are measured partially on the number of times a set of eyeballs views a banner but more importantly how many people click through the banner, and even more importantly how many of those clicking actually sign up to play. These statistics are all tracked in great detail. The best thing you can do is what you have been doing, clicking on the banners. Soon my partners are going to start buying some advertising to get some fresh visitors. We are happy to have a very loyal following but repeat customers are less likely to pay attention to the ads. That is why we plan to start buying traffic to the site. Again I appreciate your help, you are definitely helping to keep the site going.
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