I just have a couple more questions for you and then I wont bug you again for a really long time. Promise. : 0 ). What the jackpot would have to be on a 8/5 20 nickel game for it to be a 100% game, keeping in mind that it takes 20 nickels to be eligible for the jackpot? What about the same machine on a 7/5 game? And finally, what would it have to be on an 8/5 quarter machine that requires eight coins to be eligible for the jackpot. I would also like to take this opportunity to thank you for your sage advice. It has made gambling a lot more enjoyable!

Vladimir

You're welcome! In an 8/5 game, the jackpot would have to reach 37,704 coins to reach 100%, assuming you have to play 20 coins to win it. Assuming only 8 coins, the meter would have to reach 15,082 coins. On a 7/5 machine and 20 coins required the meter would have to reach, 46,956 coins. These figures assume you are playing the proper strategy for these pay tables with a per coin payoff for a royal flush of 800. As the jackpot grows some strategy adjustments are called for to more aggressively try for the royal. These adjustments were not calculated in this answer. It doesn't make any difference what the coinage is.

I've noticed some new video slot machines (Money to burn, High Bid, Money for nothing, Who Dun it, etc) that differ from the normal three-reel slots in the following ways -- first they have five reels. You can typically bet on 1 to 9 pay-lines (even though some have as many as 15 different pay lines), and multiple coins per line; thus, with nine pay-lines and five coins played per line, you would have a total bet of 45 coins (even in nickles, this can start to add up!). Most payoffs are multiples of the line bet, even though there are some "bonus" wins that pay multiples of the total amount bet. Is it best to always pay all possible pay lines, or is there an optimum combination of pay lines to play to achieve the best return? I suspect that getting a winning combination on any particular pay line is the same for all, but wondered if you have any better insight to share.

Scott from Leawood, USA

Each frame in these video slots is weighted equally. Any given line is equally likely to produce any given combination. Thus, the return is the same regardless of the number of coins played.

Your site is definitely the best one I've ever seen regarding gambling, and I commend you for providing some light and truth in a seemingly endless sea of "winning gambling strategies, tips & tricks." My question is this. I'm no slot player, but obviously when a progressive jackpot reaches a certain point, the edge would shift from the house to the player. I was wondering if there are any "groups" or "clubs" that go out into the casinos when this happens, (virtually) monopolize the machines, capitalize on the opportunity, and split the winnings? I have never heard of any, but they've got to be out there.

Bryan from Palmdale, USA

Thanks for the kind words. I have barely heard of teams of slot players doing this. However, this is very common with progressive video poker players. There are teams of these professional players who routinely check the meters and when they find one high enough they call their teammates in an attempt to monopolize the machines until somebody hits the jackpot.

The problem with slots is that it is not clear to the player what the odds are of hitting the jackpot so it is not obvious what the jackpot size has to reach for the machine to become profitable. Plus, it probably rarely happens that a meter gets high enough to overcome the house edge.

This is a question regarding fixed odds betting. If you say that the odds are 4 to 1 on something happening, then is that equivalent to saying the probability is 1 in 4 i.e. 0.25? If you consistently bet on 4 to 1 shots would you simply break even over time? Therefore could you not beat fixed odds betting by doubling up after every loss since you would expect a winner every fourth bet?

Calvin from Long Beach, USA

If the odds **against** something are 4 to 1 then there are 4 chances it won't happen and one chance that it will. So, in this example, the probability would be 1/5. It doesn't matter what the probability is, if the events are independent then the past does not matter.

Do you feel it's better to play one slot machine or many, and how much should I feed before walking away. If given a touch screen to stop tumblers should I stop them.

Gene from Laguna, USA

None of these factors matter. Walk away when you're not having fun any longer.

In your slot machine advice, you indicate to play machines with variable states that are in a high state or progressive machines with the meter high. Could you please explain? How do you know a machine is in a high state?

Ken from Naperville, Illinois

For variable-state slots, you have to know what the positive point is for that model of machine. For example, on the Piggy Bankin' slot machine, I think it becomes positive when there are about 40 credits in the bank. At that point the player is supposed to play one coin at a time until the bank is hit. The book Robbing the One-Armed Bandits by Charles Lund (1999) covers specific positive points for various machines, however many of the machines covered in that book are now hard to find.

As for how to determine when a progressive jackpot is unusually high, you'll either have to observe it over a long period of time or find someone who has done the same. For example, SlotCharts.com keeps data on progressive slots at online casinos. But even when a progressive slot is unusually high, it's impossible to know at what point it becomes high enough to be a positive-expectation game without knowing how the probabilities on the machine are programmed. In my section Deconstructing Megabucks I attempt to figure out when the jackpot is large enough to have a player advantage.

**Update:** Since this question was published, SlotCharts.com is blocked to U.S. traffic.

Great site! Is it better to go max three quarters on a quarter machine or drop one dollar in a dollar machine?

Anonymous

Thanks. This is a good question and I wish I had a firm answer. The exact answer depends on the theoretical return of both machines, and nobody ever reveals this information. Yes, you do get a better return in general on dollar machines than quarters, but you are giving up the max-coin bonus. I think the house edge will do down about 2% making the jump from quarters to dollars. However, without reel weightings, I can't tell you the cost of not playing max coins. My general advice is to find a slot machine without a max-coin incentive and then bet one coin at a time.

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 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.

If you are playing Slots at an online casino, but have only a limited amount of money to spend, (ex. $100), is it wiser to play for instance, 25cent slots 1 coin at a time?-or-would it be wiser to play the MAX on one machine even if you seem to be losing it faster?

Lori from Allentown, USA

I believe that most online slots have a fixed return, regardless of the coinage. This is unlike slots in real casinos, which return more the greater the coinage. What you should do depends on your priorities. If you want playing longevity then you should play as little as possible per spin. If you want hope for a big win then you should play as much as possible per spin. However the house edge is likely the same either way.

I play 50 cent slots and higher. I am happy with making a profit of $20 to $150 each session. I quit playing when I reach these levels. Are the high volatility, low frequency and low jackpot machines the best to play using this strategy? Please give me names of particular lines of machines to play.

Darin from Iroquois, Canada

No. If your goal is a small win then you should be playing low volatility, high hit frequency games. I can’t suggest any particular games but look for ones with comparatively small jackpots. These will also help you to play longer.

Have you calculated any of the odds for the slot machines at Harrah’s Cherokee Casino? NC law requires games of skill. As a result of this law all of the common slots such as Double Diamond, Red-White-Blue, etc were installed with a two spin option. After the first spin you may hold or respin any of the three rows to obtain final results. Charts are available on every machine to show the total number of each symbol and blanks in each row. Since these machines are IGT machines I assume that the symbols are weighted and randomly selected as posted. If this is true then the payback % can be calculated just as it is in video poker. Just curious if you had any info.

David from Peachland, North Carolina

I’ve been asked about these North Carolina slot machines so many times I’m tempted to fly there just to see them for myself. Yes, if they did give the probability of each symbol for each reel then an optimal strategy and a return could be fairly easily calculated. However I have never actually seen such a table and have never worked out the odds.

Dear Wizard, I was wondering if it reduces the expected loss to a player to play multiple lines in multi-play video poker as opposed to one line at a time (where all lines share the first 5 cards and independently draw the non-held cards). It seems that on multi lines, when you get lucky and the first five cards are a winner (such as a natural flush draw), it guarantees that EVERY hand of multi-play will also be a winner. However, no matter how bad the first five cards are, it does not guarantee that EVERY hand will be a loser on the draw because every hand will have an independent draw. It seems like there must be some difference in odds playing 10 lines sharing first five cards vs playing 10 independent hands?? I enjoy your website.

Kevin

The odds are exactly the same on a one line, 10 line, and n-line video poker machine. When you get a trash hand in 100-play you can expect to get about 36% of your original bet back. In 10-play it is still 36% but there is more volatility. In 1 play it is still 36% but you can get lucky and get a high paying hand on the draw. In other words you are more likely to hit it big on the draw in single play, but at the expense of lots more non-paying hands.

If a person is playing one of the 5-cent ticket machines, and while making a 9 line bet, a winning combination comes up. . . if they had bet 1 line, or 45 lines instead, would that same combination of symbols have come up, or does each type of bet and amount carry its own set of combinations, probabilities, and house percentage payoffs? In other words, if a person is betting 1 line for several spins, and then when they feel that the machine is about due to hit a combination pay off, they start betting a few 45 lines. Is this a good strategy, or are they just fooling themselves because the 1 line set of combinations, and the 45 line set of combinations are two totally separate things?

Robert

For purposes of determining the game outcome the slot machine does not consider how many lines you bet or how much per line. The only thing that matters is the exact nanosecond you pressed the spin button. Random numbers drawn at exactly that time will determine the outcome, since the machine is picking numbers even when you’re not playing.

The Wynn invited me to a slot tournament with the following prize structure.

1st place: $1,000,000

2nd place: $150,000

3rd-6th place: $25,000

7th-8th place: $20,000

9th-50th place: $5,000

The cost is $25,000, and the tournament is limited to 50 players. It is easy to see the expected win is $30,000. However, it is a huge long-shot. What would be the required bankroll for entry to be a sound bet under the Kelly Criterion?

Anonymous

The Kelly Approximation is the advantage divided by the variance. The possible outcomes are a win of 39, 5, 0, -0.2, and -0.8 times the bet amount. The advantage is (1/50)×39 + (1/50)×5 + (4/50)×0 + (2/50)× -0.2 + (42/50)×-0.8 = 0.2.

The variance is Expected(win^{2}) - (Expected(win))^{2} = (1/50)×39^{2} + (1/50)×5^{2} + (4/50)×0^{2} + (2/50)× -0.2^{2} + (42/50)×-0.8^{2} − 0.2^{2} = 31.4192

So, the approximate optimal Kelly bet is 0.2/31.492 = 0.0063655 times the bankroll. For a full entry of $25,000, the required bankroll would have to be 25,000/0.0063655 = $3,927,400.

However, for large bets like this, I think it is worth the time to find the exact optimal Kelly bet. Next, find the bet size b, which maximizes the expected log of the bankroll after the tournament, as follows.

Log of bankroll after tournament = (1/50)*log(1+39×b) + (1/50)*log(1+5×b) + (4/50)*log(1) + (2/50)*log(1-0.2×b) + (42/50)*log(1-0.8×b)

There is no easy way to solve for b. Personally, I recommend the "Goal Seek" feature in Excel. The answer will come out to 0.0083418. So, the exact Kelly bet should be 0.0083418 times your bankroll. To justify the $25,000 entry fee, your bankroll should be $25,000/0.0083418 = $2,996,937.

A reader asked about a slot tournament at the Wynn. The cost to enter was $25,000, and the average prize was $30,000. You said that you need a bankroll of about three million to enter, according to the Kelly Criterion. I have two questions:

1. Does this take into account the unknown house edge on the slot machines?

2. What would be the playing strategy for the best overall return? Could you just sit back and not gamble, and hope that the other 49 players all end up behind, while you break even and take the grand prize of $1,000,000?

Gray C. from Silicon Valley, CA

Slot tournaments are always held on dedicated tournament machines. Usually these machines don’t accept bets, so your balance will either stay even or go up, after each play. So it doesn’t make any difference what the return is; the more you play, the more you can expect your balance to go up. Even if you had to play conventional slot machines, I would still bet as fast as possible, stopping only if I got a jackpot large enough to likely win the tournament. The reason is that it is very unlikely that 49 out of 49 players would be negative.

Interestingly, there was once a slot tournament at Caesars Palace where they gave a prize to the person who finished last. However, they didn’t announce this rule until the award ceremony. If you somehow knew of such a rule, indeed, it might be best to not bet.

My wife wants to win big on slots. She has $5 free play. What is her best strategy? She is not interested in prolonging her time playing and will leave after her initial $5 is used up, she will not play any won money.

Scott from Albuquerque

I would play once on a $5 three-reel single-line game. Win or lose, walk away after one spin.