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Tommy, who is one of my blog readers asked how to calculate payout percentage of any given slot machine after reading this slot strategies article. I started writing a reply to his question in the comment, but the answer turned out much longer than I had initially planned so I decided to dedicate the answer a full post I believe it deserves.
Top 10 Slots with the Highest RTP – Play with the Best Odds. By: Cat Marshall February 27, 2018 Whilst many people decide which slot to play based on the theme, special features or promotional offers, the savvy gamblers steer towards slots with the highest RTP.
Please note that the payout percentage can only be calculated this way if each spin is completely random. The only way you can be sure it's completely random is if you play in a casino, which is licensed by a jurisdiction dictating the outcome of each slot spin must NOT be predetermined, it has to be completely random. Casinos bound by this restriction are all legally operating casinos in Las Vegas and Atlantic City as well as most licensed online casinos.
In order to calculate payout percentage on a slot machine with completely random RNG (Random Number Generator), you need to know 2 things beforehand: occurrence of all symbols on each reel and paytable. In a very simplistic example suppose we have a slot machine with 3 reels and with only 2 symbols
and
Total number of symbols on each reel is 3: 2xBAR and 1xSeven
Payout table shows 2 winning combinations for each $1 bet as follows:
wins $1
wins $15
First we need calculate the probability of each combination:
For 3xBAR the probability is 2/3 * 2/3 * 2/3 = 0.3
For 3xSeven the probability is 1/3 * 1/3 * 1/3 = 0.037
Note that the probability to get BAR on 1 reel is 2 out of 3 times, hence 2/3 in the formula and for Seven it's 1 out of 3 (1/3)
We multiplied probabilities 3 times because the combination is made up from 3 times the symbol.
Now we can calculate the payout of each combination:
For 3xBAR the payout is $1 * 0.3 = $0.3
For 3xSeven the payout is $15 * 0.037 = $0.56
Finally we add the payouts of each combination together to get the total payout:
$0.3 + $0.56 = $0.86
Since we payout we just calculated is for $1 nomination (according to the paytable) then the payout for this nomination is $0.86 (each time we bet $1, on average we win back $0.86) or in other words the payout for $1 nomination is 86% (without bonus game or progressive jackpot)
Note that payout percentage can vary depending on the nomination. Higher nominations often offer better payback.
If the slot game has a bonus round, we also need to take that into account and start by calculating the probability of getting into the bonus round. Then multiply it with the average amount you can win at the bonus round and add the result to the total payout.
Suppose in our example 3xSeven puts us into a bonus round where we are given a choice of 3 pots of gold. If we choose the right one, we win additional $3
On average we would win 1 out of 3 times in the bonus round. Since the win amount is $3, then the total amount we would win on average is 1/3 * $3 = $1 each time we get to the bonus round.
Since we have already calculated the probability to get to the bonus round (3xSeven = 0.037), then we can add another $1 * 0.037 = $0.037 to the total payout which now stands at $0.86 + $0.037 = $0.90. Now that we have taken the bonus round into account, the total payout is 90%.
If it's a progressive slot, we need to multiply the probability to hit the jackpot with the jackpot amount and add the result to the total payout as well.
Suppose the probability to hit the progressive is one in a million and the jackpot is $10 000
1/1 000 000 * $10 000 = $0.01
After adding it to the total payout, we get $0.9 + $0.01 = $0.91 or 91% payout.
Suppose the progressive jackpot is $100 000 instead
1/1 000 000 * $100 000 = $0.1
After adding it to the total payout, we get $0.9 + $0.1 = $1 or in other words 100% payout.
If you were an advantage gambler who has done the homework like we just did here, you would know that whenever the progressive on this slot machine reaches $100 000, the total payout percentage reaches 100%, at which point playing on that slot machines becomes profitable in the long run. ‘A long run' in this case would probably mean a few million spins, but you would be guaranteed to make profit if you had a sufficient bankroll and a lot of patience (or an army of apes pulling levers).
As you can see the math behind calculating the slot machine payout is quite simple. The most difficult part of the whole process is probably finding the information regarding the occurrence of each symbol on the reel as casinos don't tend to publish this simply because an average gambler has no need for this type of information.
If you have any questions, feel free to post them as comments and I'll try answer them as best as I can.
UPDATE: Tommy asked how to calculate the keno video slot payout percentage, so I figured I'd throw it in here as well.
I have to admit I'm not a big fan of keno video slotmachines myself, but I believe I have a fairly good understanding how they work.
Suppose we mark 3 spots. First we need to calculate the total number of ways possible to draw 3 balls out of 80.
80/1* 79/2 * 78/3 = 82 160
Notice we substract 1 after each draw. That's because the ball we just drew cannot be drawn again, it's now out of the 'bubble'.
Since the game draws 20 winning balls, we have to calculate the total number of ways 3 spots can be amongst the winning 20.
20/1 * 19/2 * 18/3 = 1140
The probability to hit all 3 spots is therefore 1140/82160 = 0.0139 or 1.39%
Suppose the paytable shows $40 prize for hitting all 3 on a $1 bet. The payout for hitting 3 spots out of 3 is then $40 * 0.0139 = $0.56
Suppose paytable is generous enough to award us $2 should we hit 2 spots out of 3 with every $1 bet.
The total number of ways to hit 2 spots out of the winning 20 is 20/1 * 19/2 = 190 and the total number of ways possible, that 1 ball remains amongst the 60 that don't get drawn, is 60/1 = 60. This means there are a total of 190*60 = 11 400 different possible ways to draw 2 winning balls and 1 losing ball.
We already calculated there are 82 160 possible ways to draw 3 balls, therefore probability to draw 2 winning + 1 losing ball is 11400/82160 = 0.14
This adds another $2 * 0.14 = $0.28 to the total payout which is now at $0.56 + $0.28 = $0.84. That means the total payout is 84% for $1 card played with 3 spots.
If the paytable is the same for both 1- and 20-card version, the payout percentage remains unaffected so whether you play 1-card keno 20 times or 20-card keno once, it doesn't really matter.
Players share their thoughts on beating the Slot machines
By John Grochowski
When penny slots emerged, the game manufacturers needed a way to make bonus wins big enough that players thought they were worth playing for. Games with higher volatility, and bigger payoffs, were necessary in order to make them seem worthwhile to penny players
Slot machines are not 'strategic' games like blackjack or video poker. There are slots that require you to make decisions, but none that are going to shift the long-term odds of the game.
That doesn't stop players from trying to think of ways to beat the slots, and many have emailed to ask if there is any validity to their strategies. Let's check a few out:
Tim, Pennsylvania: 'I know that on video slots we don't have to bet the max anymore. I usually just cover the all paylines with one coin bets. But one day I doing well—I was up to five coins a line on a penny slot, and I got to thinking. Would I have been better off to switch to one coin a line on a nickel slot? The nickels have higher paybacks, right?'
That's a theory that gets a qualified 'yes,' but with a whole lot of reservations. For one thing, Tim's theory assumes that you can find the same game on both pennies and nickels in the same casino. That's by no means a given.
Even if you do find the game at both levels, the penny and nickel version won't always have the same number of paylines. If you're on a penny game with 20 or more lines, will you be satisfied to find an older nickel version with nine or 15 lines? If fewer paylines won't keep you entertained, there's no point in putting your money in the machine.
Then there are a whole slew of 'ifs' about the type of game, such as:
Is the payoff on every winning combination simply multiplied by the coins-per-line wager, or is there a disproportionate jump with bigger bets? The disproportionate jump is why three-reel slots have higher payback percentages when you bet the max. Most video slots don't have that kind of disproportionate jackpot jump, but double-checking is prudent.
Does the game have a progressive for which you'd be ineligible if you bet only one coin per line? Progressives have enough of their overall return tied up in the jackpots that you shouldn't play if you can't get the full pay.
Are there symbols or bonuses that are unlocked with higher wagers? Bally has a video version of Blazing 7s that works this way, where a one-coin per line bet won't activate the 7s. I recently played a version of the Cars game from Incredible Technology that needed at least a two-penny bet per line to unlock a bonus event. If you can't get all that a game has to offer for a one-coin per line bet, and betting more than one per line is outside your bankroll's comfort zone, then you need to find a different game.
If the game is a pure multiplier, and you can get all the features with one coin per line bets, then yes, the game's payback percentage probably is higher on nickel versions than on penny machines. It's standard operating procedure for casinos to offer games with lower payback percentages on pennies than on nickels, which pay less than quarters, and so on up the line.
Scott, Indiana: 'I go to a casino that has signs on slot machines saying that some give double points every day, some give 3x points, and others give 4x points. They're not the flashiest games. They're not offering that deal on The Hangover or The Wizard of Oz. They're mostly penny video free-spin kinds of games. Can those extra slot points make the games profitable?'
If multiple points were enough to turn no-skill games like slot machines into profit centers for players, the casino wouldn't be making the offer.
Let's make a couple of assumptions and do a little arithmetic. First, let's assume the games pay 87 percent, which is pretty normal for a penny slot. And let's assume the player rewards club pays 0.25 percent in free play. An example of that would be a club in which each $4 in play earns one point, and each 100 points is redeemable for $1.
At those levels, single points effectively turns an 87 percent game into an 87.25 percent payer, with the combined return going up to 87.5 percent at double points, 87.75 percent at triple points, and 88 percent at quadruple points.
Multiple slot club points can't even begin to make up the entire house edge on penny slots. Even on dollar slots, where some generous casinos return 95 percent, 4x points raise that only to 96 percent—nowhere near profit level.
If there's an opportunity for slot club points to turn a game profitable, it's on video poker in casinos that offer top-notch pay tables. Full-pay Deuces Wild (100.8 percent) and 10-7-5 Double Bonus Poker (100.2 percent) are among a handful of games that return more than 100 percent to the few who play at expert level.
Those games are few and far between. Even in Las Vegas, those pay tables are becoming rare, and there are some jurisdictions in the United States where they are illegal. Illinois, for example, won't allow any games with a theoretical payback percentage of greater than 100 percent.
In some circumstances, multiple slot club points can turn the next tier of games into profitable possibilities, provided you take the time to learn to play them well. Full-pay 9-6 Jacks or Better returns 99.5 percent with expert play. A 0.5 percent player rewards bonus turns it into a potentially profitable game.
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But Scott didn't mention video poker in the list of games drawing multiple points where he plays. So that rewards bonanza is just a nice little perk—something extra to take away if you enjoy the games that bring the added points.
Ella, Louisiana: 'My strategy on the video slots is to look for games that have those bonuses where you make picks. I seem to be able to play a lot longer and have more fun on those games. My sister doesn't agree. She likes the games with the free spins and says my games are boring, and that you can't win anything playing them. Do you think that's the right strategy, going for the pick games?'
There is a difference between pick-‘em and free-spin games that Ella is picking up. When video slots made their breakthrough in the United States in the late 1990s, they mostly had pick'em-type bonus events. They were low volatility games designed to keep players in their seats. Big jackpots weren't the order of the day. It was all about small, frequent bonus wins to extend play and entertain customers.
Many fans of three-reel slot games found that style boring. To them, the thrill was in chasing the jackpots, even at the risk of fast losses.
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When penny slots emerged, the game manufacturers needed a way to make bonus wins big enough that players thought they were worth playing for. Two hundred nickels thrilled some on the first video slots, but 200 credits on a penny machine is only two bucks. Games with higher volatility, and bigger payoffs, were necessary in order to make them seem worthwhile to penny players.
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That's where free spins came in. The math of the games can work so that it's possible to win thousands or tens of thousands of credits in five or 10 or 20 free spins, but it's also possible to win next to nothing. Artistocrat Technologies of Australia was already making free-spin games. Other manufacturers followed suit, and it became an extremely popular format.
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Nowadays, with many of the most popular video slots featuring multiple bonus events, it's a bit of an oversimplification to say free-spin games are for jackpot chasers, and pick'em games are for those who want to sit back and be entertained. But that's where the roots are, and it remains true to some extent. In seeking out pick'em games, Ella has the right strategy for getting what she wants from a game—extended play, and lots of fun.
