Today, the mathematics of slot machines. The University of Houston mathematics department presents this program about the machines that make our civilization run, and the people whose ingenuity created them.
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Mathematicians first got interested in randomness by studying games of chance. Ever since, the histories of mathematics and gambling have been intertwined. Clever gamblers use mathematics to look for the smallest advantages, and casinos use sophisticated mathematical tools to devise new ways of drawing in players.
A slot machine (American English), known variously as a fruit machine (British English), puggy (Scottish English), the slots (Canadian English and American English), poker machine/pokies (Australian English and New Zealand English), fruities (British English) or slots (American English), is a gambling machine that creates a game of chance for its customers. Slot machines are also known. That is 'how slot machines equalize their odds.' They don't ever really pay out more the next spin to compensate for losing money from a previous spin. The best way to truly understand slot machines is to understand probabilities. I'll re-explain my explanation in the OP a bit: We have a 6 sided die.
Indeed, a patent granted to the Norwegian mathematician Inge Telnaes in 1984 transformed the gambling industry. Prior to Telnaes’ invention, slot machines were essentially mechanical devices. Besides being difficult to tune and maintain, mechanical slot machines suffered from an essential problem: Let’s look at a machine with three reels, each with 12 symbols, with one of those 12 symbols a cherry. The likelihood of getting three cherries, and winning the jackpot, is 1 in 1,728. If the casino wants to make money, the jackpot payout should be, say $1,700 on a $1 bet. That does not seem attractive by today’s standards. However, the only way to increase the payout is to decrease the chances of hitting a jackpot.
Adding another reel is a possibility. For instance adding a fourth reel in the previous example would get us to a jackpot of about $20,000. But people do not like machines with more reels — they intuitively, and rightfully, feel that extra reels diminish their chance of winning. Another possibility is to put more symbols on each reel. But the astronomical jackpots you see in casinos today would then require truly enormous machines.
Inge Telnaes proposed a simple solution: Let a random number generator — a computer chip — determine the combination of symbols that appear when the reels stop. In other words, use a chip to control where the reels stop on a spin, but create the illusion that the wheels stopped on their own. The number of possible outcomes on the slot machine does not change. However, by reprogramming the chip, the operator has full control over the likelihood of each of the different outcomes. For instance, the operator could make the three cherries appear only once in a million spins.
This was a brilliant insight: Suppose I pick a number between one and a million. Would you be willing to bet that you can guess that number? The answer is probably not. But let a computer chip pick such a number, put the chip in a machine with blinking lights and spinning reels, and many people will be more than willing to make the bet. It is simply because what people assume is happening in a slot machine is very different from what is actually happening.
The Magician oil painting by Hieronymus Boschfrom between 1475 and 1480
The history of gambling is also intertwined with that of a less reputable group — tricksters and swindlers. In the long run, the only sure way to make money by gambling is to create the illusion that your opponent can win, while keeping the odds firmly on your side. And that gives those who know math a very solid advantage.
I'm Krešimir Josić, at the University of Houston, where we're interested in the way inventive minds work.
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NOTE: In the example with three cherries, I assumed that one only wins in the case the spin results in three cherries, and there is no other winning combination. In actuality, there are typically many winning combination, and as a result, the jackpot would have to be even smaller.
The following story in Wired Magazine shows the drawbacks of the new generation of slot machines — they are easier to hack and to counterfit than their mechanical counterpart http://www.wired.com/magazine/2011/07/ff_scammingslots/.
Here is a more exhaustive discussion of the history of slot machines, and the random number generators within them http://catlin.casinocitytimes.com/article/non-random-randomness-part-1-1243. You may want to scroll towards the end of the article to read about how flaws in the design of gambling machine resulted in somebody picking 19 out of 20 winning numbers in a game of KENO — and doing so 3 times in a row. That person walked away with $620,000, but only after some controversy.
Both images are from Wikipedia. The slot machine image was taken by Jeff Kubina.
For more mathematics in everyday life, visitkjosic.wordpress.com.
This episode was first aired on September 7th, 2011
Players who prefer slot machines to other casino games do not gamble simply for profit, but they also want to have a good time playing. So in order to play the game for longer and benefit from your favorite slot games we recommend you to follow some slots tips that have been developed by experienced players. They will help not to lose at slot machines or online slots of different types and become a real long-term winner regardless the size of the bankroll.
Quick Slot Tips
If you are going to visit a land or online casino to get the rush and thrill of slot machines do not forget to follow some basic slot recommendations. Even if you do not use any special slot machine strategies you can still end up a winner every time you gamble. So, below we explain some do's and don'ts when you play slots.
| DOs | DON'Ts | ||
| 1. | Manage your bankroll and stick to betting limits. | 1. | Try to win lost money back. |
| 2. | Bet Max at progressive slots. | 2. | Play high-roller slots with a small bankroll. |
| 3. | Choose loose slots with high payback percentages. | 3. | Believe in slots myths about cold and hot machines. |
| 4. | Look for extra slot bonuses and casino comps. | 4. | Play traditional slots with minimum features. |
| 5. | Study paytables and choose slots with the highest payouts. | 5. | Play at first slot machine you find at a casino. |
| 6. | Relax and have fun when playing slots. | 6. | Get frustrated or angered when you lose a spin. |
Advanced Slot Tips
Now let's consider all the slots tips in more detail. The following advanced recommendations from the real pros are not obligatory but are considered to be the most effective methods of winning when playing online and offline.
1. Manage your bankroll.
To built up a gaming strategy, the slot player must first of all decide on the bankroll and the size of bets. The smartest tips are to stretch the betting amount, pocket all the winnings, know when to stop and never try to win money back, because you can lose even more.
2. Set up betting limits.
Choose the slot machine according to your bankroll and betting limits. Remember, slots is a gambling game, therefore make sure you treat it wisely and choose a machine according to the amount of money you can afford to wager. Otherwise you risk to reach the 'quit point' very fast.
3. Bet Max at progressive slots.
When playing at the progressive slot machines, bet the maximum amount of coins and bet on all the paylines. It will be a pity if you have the best combination but don't win the jackpot because you haven't Bet Max.
4. Look for extra slot bonuses.
Choose a machine with extra bonuses and special offers such as bonus free spins or bonus rounds. Such games are not only fun but also provide more chances of winning cash.
5. Play only loose machines.
Not all slot machines are based on the same RNG, therefore always look for loose slot machines with the highest payback. Most casinos advertise the slots payback percentages. However, if you cannot figure out the payback statistics remember that as a rule $5 (or higher) slot machines provide the highest paybacks of up to 99%.
6. Practice slots for free.
Before playing for real money, practice a lot in order to know all the game options and learn how to win at slots. You can try our free slots or play slot games in fun mode at online casinos.
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7. Check the paytable before the game.
Carefully study the slots paytable before you play to make sure that you know which combinations will win you money and to have an idea of what you are paid out for. Don't rush to play at the first machine you see but look for the slots with the highest payouts.
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8. Don't believe in slots myths.
Do not believe in the widespread slots myths. Don't forget that there is no such thing as a hot or cold machine, therefore pick the one you like and enjoy the game. Remember also that there is no 100% effective system of beating slots and any strategies offered you for buying are useless.
9. Benefit from slots comps.
Most casinos provide casino comps for slot players in the form of free lunches and dinners, hotel rooms, tickets, bonuses, etc. In such way you can save money for playing rather than spend big sums on accommodation and meals.
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10. Ask the professionals.
In case you have any questions about the rules, payouts, bonuses or other options, feel free to ask the casino support as they are there for you 24/7.