Probability Slot Machine Example

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Gambling, by definition, involves risking something of value on an uncertainevent. This can be a roll of the dice, a turn of a playing card, or the outcomeof a sporting event.

If there is a digital slot machine with, say, 3 symbol 'wheels' (they are obviously not real wheels, digital) with each having a few (say 2) corresponding states (e.g. Each have a lemon and a lime) where winning means all three states match (e.g. 3 limes), and when a button is pressed the final state of the system is determined, yet the. A push to curb illegal cash payouts for slot machine-like gaming is bringing state lawmakers and industry players together to mull potential regulatory changes. At issue are gaming machines that resemble those clustered in abundance at casinos, but in Georgia, they are found at VFWs, convenience stores, restaurants and other locations. Keywords: problem gambling, slot machines, video slots, PAR Sheets, structural characteristics, reinforcement schedules Introduction Slot machines are a very popular form of gambling in North America. For example, Ontario, Canada, has approximately 23,000 slot machines, which in the fiscal year 2002.

In that respect, gambling always involves a certain degree of luck.

But when you start examining the role of probability and decision-making ingambling, you can see that skill becomes an important aspect of gambling, too.

In fact, if there were no skill involved in gambling, the casinos wouldn’t beable to make consistent profits.

So is gambling a skill or based on luck and random chance? This post examinesthe role of both skill and luck in various types of gambling.

Everyone knows that the winner of the World Series of Poker or the WorldPoker Tour wins because he outplayed the other rounders. In fact, everyone knowsthat poker is a game of skill.

But poker is also a game of chance.

What’s the difference?

Short-term versus long-term thinking is the difference between luck and skillwhen it comes to gambling of all kinds.

Let’s say you’re playing at a table with nine players, and you have pocketaces. In a no-limit hold’em game, you’d want to go all-in and hope that all theother players also went all-in.

You’ll win this hand only 1/3 of the time. Most of the time — 2/3 of thetime, in fact — the other players are going to draw out on you.

But look who’s going to win the most money in this situation.

Example

Assume that every time you do this, you have $100 in front of you.

With nine players at the table, you’ll win $800 on three out of nineoccasions, or $2,400.

You’ll lose $100 on six of those hands, or $600.

That’s a profit of $1,800 over nine hands, or an average of $200 per hand.

Most situations in poker aren’t that cut and dried, but it’s a perfectillustration of how skilled play means you’ll profit in the long run.

But in the short term, some of the time — even most of the time — someoneelse will win.

It’s all about long-term expectation.

Casino Games Are an Example of the Casino Having More Skill Than the Player

All casino games pay out bets at odds lower than the odds of winning. Theclassic example is roulette, where you get paid off even-money on a red or blackbet.

If the probability of winning that bet were 50%, you’d break even in the longrun.

But the real probability of winning that bet is 47.37%. That’s because only18 of the 38 numbers on the wheel are red. (18 of them are black, too, but twoof them are green.)

All casino games have a gimmick that gives them this edge over the long run.

In the short run, say half an hour or an hour, it’s relatively easy to walkaway from a game like roulette as a winner.

But if you keep playing long enough, eventually, thehouse edge will win out.

In this example, the skill doesn’t involve being good at predicting whichnumber will come up. THAT is a matter of pure chance or luck.

It also doesn’t involve changing the size of your bet based on what happenedon previous spins of the wheel.

And it doesn’t involve the casino having any means of controlling where theball lands.

The skill is simply in recognizing the mathematical inequity.

Slot

Games like roulette are strictly chance and luck-based, but they have along-term edge for the house.

You’ll often see gamblers or gambling experts quoted as saying that blackjackis the one game in the casino where a skilled player can get an edge over thehouse.

This is not entirely true.

If you play PERFECT blackjack, making the mathematically perfect move onevery single hand, you’ll reduce the house edge to a low percentage — less than1%.

But the house STILL has an edge.

In a low-volatility game like blackjack, a low house edge means that you havea closer to 50% probability of having a winning session than you would inhigher-volatility games or in games with a higher house edge.

That probability, though, is still less than 50%.

There’s an exception, though.

If you count cards in addition to playing with perfect basic strategy, youcan get an edge over the house.

Here’s the thing about that edge, though. It’s a long-term edge.

In the short run, even a skilled card counter can lose lots of money. And byshort run, I’m talking about a single session, several short sessions, or asingle casino trip.

The long run doesn’t really kick in until 1,000 hands, and even then, yourresults can be off by 1% or more in either direction.

To be confident that you’re looking at your actual long-term results, youneed to get in at least 10,000 bets.

Example

Even if you’re playing heads-up against the dealer and getting in 200 handsper hour, you’re looking at 50 hours of play before you can be confident thatyour results are truly long-term.

If you’re playing at average tables, where you’re getting 50 to 100 hands perhour, you’re looking at between 100 and 200 hours of play.

What About Gambling on Your Own Performance?

Everyone knows that you canbet on sports,but it’s tough to pick winners the 53% or more of the time needed to generate aprofit.

But what if you’re the athlete?

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Probability Slot Machine Example

Some people participate in darts tournaments, for example. If you’ve everplayed darts with someone who’s good at it, you’ll understand that it’s a gameof skill.

But no one throws a bullseye every time he throws a dart, either.

The outcome is uncertain, especially if you’re dealing with someone of thesame skill level. Often, handicaps will be involved when playing darts in atournament.

This same line of thought applies to games like billiards and shuffleboard,or even in more sporty endeavors like touch football or soccer.

Yeah, you can shoot pool in a bar with someone for money, and yes, it’s agame of skill.

Some of the skills involved might be more involved than just putting theballs in the pockets, too. Some psychology might be involved.

Watch a couple of movies like The Hustler or The Color of Moneyto get a clearer idea of how that works.

Purely Random Games Like Slot Machines and the Lottery

You can gamble on some games where luck is the sole factor. Slot machines andthe lottery are both examples of these kinds of games.

When you play a slot machine, not only are you unable to use skill to improveyour probability, but you can’t even choose one game over another. Identicalslot machine games might be programmed with entirely different probabilities.

For example, you might play a game where you have a 1 in 2000 probability ofwinning the top jackpot of 1000 coins, but the identical machine right next toit might only give you a 1 in 2200 probability of winning that same amount.

Modern slot machines use a random number generator (RNG), which is a computerprogram that generates the results on gambling machines. This random numbergenerator can be set to provide whatever kind of payback percentage the gamedesigner and the casino prefer.

It’s entirely random, still, but the house gets an edge because of thediscrepancy between the payout odds and the odds of winning.

The lottery, on the other hand, is a game where you can calculate the odds ofwinning. In fact, if the jackpot gets big enough, you could be playing a gamewhere your mathematical expectation is positive.

With Mega Millions, for example, the odds of winning are based (at least inpart) on the number of tickets sold. If the jackpot gets between $220 millionand $260 million, you’re looking at a game with a break-even expected value.

The bigger the jackpot gets beyond that point, the higher the expected valuebecomes.

The problem is that the odds of winning are so small that expected valuebecomes irrelevant.

If you bought $150 million worth of tickets, you might have a 50% probabilityof winning the jackpot and showing a profit. But who really has that kind ofmoney to wager?

But if you wager just $1,000, you’re still looking at odds of winning thatare comparable to being struck by lightning.

That’s not skilled gambling.

That’s plain insanity.

I could list examples of the roles played by skill versus luck in the lotteryall day, but I know you’ve got to get back to work. And so do I.

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I’ll leave you with this, though. Gambling is almost always a negativeexpectation bet, so you should never bet money you can’t afford to lose.

Even the most skilled gamblers are only pressing the smallest of edges, andthey can go broke even when the odds are in their favor.

Remember the movie National Lampoon’s Vegas Vacation, when gambling fever consumes Chevy Chase’s character, Clark W. Griswold? He goes on a losing streak to beat all losing streaks while his son, Rusty, wins four cars by playing the slot machines. Maybe Clark would have done better if he had read Probability For Dummies! In this article, you discover the basic ideas behind slot machines and how they work, so that you can get past the myths and develop a strategy based on sound probability.

Understanding average payout

When casinos advertise that their slot machines pay out an average of 90 percent, the fine print they don’t want you to read says that you lose 10 cents from each dollar you put into the machines in the long term. (In probability terms, this advertisement means that your expected winnings are minus 10 cents on every dollar you spend every time the money goes through the machines.)

Probability Slot Machine Example Problem

Suppose you start with $100 and bet a dollar at a time, for example. After inserting all $100 into the slot, 100 pulls later you’ll end up on average with $90, because you lose 10 percent of your money. If you run the $90 back through the machine, you’ll end up with 90 percent of it back, which is 0.90 x 90 = $81. If you run that amount through in 81 pulls, you’ll have $72.90 afterward (0.90 x 81 = 72.90). If you keep going for 44 rounds, on average, the money will be gone, unless you have the luck of Rusty Griswold!

How many pulls on the machine does your $100 give you at this rate? Each time you have less money to run through the machine, so you have fewer pulls left. If you insert $1 at a time, you can expect 972 total pulls in the long term with these average payouts (that’s the total pulls in 44 rounds). But keep in mind that casinos are designing slot machines to go faster and faster between spins. Some are even doing away with the handles and tokens by using digital readouts on gaming cards that you put into the machines. The faster machines can play up to 25 spins per hour, and 972 spins divided by 25 spins per minute is 38.88 minutes. You don’t have a very long time to enjoy your $100 before it’s gone!

The worst part? Casinos often advertise that their “average payouts” are even as high as 95 percent. But beware: That number applies only to certain machines, and the casinos don’t rush to tell you which ones. You really need to read or ask about the fine print before playing. You can also try to check the information on the machine to see if it lists its payouts. (Don’t expect this information to be front and center.)

Implementing a simple strategy for slots

Advice varies regarding whether you should play nickel, quarter, or dollar slot machines and whether you should max out the number of coins you bet or not (you usually get to choose between one and five coins to bet on a standard slot machine). In this section, you’ll find a few tips for getting the most bang for your buck (or nickel) when playing slot machines.

Basically, when it comes to slot machines, strategy boils down to this: Know the rules, your probability of winning, and the expected payouts; dispel any myths; and quit while you’re ahead. If you win $100, cash out $50 and play with the rest, for example. After you lose a certain amount (determined by you in advance), don’t hesitate to quit. Go to the all-you-can-eat buffet and try your luck with the casino food; odds are it’s pretty good!

Choosing among nickel, quarter, and dollar machines

The machines that have the higher denominations usually give the best payouts. So, between the nickel and quarter slots, for example, the quarter slots generally give better payouts. However, you run the risk of getting in way over your head in a hurry, so don’t bet more than you can afford to lose. The bottom line: Always choose a level that you have fun playing at and that allows you to play for your full set time limit.

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Deciding how many coins to play at a time

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When deciding on the number of coins you should play per spin, keep in mind that more is sometimes better. If the slot machine gives you more than two times the payout when you put in two times the number of coins, for example, you should max it out instead of playing single coins because you increase your chances of winning a bigger pot, and the expected value is higher. If the machine just gives you k times the payout for k coins, it doesn’t matter if you use the maximum number of coins. You may as well play one at a time until you can make some money and leave so your money lasts a little longer.

Probability Slot Machine Example Answer

For example, say a quarter machine pays 10 credits for the outcome 777 when you play only a single quarter, but if you play two quarters, it gives you 25 credits for the same outcome. And if you play the maximum number of quarters (say, four), a 777 results in 1,000 credits. You can see that playing four quarters at a time gives you a better chance of winning a bigger pot in the long run (if you win, that is) compared to playing a single quarter at a time for four consecutive tries.

Probability Slot Machine Example

The latest slot machine sweeping the nation is the so-called “penny slot machine.” Although it professes to require only a penny for a spin, you get this rate only if you want to bet one penny at a time. The machines entice you to bet way more than one penny at a time; in fact, on some machines, you can bet more than 1,000 coins (called lines) on each spin — $10 a shot here, folks. Because these machines take any denomination of paper bill, as well as credit cards, your money can go faster on penny machines than on dollar machines because you can quickly lose track of your spendings. Pinching pennies may not be worth it after all!