Math Casino
- The Hangover Math Casino Scene
- Casino Math Formulas
- Math Casino Games
- Casino Math Pdf
- Casino Math Assessment Test
- Math Canonical
- Casino Math Test
Mathematics in casino gaming management. The reader will gain an understanding of how and why casino games produce the expected revenues. Topics discussed in this text range from the basic principles of probability, odds, expectation, house advantage, and the law of averages, to price setting using game odds, gaming.
- Soon after their initial discovery, mathematicians started applying the laws of probability to many different parts of life – including casino games. One of these mathematicians was Karl Pearson Karl Pearson (1857 – 1936) was an English mathematician and statistician.
- The game of poker is a card game played among two or more players for several rounds. There are several varieties of the game, but they all tend to have these aspects in common: The game begins with each player putting down money allocated for betting. During each round of play, players are dealt cards from a standard 52-card deck, and the goal of each player is to have the best 5-card hand at.
If you’re looking for a combination of an easy gambling game and a low house edge, baccarat is exactly what you’re looking for. The house edge is lower than almost every other option in the casino, and you only need to know how to make a single wager.
Everything you need to know about baccarat is based on math, but you don’t have to figure out any of the logistics by yourself. Here are five things that you need to know about baccarat math. Once you learn these five things, you can quickly use them to help you win.
This page is about baccarat games available at smaller tables. This is called midi or mini baccarat, and the casino has a dealer that runs the game. The baccarat game at larger tables is basically the same, but players are more involved in dealing the game.
1 – The Banker Bet and the Commission
The thing about baccarat that can be a little bit confusing is the commission that the dealer takes out of winning banker wagers. This isn’t a big deal, but some players struggle with understanding the process and how it influences how much they win or lose.
Basically, any time you place a wager on the banker hand and win, the casino collects a 5% commission. This means that if you make a wager of $100 and win, you only get back $95. Or, if you bet $20, you only get back $19.
This seems simple enough, but where some baccarat players get confused is when they try to understand the house edge on the banker hand wager. The house edge on this wager is 1.06% after the casino collects the commission. This is really all you need to know.
The problem is, if you don’t understand that this is the edge after the commission, it might lead you to think that the player hand wager is better. The banker hand wager is always the best bet when you play baccarat. You don’t have to compute the commission, so there’s really no reason why you shouldn’t make the banker hand wager every time.
It’s best to make wagers that are easy to compute the commission so you know that the dealer doesn’t make a mistake. If you usually wager $20 a hand, keep a stack of $1 chips. The dealer can pay you $20, and you can slide a $1 chip forward to pay the commission.
2 – Player Bet Math
The second wagering option at the baccarat table is the player wager. The player hand doesn’t charge a commission when you win. But even without the commission, it has a slightly higher house edge. The house edge on the player hand wager is 1.24%.
This is not the worst wager you can make, and in truth, it doesn’t cost you too much more to wager on the player hand than the banker. Here are some exact numbers to show you the long-term difference in losses.
| Total Amount Wagered | Banker Hand Expected Loss | Player Hand Expected Loss |
| $100 | $1.06 | $1.24 |
| $500 | $5.30 | $6.20 |
| $1,000 | $10.60 | $12.40 |
| $2,000 | $21.12 | $24.80 |
| $5,000 | $53.00 | $62.00 |
| $10,000 | $106.00 | $124.00 |
| $100,000 | $1,060.00 | $1,240.00 |
As you can see, the expected loss difference, even at $10,000 total wagered, is only $18. This means that if you simply want to avoid the commission that comes with the banker hand wager, you can lose a small amount more in the long run and use the player hand option. The choice is yours.
I still recommend the banker option because the casino takes care of taking the commission. This way, you don’t have to do anything except make the wager.
3 – Tie Bet Math
I know that this page is about baccarat math, but there’s no need to dig very deep in the math behind the tie wager in baccarat. The main reason why is because the tie bet is so bad that you should never make it, no matter what.
The house edge at most baccarat tables for the tie wager is a huge 14.36%. Let me put this in perspective a couple of different ways.
The first way to put this in perspective is that almost every other wagering opportunity in the casino is better than this.
Another way to put this in perspective is to do some quick math to show your expected loss on the tie wager. Every $100 you wager on the baccarat tie option costs you $14.36. Every $1,000 you risk on this wager costs you $143.60.
Skip the math behind it, and simply skip the tie wager option at the baccarat table.
4 – Bet Sizing Considerations
I’m going to give you the answer to the question first because it’s simple. The best wager size when you’re playing baccarat is the smallest wager you can make. When you’re playing baccarat in land-based casinos, this is the table minimum.
When you’re playing baccarat in an online casino, this is the smallest wager they accept.
The Hangover Math Casino Scene
This is the answer to what size wager you should make when playing baccarat. This means that the best course of action is to not play at all, and the second-best course of action is to always make the banker wager with the lowest possible bet amount.
This advice is true for almost any casino game you play. You need to learn the best strategy, then play with the lowest possible bet amount. Any gambling option that has a house edge, and this is almost all of them, needs to be played with the lowest wager possible.
5 – Baccarat and Slot Machines
It might seem strange to find a section about baccarat and slot machines on a page about baccarat math, but there’s something important that every slot machine player needs to know.
People play slots for many different reasons, but one of the main reasons they play is because it’s easy. All they have to do is put some money in and press a button. The biggest problem with slot machines is that they have a higher house edge than most other gambling options in the casino.
You might think that this doesn’t make as much difference because you’re making smaller wagers, but this is offset by how many wagers you make in an hour.
If you’re wagering $2.50 on every spin and take 550 spins every hour, you’re risking $1,375 every hour. Compare this to wagering $20 on every hand at a baccarat table and playing 70 hands every hour. In this case, you’re risking $1,400 every hour.
Now, consider how much you can expect to lose playing slots and baccarat. If the slot machine has a 5% house edge, you’re expected loss is $68.75 every hour. Your expected loss playing baccarat is only $14.84.
As you can clearly see, baccarat is much less costly to play than slot machines. And it’s just as easy to play online baccarat as it is to play online slot machines. All you have to do is place a bet on the dealer hand. Everything else is taken care of by the casino, just like when you bet on slot machines.
Many gamblers worry about the need to understand how baccarat is played and scored. You’re welcome to learn all about how to score baccarat hands, but you don’t need to know anything about the game to play.
The only reason why you might want to learn how to score baccarat hands is to make sure the dealer doesn’t cheat you out of a win. And this isn’t something you need to worry about in most modern casinos.
Conclusion
Baccarat is as simple as any game in the casino. All you have to do is place a wager and wait for the result. And baccarat offers a much lower house edge than slot machines and many other options in the casino.
The best strategy is to use the banker hand every time you play, even with the commission on winning wagers. With a house edge of just over 1%, your bankroll is going to last longer and you’re going to have a better chance to walk away from the table a winner than most games give you.
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The LIFE Science Library about several broad topics, published in the 1960s, included the tome Mathematics. The section on probability and combinatorics featured games with playing cards. The study of games of chance have a long and venerable history as a gateway to statistical sciences.
In addition to games of pure chance, we have games of skill, often with an element of luck vs. misfortune. The nature of casino gambling is not fixed for all time and in this curriculum segment our games may well serve a philanthropic purpose, in that winnings are committed to some worthy cause or charity.
Casino Math, by virtue of including the topic of permutations, may be extended to include simple group theory concepts.
Note to teachers: one option is to introduce the J language (a computer language) and its native primitive for outputting in cyclic notation. Introducing more than one computer language is in keeping with the overall agenda for these four interconnected curriculum segments: Casino Math, Supermarket Math, Neolithic Math and Martian Math.
Casino Math Formulas
Note to teachers: playing games of chance (and some skill) need not imply one is gambling for money (consider solitaire). If your community actively discourages gambling and expects you to share this attitude, then you should feel free to defend your ethical position without neglecting your responsibility to model random or chance events, accidents, preferably in the context of simulations and/or games, to reduce the chance of injury.
Historical note: a casino need not be for gambling, may be a gathering place or public hall. For example, the casino on Catalina Island in the town of Avalon, is a movie palace at the time of this writing. Math games played in a casino setting might have more to do with monitoring work flow in some settings (like mission control?).
Depending on the needs of the surrounding curriculum, you may want to build this as a straight statistics course.
On the other hand, you may live in a subculture that actually staffs real casinos, or trains some of its people to program a next generation of game.
Math Casino Games
Either way, Casino Math may become your laboratory for discovering object oriented programming and its potential to satisfactorily define simplified (better understood) simulations of real, naturally occurring systems.
Chaotic Sequences
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An original purpose of the RAND Corporation was to publish sets of random numbers. However, any sequence generated by a computer program that might be duplicated is deterministic and in that sense pseudo-random. Chaotic sequences have statistical properties without being precisely predictable over the long run by means of algorithmic short cuts.
Because these limits to precision may have major long term consequences (the butterfly effect), the idea of a strange attractor (e.g. the Lorenz Attractor) became important. Chaotic sequences are not without order, even where the algorithms, often dependent on previous results, provide no short cut to the future.
Studies of chaotic sequences and their properties may involve forays into cellular automata, fractal geometry. A library of machine executable pseudo-random number generators should be harnessed and pressed into service, if the requisite hardware and electricity is available. Python's random module might be a place to start.
Casino Math Pdf
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Card Playing Objects
Games of cards provide a rich coding environment for object oriented languages in that one expects Card, Deck and Player objects at least.
- A deck comes with methods for shuffling and dealing, keeping track of how many cards have been dealt. A discard pile may also be modeled as a deck.
- A card object has attributes of suit and rank, and methods for comparing its value with other cards.
- Player objects would typically consist of hands, rules for their evaluation.
A player might also have methods, based on probablistic analysis, for guessing the contents of other player hands (or hidden cards in the player's own hand).
The object oriented apparatus of polymorphism, inheritance, getters and setters, private and public variables, class blueprints versus objects (instances), has the potential to come through clearly provided the student has some previous grounding in card games.
The rules of chance are best explored in non-punitive environments, which is why the practice of gambling for money may be excluded by one's subculture as too likely to cause harm (too risky in a foolhardy sense). Please note that dissecting (analyzing) games of chance, coding them in software, does not constitute an endorsement for gambling or investing in the stock market.
Unlocking Codes
Information Theory suggests that random noise and high bandwidth communication share the same lack of redundancy or predictability.
In other words, an information stream such as the digits of pi, with completely predictable content, might be considered low in information content in the sense of highly compressible. The same information could be packaged far more efficiently.
On the other hand, information with no discernable rules for lossless compression, have the appearance of being maximally dense, which may mean they're maximally informative communications, or they may be random noise.
Casino Math includes the idea of making some information secret, perhaps through cryptographic techniques, with the flip side being the game of deciphering secrets, recovering lost and/or hidden messages. These topics are sometimes packaged under Spy Math by some authors.
Casino Math Assessment Test
Note to teachers: the topic of public or symmetric key cryptography, RSA for example, might be undertaken in connection with deciphering, the related statistical studies around word and/or vowel sound frequencies (cite Who is Fourier?). On the other hand, this topic might be relegated to Supermarket Math, in connection with eCommerce.
Investing in Possible Futures
Casino Math provides students with the means to appreciate the scientific method. Thanks to educated guesses or hypotheses, either purely speculative or reality-checked by experiment, one potentially reduces one's reliance on pure luck or miracles and maximizes one's chances of realizing one's plans.
Work consistent with nature's principles (e.g. in cahoots with the weather) is more likely to bear fruit than work undertaken blindly and/or with only minimal appreciation for the underlying patterns and systems.
Math Canonical
Thanks to scientific study, many natural systems have yielded enough secrets to have become both predictable and sometimes even manageable to some degree. This frees us to devote more attention to as yet poorly understood yet often critical systems.
Engineering is about leaving no more to chance than is necessary, is about optimizing the trade-offs, maybe getting a better outcome in exchange for concerted study. As our knowledge and level of mastery increases, we're able to do more with less, creating more life support (wealth) for more people, for more days into the future.
Casino Math Test
We look at Neolithic Math (one of three related modules) as marking the advent of a long epic saga about learning to work more sustainably and effectively within our shared natural environment, Spaceship Earth and surroundings.