Push Your Luck at Cool Math Games: Step up and spin the wheel! Guess higher or lower to win big points. Will you play it safe or risk it all? 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.
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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.
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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.
Casino Math Jobs
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
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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.
The Gambler’s Fallacy
The above video is an excellent introduction to the gambler’s fallacy. This is the misconception that prior outcomes will have an effect on subsequent independent events. The classic example for this is the gambler who watches a run of 9 blacks on a roulette wheel with only red and black, and rushes to place all his money on red. He is sure that red must come up – after all the probability of a run of 10 blacks in a row is 1/1024. However, because the prior outcomes have no influence on the next spin actually the probability remains at 1/2.
Maths is integral to all forms of gambling – the bookmakers and casino owners work out the Expected Value (EV) for every bet that a gambler makes. In a purely fair game where both outcome was equally likely (like tossing a coin) the EV would be 0. If you were betting on the toss of a coin, the over the long run you would expect to win nothing and lose nothing. On a game like roulette with 18 red, 18 black and 2 green, we can work out the EV as follows:
$1 x 18/38 represents our expected winnings
-$1 x 20/38 represents our expected losses.
Therefore the strategy of always betting $1 on red has an EV of -2/38. This means that on average we would expect to lose about 5% of our money every stake.
Expected value can be used by gamblers to work out which games are most balanced in their favour – and in games of skill like poker, top players will have positive EV from every hand. Blackjack players can achieve positive EV by counting cards (not allowed in casinos) – and so casino bosses will actually monitor the long term fortunes of players to see who may be using this technique.
Understanding expected value also helps maximise winnings. Say 2 people both enter the lottery – one chooses 1,2,3,4,5,6 and the other a randomly chosen combination. Both tickets have exactly the same probability of winning (about 1 in 14 million in the UK) – but both have very different EV. The randomly chosen combination will likely be the only such combination chosen – whereas a staggering 10,000 people choose 1,2,3,4,5,6 each week. So whilst both tickets are equally likely to win, the random combination still has an EV 10,000 times higher than the consecutive numbers.
Incidentally it’s worth watching Derren Brown (above). Filmed under controlled conditions with no camera trickery he is still able to toss a coin 10 times and get heads each time. The question is, how is this possible? The answer – that this short clip was taken from 9 hours of solid filming is quite illuminating about our susceptibility to be manipulated with probability and statistics. This particular technique is called data mining (where multiple trials are conducted and then only a small portion of those trials are honed in on to show patterns) and is an easy statistical manipulation of scientific and medical investigations.
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IB Revision
If you’re already thinking about your coursework then it’s probably also time to start planning some revision, either for the end of Year 12 school exams or Year 13 final exams. There’s a really great website that I would strongly recommend students use – you choose your subject (HL/SL/Studies if your exam is in 2020 or Applications/Analysis if your exam is in 2021), and then have the following resources:
The Questionbank takes you to a breakdown of each main subject area (e.g. Algebra, Calculus etc) and each area then has a number of graded questions. What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial. Really useful!
The Practice Exams section takes you to ready made exams on each topic – again with worked solutions. This also has some harder exams for those students aiming for 6s and 7s and the Past IB Exams section takes you to full video worked solutions to every question on every past paper – and you can also get a prediction exam for the upcoming year.
I would really recommend everyone making use of this – there is a mixture of a lot of free content as well as premium content so have a look and see what you think.