a complete guide to gaming with maths
“The casinos believe in math (and I don’t mean numerology). They believe in the power of percentages and short pays, not in the power of magic stones, amulets and omens.”Frank Scoblete
“It’s my lucky day!”“I was holding my lucky rabbit’s foot!”“I had my lucky coin!” All expressions that any online gamer may have come across, or even used when it comes to gunning for a massive win. Online gaming and, in fact, any type of gambling are often linked with luck when it comes to wins. For players with limited experience, it makes sense to keep trying your luck with each game you play. However, over time, it becomes apparent that behind the scenes, there is something magical happening.
Winning is so much more than luck. There is a science behind it that revolves around all thingsmaths.That is the purpose of this guide – a detailed breakdown of how you can use maths to get an edge at almost any game when playing online.
With maths and online gaming, there are some terms that you are bound to come across. These can be related to almost any online game.Here is what you need to be familiar with.
Probability when gaming
“Never show all your cards.”
There are certain chances that a player will win or lose when they are playing a casino game. These chances are known as probabilities. Probability touches on almost all strategies or options when it comesto using maths. Probability is expressed in various ways, including percentages, fractions and odds.Probabilities do not exceed the value of one. This is because they look at the space of something that may not happen at zero, and something reaching completion at one.
Using probability, it becomes easier to estimate or calculate an outcome. When gambling, you need to consider all of the possible outcomes, and probability allows for this. By using this method, you can plan on what chances to take, or which risks will be worthwhile in the long run.
There is a simple formula that you can use to calculate an implied probability of an outcome. Implied means that it is not the actual probability but is close to what is expected. The formula is:the total amount wagered / the total payout. The results are expressed as a percentage. This is a great formula to use when you are working on games where the odds keep changing.
The casino edge
“We cannot change the cards we are dealt, just how we play the hand.” Randy Pausch
The casino edge, also known as the house edge, is a number worth noting. It is the one that gives the casino its advantage over the player. Remember, the casino is in place to make a profit by offering entertainment through online games. Understanding the underlying maths when it comes to calculating this edge can help the player identify advantages. One of the ways that you can reduce the house advantage is by playing games that have a low house edge.
For example, when playing a slot game, you can look to see whether it has an in-play bonus mode. For many games, when these bonus modes are in effect, the house edge is marginally altered. Try looking for those that include free spins, multipliers, pick and click and substituting wilds features. Slots that have a high variance are preferred by high rollers since they can try to benefit from larger cash prizes.
Timing can also be beneficial when you are considering the house edge. This requires you to have played for some time and noted the patterns of your play. This will give you an idea of how much you lose within an hour or every 30minutes. With this information, and compared to the house edge, you can estimate how long to play before you start incurring large losses.
Breaking down the negative expectation (-EV)
“It’s hard to convince a winner that he’s losing.”
When it comes to gambling, this is a maths term that is used often. All casino games have a negative expected value. Expected value refers to the amount of money that a player could win or lose when gaming in the long run. It can be affected by the pay-outs offered for the game, or the odds. It is normally expressed as a percentage of the money that has been wagered. For it to be highly accurate, it is necessary for plenty of trials to be done so that the value can be as expected. Actual results vary from game to game, so it is worth taking time to understand negative expectation for the long term to get the desired result.
For a quick look at the negative expected values of key casino games, view the list below:
- Slot machines – 10% (this may vary depending on the game being played)
- Roulette (American) – 5.26%
- Roulette (European) – 2.7%
- Baccarat banker – 1.05%
- Baccarat player – 1.2%
- Blackjack – 0.5%
- Video poker – 1%
What happens when you come across a game that has no house edge thathas been fixed? This does not mean that there is not one available, it just means that you need to take some time to calculate it for yourself. There is a simple equation that you can follow:
Expected value = (probability to win) x (profit) – (probability to lose)
A simple example can be used for a dozen in roulette. The probability of winning is 12/37. This is because the bet being made is on 12 of the numbers from a possible total of 37. With the wager being made, the potential profit will be 2 units. 25 of the 37 numbers on the wheel could result in a loss, meaning that the probability is 25/37. With all these figures available, here is what the expected value looks like:
Expected value = 12/37 x2 - 25/37
Expected value = 0.648648 – 0.675675 = - 0.027 = -2.7%
Now you know why over the long run, you are likely to lose a total of 2.7% of the amount you have wagered.
To use this equation and apply it to all games, you should know what the probability is to win. From this, calculating the probability to lose is quick and effective. That way, you have the power to calculate the advantages as well as the disadvantages that can be expected from any wager you want to make.
Understanding odds in gambling
“Cards are war, disguised as a sport.”
In all games, there are chances that there will be a certain outcome. Odds and probability are quite similar, so you will find them being interchanged depending on the game you are playing. They provide details on how much a player should wager, and the amount they can receive should they win their wager.
Consider that you have made a wager on a tennis game, with the odds being 5:1. This means that if you win your bet, you receive five times the amount you invested. Now, there could be another game that is offering 7:1 odds, which means that you will receive seven times your wager if you win. With this scenario, it makes sense to take the 7:1 slot as you will have the chance to receive much more – although you must bear in mind that the odds of winning are lower in this instance, even if the payback will be better.
There are certain elements that will influence your odds. These elements include:
- The rules – There are table and card games that have tens of variations for players to choose from. Before playing, you need to pay attention to the rules so that you can calculate your odds. Take blackjack, for example. Some of the rules include splitting pairs and splitting aces, where you may or may not be able to take these actions. This is where the odds begin to change.
- Number of players – Online casino games often attract hundreds of players. Simply put, when you are betting against 300 people, your odds are not great. This can sometimes occur with table games. If you bet against six people, then the odds become much less favourable. Less competition can help to increase your odds of winning to a certain extent.
- Total number of decks – When playing card games, it is easier to calculate your odds if you have fewer decks to contend with. This is because you can try card counting with fewer decks and end up with a good result. Having fewer cards in hand, the odds are in the favour of the players. When there are more decks in play and the games become more difficult, the odds are much worse.
Get ready for battle
“It’s not gambling if you know you’re going to win.”
Winning using maths is a battle – and the casino is ready to go on the defence. Online casinos have mastered the art of using maths to ensure that they make a profit in the long run. As a player, you can do the same for the opposite reason – to become a winner.
To prepare for the battle, you need to know about variance. This mathematical term refers to the difference between the amount of money that a player expects to win on average in the long term, and the results that they are receiving within the short term.
Another simple example of variance can be seen in flipping coins. A coin has two sides, so you can get either one of them when you flip them. However, when you flip them, there is no guarantee that you will have heads and then tails following each other perfectly. The more you flip the coins, the easier it becomes to determine the variance.
Choose your games wisely
“You got twobig choices. Do it now, orregret it later.”
When visiting the online casino, you will be greeted with a wide option of games to experience. These include slots, progressive jackpot slots, table games and card games such asroulette, baccarat, blackjack and more. The first step in using maths to win is to establish which games give the highest profits to the casino. Higher profits for the casino directly equate to higher losses for the players.
It has been discovered that more than 70% of the profits from an online casino will come through the slot games. Random number generators are used with slot games, both online and in land-based casinos.However, these games also take a significant spend to get to a win. There are some mathematical tips and tricks that can give you an edge.
The mathematics of slot games
“They love what you do, they just hate that it’s you doing it.”
Of all casino games, slot games are most attributed to luck with no real strategy that one can follow. This myth is about to be dispelled in this section. There are thousands of slot games available online, making it a challenge to explore a one-size-fits-all approach to maths. However, there are some features that all these games have in common. These include the random number generator and the volatility of the games.
With table games, strategy can get you the result that you want when it comes to using maths. With slot games, you need to focus on probabilities, payback percentages, and any other numbers available to you.
To understand how this works, it is necessary to walk through the process of playing a slot game. First, the lever is pulled, and a button pushed. This ensures that the slot reels begin to spin, and random combos of symbols appear. The random number generator is in place to ensure that each spin is independent. Probability thus offers a solution.
Probability will focus on the number of reels, and the symbols per reel. To win using maths, use the following steps:
- Multiply the number of symbols that each reel has. For example, a three-reel slot machine may have six symbols. The multiplication will then be 6 x 6 x 6 to get 216. If it has 10 symbols, then the multiplication will be 10 x 10 x 10 to get 1,000. The result that you get will let you know how many possible combinations there are within a slot machine game.
- The slot game will provide details on the number of winning combinations. For the next step, you will need to divide the number of winning combinations by the number of possible combinations. This will give you the odds of the machine or game you are playing.
- Next are the symbols. The number of symbols and the combinations they appear in will give you an idea of what you could win.
Here is how all of these come together. Consider a slot game that has three reels. Let’s say that these reels have 20 stops on them. Each stop will have symbols on them, such as lucky number seven.The game may be programmed using the random number generator to have a probability of 1/20. On a three-reel machine, the chances of finding threelucky number sevens lined up on each reel is 20 x 20 x 20, or 8,000.
This is where maths comes in from the design angle to make it challenging for the player to win. The designer may choose to program the slot to pay off 6,000 to 1 should three cherries appear on a roll. As great as this may sound, consider the spend. If each spin cost a player μ₿1, and they made 8,000 spins, then the casino would be paid μ₿8,000. The wins are only equal to μ₿6,000. This means that the casino would be able to keep μ₿2,000.
When considering maths to play online slots, you should also think about how easy the slot game is to play. Games that are easy will normally have the worst odds (although this isn't always the case). This means that you can count on your bankroll running out quickly. It is better to look for slots that are challenging to play and you might be able to secure some wins.
Another tip to help you win with an online slot is to select a game that has a small jackpot. Smaller jackpots are typically much easier to win. Those who want to play bigger jackpots will find that they could lose a large portion of their bankroll.
Here is an example that you can apply to any slot game that features fruits, such as Fruit Zen and Fruit Bonanza. This requires you to use maths by paying attention to the symbols in the games. Consider that you are playing a game that has ten stops on each wheel and uses cherries as a symbol. The chances that you will get a cherry on each reel are 1/10. Should you get three cherries, you will win 900 coins. The probability of getting three cherries comes to 1/1,000. This means that the terms in odds are 999 to 1.
Let us consider that you are playing a game where you can bet µ₿100 for each spin. You do a total of 1,000 spins, and you lose a total of 999 spins at µ₿100 each. This means that you are out µ₿99,900. You have one spin hanging in the balance. When you do this spin, you win a total of 900 coins, or in monetary terms,µ₿90,000.Although you are not at a profit, you would have lost a total of µ₿9,900. Looking at this loss, it becomes easy to understand the house edge and how it ties in to what you would need to give back to the casino. This is how slots are designed, which is one of the reasons that maths with slots can be so challenging.
The mathematics of baccarat
“Baccarat is a game whereby the croupier gathers in money with a flexible sculling oar, then rakes it home. If I could have borrowed his oar, I would have stayed.”Mark Twain
Baccarat has long attracted players who want to utilise maths to help them win, and hopefully, win big. To make the most of maths with this game, two key factors need to be considered, as follows:
- The house advantage – The house advantage varies based on the type of bet being made. This requires understanding of the banker bet, player bet and tie bet.
- The 1-3-2-6 system –A progression betting system thatis based on the Paroli technique.
The Allan N. Wilson formula
This is a formula that you should use to control loss, rather than to win big. The Allan N. Wilson formula can be used for managing losses by avoidance of the tie bet. With the banker bet, the casino will have an advantage of 1.06%. This is a highly popular type of bet, though one must remember that the winnings will be deducted by 5%, which serves as a commission for the casino. This bet features 1-to-1 payoff and assumes that the banker bet will be equal to or closest to the value of nine. This bet will have the lowest house edge.
The player bet then has an advantage of 1.23%. When this is chosen, the casino customer will place a bet based on the probability that the player bet will be equal to nine, or closer to the value of nine than the banker bet. This bet has a 1-to-1 payoff and has a house edge that is a little higher than the banker bet.
The tie bet has an advantage of 14.05%. This means that compared with the other two types of bets, you will lose more frequently with the tie bet. This bet centres on the assumption that the banker and player hands have the same total. This has incredibly low odds, which gives the casino an enormous advantage. One would need to be adept at card counting to have an idea of which cards are unplayed as that is where this strategy can be used.
The 1-3-2-6 system
Paroli created a betting system in the 16th century that continues to be in use today because it has been tried and tested, and it works to a certain extent. It is a positive betting progression system. It only works when wins are being experienced consecutively. It calls for a player to double their wager following each win. If a player loses a bet along the way, then they start afresh with a single unit. The theory behind this system is that the player should only lose their single unit bet in the first round – except in the second round, where the player could lose two units and briefly be in the negative. It is around this theory that the 1-3-2-6 system was created.
The 1-3-2-6 system is a technique that requires players to pay attention to trends when they are making bets. This can be observed over four consecutive rounds. The first round calls for a single-unit bet. Should the player win the first round, they make the next bet with three units. These will be the two that are in possession, as well as one more. If this round is won, then they need to deduct a total of four units from their winnings. This will leave them with two units, which should be bet in the third round. If the player wins the third round, then they should add two units to their winnings so that they can make a bet that has six units in the fourth round.
With this system, once the cycle of four rounds is complete, assuming that each round has been won, the player will have a profit that comes to 12 units for the game. This strategy is ideal for players who are averse to risk. The reason is that it saves players from losing their full bankroll when playing and also manages the amount of loss that one may experience.
The mathematics of blackjack
“Blackjack is the only casino game an amateur can learn to play and at which he can definitely win.” LawrenceRevere
The game most associated with using maths to get a win is blackjack. This card game is simple and easy to play, making it also a good choice for players looking to elevate their wins with maths. The reason why maths works so well as a strategy with blackjack is that it is a game that is all about counting. Yes, there are sites that frown upon card counting, but this does not mean that card counting has stopped. Even with all the maths skills in the world, it is worth noting that there is always an element of chance with this game.
The first step to using maths in blackjack is to make sure that the odds are in your favour. Having a starting hand of 17 or higher is a strong position while a starting hand of 11 or lower is not as strong – this should be one of the first things you consider as you check your cards when you are dealt into a game of blackjack.
There are different blackjack probability tables that you can refer to based on the variation of blackjack that you are playing. These are able to guide you on when it is best to stand, hit, double, split, and surrender.
The Oscar betting system
When experiencing a winning streak, an excellent strategy to use would be the Oscar system. This maths system uses positive progression as the style of betting, and the aim is to keep winning with one unit in each cycle. This allows players to win small amounts regularly, rather than aiming for a big win with multiple bets. It is the ideal option for any player seeking continuous gameplay. The cycle comes to an end when a player loses. Rather than pulling back the winnings to keep increasing the bet, one unit is consistently wagered through the game. This method helps to minimise loss.
This system is also known as the Grind as it takes a considerable amount of time to grind out a profit.
The Martingale system
With most games, the more time that you spend playing, the higher the likelihood that you will lose. This is where the Martingale system comes in. This system looks at losing as an opportunity opening up for players to win. To ensure that loss is minimal, a player needs to proceed by choosing the lowest minimumbet tables. Every time you lose a hand, you double your bet. The result is that you will win back the money that you have lost.
Here are a few tips that make using maths with blackjack much easier:
- Card counting will not work when you are playing online. The cards are automatically reshuffled after each hand due to the random number generator. This makes it challenging to keep track of all the cards. If you do want to attempt card counting, then it is best to find a table that is using just two decks.
- Make the right choice when choosing a table. For example, a table that will pay 3 to 2 shall give you higher returns the longer you play, compared to a table that pays 6 to 5.
The way that a player wagers and wins differs with blackjack and other table and card games, compared to slots. With a slot, when someone places a wager, the amount is immediately deducted from the credit balance, and the win is calculated based on the symbols that appear once the reels have been spun. With blackjack, the wager is based on ratios. For example, a ratio could be 10:1. If a player bets and wins, they receive the equivalent of µ₿100 (assuming they wagered µ₿10) and a return of the µ₿10 they wagered. If they lose, they lose the µ₿10.
An example is needed to better explain blackjack and its strong affiliation with numbers. There are various options you can choose on Bitcasino, including Blackjack Classic and European Blackjack GOLD. The beauty of a game of blackjack is that you can depend on your memory. Where other table and card games are often up to chance, strategy comes in handy here.
Now, consider playing the games with one deck. Each time that a card is taken out of the deck, the probabilities of all the other cards being available changes. You are focused on ensuring that you get a blackjack. The best way to use maths to win is to keep track of the way that the deck is changing.
When the game begins, you will be aiming to get an ace so that you can get a blackjack with the first hand that is dealt. There are four aces in the deck, and your chances of getting one is 1/13. In addition to this ace, you will need a card valued at 10 to get a blackjack. The cards that have 10values are the number 10, the Jack, Queen and King. This means that there are a total of 16 cards. If you have already dealt the first card, then the odds of getting a second card valued at 10 is 16/51.
Now you need to calculate the frequency with which you can get a blackjack. So, you take your odds of receiving a card that will have a value of 10, and multiply that by the odds of getting an Ace as the first or second card. This would look something like this:
1/13 x 16/51 = 32/663
When rounded off, the answer comes to 5%. For your estimation, every 20 hands should result in you getting a blackjack.
The mathematics of roulette
“If you don’t hold your breath as the Roulette ball falls into its place, then you are not playing it right.” The Rambler Gambler
Probability and roulette invariably go hand in hand. With card games, it is easy to come up with probabilities depending on the way that the cards are dealt. With roulette, it is a little more complicated.
Two main roulette wheels are used in online casinos. These are the American wheel and the European wheel. It is noted that the American wheel has two zeros.For the player, this means that the odds of the ball landing in any slot on the wheel are 37 to 1. Should you land on a number, the casino will pay 35 to 1.Therefore, for every 38 chips thatyou bet, the casino will take two. Using this maths, the house edge can be calculated at 5.26%. This means that the casino has a double advantage, and players can lose 5.26% of any money they bet. With the European wheel, the probability of losing any bet would be 2.7%.
Another key detail to observe when looking at the layout is the way that the numbers have been arranged. The patterns may be similar in regard to the colours, but the order of the numbers is different. When the zero values of the wheels are removed, the American wheel will have consecutive reds on one side, and blacks on the other side. This is different from the European wheel. Within the layout, it is also clear that the numbers alternate between low and high. The American wheel does not apply this much. For this reason, it is not considered balanced.
With these facts in mind, the maths needs to be combined with strategy. Winning at roulette using maths is challenging, as in the long run, the casino wins. For this reason, maths strategies should only be used for short-term gaming.
Some of the roulette tables that you can try out at Bitcasino include American roulette and European roulette. These are excellent for players of all levels, and there are also a host of other options. There are several ways that you can use maths. For example, consider that you want to place a bet assuming that the ball will land in a green pocket – meaning where there is a zero. The probability of this may be 19 to 1 with an American table, or 18 to 1 on a European table. If you are betting that the ball will land on a red pocket, then the probability is 9 to 19, or 18 to 37. You can use this formula if you are making a bet that will land on odd or even numbers –it all depends on the preference of the players
The sign-upbonus trick
An attractive high sign-up bonus may be what calls you to start playing with a certain online casino. It may seem like a no-brainer to take advantage of free funds being given, especially if one can win real money with them. However, beyond the glitz and glamour lies the small print which you must read carefully to make sure you get the best advantage possible.
To win, make low deposits for trial purposes and accept the bonus you receive.
When using maths as the science of winning, remember that each bet is an independent event. Looking at betting this way will ensure that players are able to manage their losses.
Online gamers who experience casino games may not believe in maths as a science to win. It cannot be denied that for the most part, the casino is set up so that players lose, and the casino is able to profit. No matter what you do, this will happen. However, by making use of maths, you can lower the probability of this coming to pass and elevate your total wins.
Making the most of maths requires an understanding of the casino edge, or house edge. Every game has its own house edge, which determines how much you will need to give the casino for each dollar you put in. The one thing to remember is to look for a casino that has a low house edge.
The house edge directly connects with the negative expected value. Expected value is the amount you will win, or possibly lose, while playing in the long run. You will find it expressed as a percentage of the amount that has been wagered.
The odds of a game let you know how much you can win, depending on the amount you bet. It is normally expressed as a ratio and can vary even within the same games. Factors that can affect odds include the number of players that are present at a table, or even the number of decks when playing a card game.
With the number of games at Bitcasino, the question would be, which is the best to chance with maths? The slots require long-term consistent play to get any result from maths.
With baccarat, the system becomes a little more scientific, and you can experience the process of counting for the first time. It is worth remembering that using maths with baccarat will not guarantee that you can win – instead, it will help you to manage any losses.
Blackjack is most suited to maths, though you can only really have success if you choose this game. For the best results, the fewerdecks you have, the better. You will need to pay attention and keep track of key cards. There is no need to track all the cards – just the ones that have key values. These include the ace, as well as any cards that have a value of 10. This means that at any time, there are only 20 cards that you need to remember.
With the game of roulette, you need to focus on what element you will use maths on. Will it be a choice based on odd and even numbers? Or will it involve choosing different colours? The table, whether American or European, also affects the odds due to the number of pockets that have been numbered.
The more you play, the better you become. Choose maths if you are seeking to play a more competitive game and want to make those long-term wins.