An easy-to-understand explanation of the casino Monte Carlo method! Simulation of roulette and horse racing

Home » An easy-to-understand explanation of the casino Monte Carlo method! Simulation of roulette and horse racing

In this article, we will introduce one of the casino strategies, the Monte Carlo method.

There are several strategies to increase your odds of winning at a casino. Professional players often use these and are not setting their bets at random.

The Monte Carlo method is one of the most famous strategies available in casinos, so be sure to master it.

What is the Monte Carlo method?

In a nutshell, the Monte Carlo method is a simulation using random numbers.

First, before explaining the Monte Carlo method in detail, I will explain random numbers. Random numbers, as the name suggests, are random numbers.

For example, let's say you roll a die 600 times. In this case, the die has 6 rolls, so each roll is expected to roll 100 times. However, it is not possible to predict which roll will come out in which order using probability. In this case, random numbers are called random numbers.

And the simulation using this random number is called the Monte Carlo method. This Monte Carlo method makes it possible to estimate the solution of the problem by performing numerical calculations using random numbers.

Today, this Monte Carlo method is also used in many forms of entertainment, such as casinos and sports betting.

Monte Carlo means that you predict the probability of an outcome by running a simulation. In this case, add every variable to the system and predict the result.

For example, when using the Monte Carlo method in sports, the injury status of participating athletes, the conditions of the match venue, the weather on the day of the match, etc. are read into the system as variables, that is, parameters, and the results are predicted.

There are three main results that can be derived from the Monte Carlo method: To make it easier to understand, I will explain it while relating it to sports.

deterministic model

Deterministic models are the most basic of Monte Carlo methods. A deterministic model, as the name suggests, derives only one result through simulation.

Sports matches lead to only one clear result, such as a win for Team A, a win for Team B, or a draw. This deterministic model works well when the parameters are well defined.

stochastic model

Probabilistic models are more complex than deterministic models and differ from simple simulations that predict one outcome.

Since the probabilistic model takes into account unknown factors, it is possible to predict more detailed results, such as what is the probability that Team A will win, how many points will Team A win over Team B, and so on.

Also, these results are not just one, but multiple. Therefore, it is necessary to select the one that you think is correct from among the simulation results.

dynamic model

Finally, dynamic models are similar to probabilistic models and change their parameters according to the situation.

It is suitable when you want to derive long-term results, such as predicting the results at the end of a season rather than predicting the results of a single match. For example, when predicting the results of a season with this dynamic model, each time a match ends, the match result is added as a new parameter.

By constantly adding new information to the simulation in this way, a feature of the dynamic model is that more accurate results can be derived.

The Monte Carlo method mainly predicts results based on these three models. Since the results are derived from simulations and parameters, the results can be said to be highly credible to some extent.

However, this is only the result of a simulation, and it does not mean that the prediction is definitely correct. Since the Monte Carlo method is based on mathematical grounds, the accuracy rate is higher than that of human random prediction.

But things are always changing, especially in sports, and even with the perfect addition of parameters, there is always the possibility of something unpredictable. Therefore, instead of relying 100% on the Monte Carlo method, it is better to use it as a reference when predicting results.

A simple explanation of the Monte Carlo method

Here, we will introduce how the Monte Carlo method can be used concretely.

To use the Monte Carlo method, first get some paper and a pen. The Monte Carlo method can only be used in casino games with double and triple dividends. The method is slightly different for games with double dividends and games with triple dividends, so you need to use them depending on the game you play.

How to use in games with double dividends

First, the Monte Carlo method uses, as a rule, three consecutive numbers.

You can choose any number for this first number, but for simplicity we'll use the sequence (1,2,3).

Now, let's introduce how to use the Monte Carlo method, assuming that you are actually playing a game.

Round 1: Sequence (1, 2, 3)

First, write the sequence (1, 2, 3) on the paper you prepared.

In the Monte Carlo method, you set your bet as the sum of the numbers on either side of the sequence.

The bet at this time is 1 + 3 = 4 dollars, which is the sum of the numbers on both sides.

And let's say you lose the game in the first round. If you lose, add your bet to the end of the series. Then the sequence will look like this:

(1,2,3,4)

Round 2: Sequence (1,2,3,4)

The bet is the sum of the numbers on both sides of the sequence. So the bet for the second round is 1+4=$5.

Similarly, let's say you lose the game in the second round as well. In that case, the wager is added to the end of the sequence and the sequence looks like this:

(1,2,3,4,5)

If you continue to lose, repeat this process.

Round 3: Sequence (1,2,3,4,5)

The stake for the third round is 1+5=$6. And let's say you win the first time here.

If you win, instead of adding your bet to the end, you remove the numbers on either end. So the sequence looks like this:

(2,3,4)

If you keep winning, the numbers in this sequence will get smaller and smaller.

And in the Monte Carlo method, when the numbers in the sequence become 0 or only 1, it is the winning point, that is, the timing when profit is made.

Depending on the victory or defeat of the game, the numbers are erased or increased, and the game continues until the number becomes 0 or 1.

For games with triple payout

In the case of 3x payout games, the basic method is the same as in the case of 2x payout games.

However, in the case of a game with a triple payout, two numbers on each side of the sequence are deleted when you win.

So for the 3rd round above, the first sequence is (1 2 3 4 5). And in the game of 3x dividends, the winning times will be (3) because two numbers will be erased. In the triple payout game, 4 numbers are erased from the sequence at once, so it doesn't take long for the numbers in the sequence to become 0 or 1. Therefore, if you win in a row, you can quickly recoup your losses.

This is the only difference between games with double payouts and games with triple payouts.

When you win, remember that "remove 1 at a time for 2x dividends" and "remove 2 at a time for 3x dividends".

Monte Carlo Law Banned in Casinos?

The Monte Carlo method cannot be used at land-based casinos.

The truth of this story is not certain, but once a gambler enjoyed gambling at a casino in Monte Carlo, Principality of Monaco. At that time, I used the Monte Carlo method as a strategy, which made me a lot of money. And he is said to have closed the casino because he made so much money. For this reason, it is said that the Monte Carlo method was named after the name of the casino.

Since then, the use of the Monte Carlo method in land-based casinos has been completely banned, and continues to this day.

The truth remains the same, but this kind of anecdote shows how effective the Monte Carlo method is.

The Monte Carlo method can be used in online casinos!

The Monte Carlo method cannot be used at land-based casinos. Due to the computational complexity of the Monte Carlo method, its use requires the use of pen and paper. In land-based casinos, the Monte Carlo method cannot be used because the dealer can see the hand.

However, if you are an online casino, you are free to use the Monte Carlo method because you are just playing against a computer. Even if you use a live casino, you can freely use the Monte Carlo method because the dealer cannot see the player's hand if it is an online casino that plays through the screen.

List of casino games that can use the Monte Carlo method

The Monte Carlo method can only be used in casino games with double or triple payouts.

Games with double and triple payouts include:

Games with double payouts

- Roulette (red/black, odd/even)

-Baccarat

-black Jack

3x payout game

- Roulette (Column, Dozen Bet)

These table games are offered by almost all online casinos. In addition to casino games played against regular computers, there are also live casino games that can be played live at land-based casinos.

Simulation of the Monte Carlo method – an example of its use in roulette

Here, we will introduce a simulation using the Monte Carlo method in a red/black roulette game, that is, a game with a double payout.

Here, as in the explanation, the first series is (1,2,3). And let's say you played the game 10 times.

Simulation 1. When the number of losses is large with 3 wins and 7 losses

     

number of gamessequencewagervictory or defeatdividendprofit and loss
First time1,2,34 dollars×$0-$4
Second time1,2,3,4$510 dollars+1 dollar
Third time2,3$5×$0-$4
4th2,3,5$7×$0-$11
5th time2,3,4,5,7$9×$0-$20
6th time2,3,4,5,7,9$11$22-$9
7th time3,4,5,710 dollars×$20-$19
8th time3,4,5,7,10$13$26-$7
9th time4,5,7$11×$22-$18
10th time4,5,7,11$15×$30-$32

In this case, we lost three games in a row in the first stage, so we couldn't make up for the loss just by winning once. And the final result is also a big loss of -32 dollars.

Simulation 2. When the number of wins and losses is the same with 5 wins and 5 losses

    

number of gamessequencewagervictory or defeatdividendprofit and loss
First time1,2,34 dollars×$0-$4
Second time1,2,3,4$510 dollars+1 dollar
Third time2,3,$5×$0-$4
4th2,3,5$7×$0-$11
5th time2,3,5,7$9$18-$2
6th time3,5$8×$0-10 dollars
7th time3,5,811 no dollars×$0-$21
8th time3,5,8,9$12$24-$9
9th time5,8,$13$26+$4
10th timenonedollarnone+$4

In this way, if the number of wins and losses is the same, the sequence becomes 0 or 1 when the win continues, and the profit is confirmed and the Monte Carlo method cannot be continued.

In other words, if the winning/losing ratio is 50/50 in the Monte Carlo method, you can make a profit. However, the final profit in this case will not be a large amount.

Next, we will simulate a game with a triple dividend.

Simulation 3. When the number of wins is large with 2 wins and 8 losses  

number of gamessequencewagervictory or defeatdividendprofit and loss
First time1,2,34 dollars×$0-$4
Second time1,2,3,4$5×$0-$9
Third time1,2,3,4,5$6×$0-$15
4th1,2,3,4,5,6$7$21-1 dollar
5th time3,4$7×$0-$8
6th time3,4,710 dollars×$0-$18
7th time3,4,7,10$13×$0-$31
8th time3,4,7,10,13$16×$0-$47
9th time3,4,7,10,13,16$19×$0-$66
10th time3,4,7,10,13,16,19$22$66-$22

In this case, we have 2 wins and 8 losses, so of course the final result is profit and loss. However, in the case of games with triple dividends, the amount that can be recovered with one win is large, so even if you lose in a row, you can recover some losses with one or two wins.

Even in this simulation, if you win the 11th time, the profit and loss will turn into profit.

Monte Carlo methodSimulation – use case in horse racing

Even when using the Monte Carlo method in horse racing, the method is basically the same as casino games such as roulette.

However, in the case of horse racing, it is a golden rule to bet on things with odds of 3 times or more.

In horse racing, the payouts are not fixed at 2x or 3x like in casino games, so if the payout is 3x or more, there is no problem even if you choose an odd number such as 3.5x or 3.3x.

Also, bet 100 times or 1000 times the number sequence in horse racing. Below is a simulation of how the amount changes when odds of 3.5 are selected.

Simulation 2 wins and 8 losses with more losses

number of gamessequencewageroddsvictory or defeatdividendprofit and loss
First time1,2,34000 yen3.5×0 Yen-4000 yen
Second time1,2,3,45000 Yen3.5×0 Yen-9000 yen
Third time1,2,3,4,56000 yen3.5×0 Yen-15000 yen
4th1,2,3,4,5,67000 yen3.5Circle+2500 yen
5th time3,47000 yen3.5×0 Yen-4500 yen
6th time3,4,710000 yen3.5×0 Yen-14500 yen
7th time3,4,7,1013000 yen3.5×0 Yen-27500 yen
8th time3,4,7,10,1316000 yen3.5×0 Yen-43500 yen
9th time3,4,7,10,13,1619000 yen3.5×0 Yen-62500 yen
10th time3,4,7,10,13,16,1921000 yen3.573500 yen-10000 yen

In the case of horse racing, you can't bet with a small amount of money like you can in a casino game, so the amount is large like this. In this simulation, the odds are 3.5 times, and you can see that the higher the odds, the larger the amount that can be recovered at once.

However, the chances of winning are low, and the odds of losing are high.

What is Monte Carlo loss cut?

The Monte Carlo method is not a strategy that can recover all losses at once. So, the longer the losing streak goes on, the harder it will be to recover those losses.

If the losing streak continues, the funds may bottom out, so it is recommended to cut the loss early when things are not going well.

When to cut losses is up to the player. As a guideline, if you can't recover your profit or loss even after winning three times in a row, you can cut your losses at that time.

It is difficult to aim for a winning streak in a game with a triple dividend, so it is important to draw early.

Advantages and disadvantages of the Monte Carlo method

Advantages of the Monte Carlo method

The advantage of the Monte Carlo method is that the stakes grow slowly. If you set the first series to a small number, the numbers in the entire series will not suddenly increase, so even if you continue to lose, the increase in bets will be gradual. Therefore, even if you lose once, you will not lose a lot.

Each table has a table limit, the maximum amount you can bet. Monte Carlo bets with slowly increasing stakes rarely hit this limit, so don't worry about the table limit stopping you from continuing.

And since you can freely set the number sequence, you can play the game according to your own funds. As shown in the example above, the sequence can be started from 1, so it can be said that the advantage of the Monte Carlo method is that it can be used with a small amount of money.

Also, in the case of a game with a triple dividend, two numbers on both sides are erased at once, so if the winning streak continues, the numbers in the series will disappear in no time. This means that profits are easy to lock in.

Disadvantages of the Monte Carlo method

On the other hand, the Monte Carlo method has the disadvantage that it is not possible to recover the profit and loss up to that point at once.

If you keep losing, you'll have to win in a row to recoup all those gains and losses. The disadvantage of the Monte Carlo method is that if the number of losses is greater than the number of wins, the profit and loss will eventually increase.

Also, since the Monte Carlo method repeatedly increases and decreases the number of sequences, you will always need paper and a pen. The disadvantage of the Monte Carlo method is that it cannot be easily calculated in your head.

Summary of Monte Carlo method

The Monte Carlo method is one of the casino strategies developed on a mathematical basis. By playing the game according to the Monte Carlo method instead of setting the bets randomly, it is easier to lock in profits.

Monte Carlo is a very effective strategy used by many players. By all means, let's use the Monte Carlo method in roulette, blackjack, etc. and enjoy casino games smartly like a pro.

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