Converting odds is pretty simple. , For the binomial. The answer is the total number of outcomes. A simple example: Say you bet $100 on red. The probability of winning is 1/38 and the probability of losing is 37/38. 18 18 of these are red, and 18 18 of the slots are black. 02 = 1. Solution : Total number of outcomes = 20 C 2 = 190 Number of favorable outcomes = 10 C 1 x 10 C 1 = 100 Therefore, required probability = 100 / 190 = 10 / 19. 0. 63%, or 1-in-38. The following image shows how to find the probability that the dice lands on a number between 3 and 6: Statistics and probability 16 units · 157 skills. The probability of an event is (frac{3}{8}). Expression using fractions (1 / x) - If we express the probability using a fraction, we say that the phenomenon occurs 1 time from X attempts. 58%. The Mathematical formula to determine the proportionate value for the selection. What would your net winnings be? See full list on roulettestar. The house edge is the advantage the casino has over players. 2. Question: Create an excel formula and write down the formula and answer the following:Considering that the roulette ball can land on the numbers 1 through 36 or land on a 0 or 00, calculate the appropriate probability of landing on a red number. The probabilities to win or loose stay unchanged. 83 standard units is about . ” Summary. $> 105$ dollars) if you currently have $105$ dollars, and thus can make $105$ bets on the. Unit 2 Displaying and comparing quantitative data. A formula for calculating probability from odds is P = O / (O + 1). Type (i): This version is exactly like tossing a fair die until we get, say, a $5$. So the expected value is 0. A compound event is more complex than a simple event, as it involves the probability of more than one outcome. 0 - scaled_fitness_list. The payoffs (winnings) for a $1 bet are as follows:Roulette Probability Formula : These applications enhance the playing experience on the smartphone even further. 0000000815) and the probability of matching 5 numbers is (frac{252}{12271512} approx 0. What 2 formulas are used for the Roulette Calculator? In American roulette, the probability of guessing the number outright is just 2. The dealer will place a token on top of the dealer's stack of that color of chips to indicate the value. Here, you want to know the probability of getting a lemon on lines 1, 2, and 3. This paper derives important formulas for the martingale strategy, such as the distribution, the expected value, the standard deviation of the profit, the risk of a loss or the expected bet of one or multiple martingale rounds. The problem is that I don't know how to calclate the formula. Therefore, if E (X) = µ, we have E (X − µ) = E (X) − E (µ) = µ − µ = 0. The following step-by-step. Step 6 - Calculate standard deviation of Bernoulli distribution. 3% (5/6). Good luck and enjoy, roulette. In fitness proportionate selection, as in all selection methods, the fitness function assigns a fitness to possible solutions or chromosomes. Once your opponent has survived the first round, he or she turns into the player to go first, with probability a of winning the game, so q=a. Probability of Ruin: Probability the player goes bust before his desired play is over. Average win probability after 10000 simulations: 0. On cell E9, calculate the appropriate probability of landing on a 0 or 00. The probability of 2 blacks showing up back to back WILL happen. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected. Therefore , X ∼ B (n = 5, p = 0. The probability calculated for the pick-3 game. To make things easy we use a Binomial Distribution Function in our excel sheet where you enter. 3 is the probability of the opposite choice, so it is: 1−p. At the third spin, the probability for the number 20 to win is again 1/38, or the exact probability as any of the remaining numbers on the wheel. We compute the expected value by multiplying the value of each outcome by its probability of occurring and then add up all of the products. (You do not need to replicate the sample code. This gives b =5/6 a. You are playing with one other person. If you win once, you stop playing. At the basic mathematical level it is a formula which relates P(AjB) and PBjA). P (winning) = 381. 5. 60% American Roulette). For example, in the example for calculating the probability of rolling a “6” on two dice: P (A and B) = 1/6 x 1/6 = 1/36. If you know whether the ball picked on a given trial matches your guess, there is an optimal strategy to proceeding. I did check, however. Use the formula 1 - 1/37 to calculate the probability that a specific number won’t play. You can easily adapt this to your code by using the offspring list instead of the. It can be used only for outside bets, those that provide almost 50% chance of winning, and excluding the 0. Sometimes they resort to excel or use specialized. (5)( 1 50) = 5 50. Roulette prediction formula, roulette mean and standard deviation Roulette prediction formula Roulette prediction formula How to deposit and play. 1) 2 ⋅ 0. Roulette probability formula. It is a popular selection method used in a genetic algorithm. Here the house has a slight edge. A ball is rolled, and it falls into one of the 38 slots, giving a number and a color. The below table gives you the complete list of. So, the probability of winning when betting on the number 5 in European roulette is 1/37. The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. . A statistics expert would now interpret the probability of rolling the particular number as one-sixth, while the expert in gambling would say it is 1 chance out of 6. 02 = 1. Possible Outcomes and Sums. The probability of selecting a solution can be given by:. 302 %. 1 – 0. Repeated colour bet – American roulette Assume we place a colour bet. g. This gives lower fitness individual higher fitness (pseudo fitness for selection's sake). Content in the footer will take you to the directory index. There is a formula for questions like this, which I explain on my site see problem 116. You decide to play 6 spins of Roulette and bet each time that the ball will land on a red number. Bankroll: Game: Blackjack Baccarat Pai gow (tiles) Pai gow poker Roulette (single 0, even money bets) Roulette (double 0, even money bets) Roulette (triple 0, even money bets) Ultimate Texas Hold 'Em Three Card Poker (Ante) Three Card Poker (Pairplus) Craps. Scaled the fitness list to the range [0, 1] 3. If it is, he loses not only his bet but his life. pdf), Text File (. Is an effective and simpler method of applying the probability rules. Unit 6 Study design. If we bet on a single number, the payout is 35-to-1 when we win. Probability and random events. Jagger sprang into action. Let us take the classic example of a dice with the numbers one to six. Using the normal distribution: 1-pnorm (70. 3439. I've seen quoted in a number of places that the standard deviation for a 1-number bet on a 38 number Roulette wheel (0, 00, 1, 2, . O’Reilly members experience books. Formula, if understood well, can make clearer that probability events (or random events, or gambling) actually follow precise rules. I got two exercise questions in my book. The probability that the zero wins is 1/37, 0. Monday, 16 October 2023 13:19 Written by Martina Maritato Here at Bet and Skill we love a spin of the roulette wheel and know all there is to know about the popular casino game. Probability of "at least 2 heads in a row" is 3/8th (0. Since the probability of a winning number for a single roll of a die is 1/6, it follows the game has 5 to 1 odds. The Romanosky Strategy is a roulette betting strategy that allows players to cover 32 numbers with eight different units, while leaving five numbers blank. With a bankroll of b units, winning goal of g units, probability of winning p, and probability of losing q your probability of success is ((q/p) b-1)/((q/p) b+g-1). The house edge largely depends on which type of roulette game you are playing. European roulette single number odds, on the other hand, are just 36 to 1 (2. A) The probability p for a single zero roulette game is: p = 1/37 = 0. Unit 4 Modeling data distributions. Nothing, but nothing, has a probability. The probability of all bets in roulette can be calculated by simple counting. Exercise 3: An annuity is the promise by A(typically a life insurance company or aHere is how you should do the roulette probability formula: P(Red) x A (value for red) + P(Not red) x A (value that is not red) = 18/37 + 2 + 20/37x (-1) = 0. P (x): Probability of value. 06 percent. The probability of winning n/N games at win probability p is: $$f(n) = p^n(1-p)^{N-n}frac{N!}{n!(N-n)!}$$ Your numbers for these would be 105 and 1/38 for N and p. The program always bet on red and if it wins it will bet $1$ dollar. So, if we are covering three numbers with a bet, we have a 7. g. In other words, the RTP is just 100% minus the house edge. The probability of success is 18/37 (18 / 18 + 19). This paper derives important formulas for the martingale strategy, such as the distribution, the expected value, the standard deviation of the profit, the risk of a loss or the expected bet of one or multiple martingale rounds. It basically. A roulette wheel has slots numbered 1-38 and the number 0. The Fundamental Formula of Gambling (FFG) calculates the probability and degree of certainty for various roulette bets to miss, or sleep, or skip a number of consecutive roulette spins. 74%. Add the numbers together to convert the odds to probability. 389 1 − ( 36 / 37) 18 ≈ 0. Roulette Probabilities Calculator. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a bet. If we. 26% (if you are interested in the mathematics of roulette, the video at the end will show you how these odds are calculated). The exact answer (using the binomial formula) is . Returns the hypergeometric distribution. 4865. 63%, or 1-in-38. results, nine numbers of wheel six were showing at a rate exceeding what probability would indicate. The roulettes described by the foci of conics when rolled upon a line are sections of minimal surfaces (i. The next table notes the numerical returns of this formula for n increasing from 10 to 100 spins in increments of 10. by test19647195. 25÷ 3. 5) – ($10 x. Within our roulette payout calculator, we included multiple types of bets, so you can calculate their respective payouts with the following formula: Payout = (36/S) – 1 where S = the number of spaces covered by your bet. One-half of the numbers from 1-36 are red, and the other half are black; 0 and 00 are green. A computer simulation. 4…Calculation of Expected Value We use the above information with the formula for expected value. • A bet on an individual number which pays back 35:1, • A bet on an even number which pays back 1:1, • A bet on an odd number which pays back 1:1, • A bet on the numbers 1-6 which pays back 5:1, • A bet on the numbers 13-24 which pays back 2:1. Here is the principal mathematical formula for calculating the chance of any roulette outcome or event. Keep. The probability of a blackjack in a single deck game is 4*16/combin (52,2) = 64/1326. 34134. the number of people who vote for the democratic candidate in the next presidential election. , 4 to 1) for a winning number, the house edge may be calculated as follows: House Edge = (true odds − payout odds) / (true odds + 1) House Edge = (5 − 4)/ (5 + 1)Assume that a procedure yields a binomial distribution with a trial repeated n times. Try to mix up your bets by placing a combination of two or more outside bets. One thing that makes roulette so popular with gamblers is the game’s transparency. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. Instructions 100 XP Instructions 100 XP Run a single Monte Carlo simulation of 10,000 bets using the following steps. 4. (Two have no color). A ball is spun around the roulette wheel in one direction, then the other. 47725 , while a value between 0 and 1 has a probability of 0. The single-zero roulette game has 37 possible cases (36 numbers, plus 0). 83 and . I need a general formula for calculating the probability of an event, given specific parameters: We need to calculate the probability P(e) of the event E = [Bet B appearing X times in N trials(ie. 4. 1081 x 100 = 10. However, otherwise the bet is lost and the outcome is −1$ − 1 $ (a loss of a dollar). May 21, 2023. What are the odds in favor of this event?. Putting this together with the fact that a + b =1 gives a =6/11 and b =5/11. 10. If you win, you double your money. To pander to a larger population, we made a video covering basic concepts of probability. The fourth column of this table will provide the values you need to calculate the standard deviation. 50 (or 5/2 with an implied probability of 28. 1:1 payout means you receive 1 chip PLUS your original bet 5:1 payout means you receive 5 chips PLUS your original bet. A Venn diagram is a useful tool to visualize conditional probability. The roulette game uses a spinning horizontal wheel with 37 or 38 colored and numbered slots. The roulette table comes with six to eight sets of different colored chips, each set consisting of 300 chips. Expected Value Formula = ∑ [ x * P (x)] Example: In roulette, a player can place a $5 bet on the number 17 and have a 1/38 probability of winning. As in the previous section, consider the situation of rolling a six-sided die and first compute the probability of rolling a six: the answer is (six) =1/6. The formula for finding the. 2. How to Calculate the Probability of Winning at Roulette. The most extreme of these methods select individuals randomly with uniform probability, and thus completely disregards their individual fitness. 1%) (7. The most effective way of using the Martingale is to only bet on even-money outside bets – 1-18, 19-36, Red, Black, Even, and Odd. Multiply this number by 100 to express the probability as a percentage. The expected value formula is this: E (x) = x1 * P (x1) + x2 * P (x2) + x3 * P (x3)…. Publisher: Cengage Learning. Number of times plays a roulette: n = 5 Probability of red: p = 9 19 ≈ 0. 60 On an American wheel you can expect to lose 5. Create an excel formula and write down the formula and answer the following: Considering that the roulette ball can land on the numbers 1 through 36 or land on a 0 or 00, calculate the appropriate probability of landing on a red number. The calculation of roulette wheel probabilities is very simple. In European roulette, there can be 37 different outcomes. You are meant to lose at casinos; you are not meant to win; if you win consistently, they will make you pay; 2. The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory. def Indvs_wieght(Indvs): # to comput probality of selecting each Indvs by its fitness s=1 s=sum(i. European. Blackjack payout side bet . How large is the probability that the next. By applying these techniques to a standard casino-grade European roulette wheel, we demonstrate an expected return of at least 18%, well above the -2. spins) ] We know: N= the. The probability of at least breaking even and being ahead for various betting options with a 200 unit stake. They both place bets on red on 3 spins of the roulette wheel before Xavier has to leave. Unit 1 Analyzing categorical data. Hello I have a basic but quite difficult question about roulette probabilities (assuming roulette has 37 numbers 0-36). The probability of success is 18/37 (18 / 18 + 19). The roulettes described by the foci of conics when rolled upon a line are sections of minimal surfaces (i. Formula in D10 is D7/C9. For DC = 66. You can later apply this to other games. You have a sequence of N = 25000 N = 25000 independent Bernoulli trials, where I'll consider a "success" to be a spin not from 1 to 12. Welcome! Random is a website devoted to probability, mathematical statistics, and stochastic processes, and is intended for teachers and students of these subjects. Firstly, to understand what it is you are up against you can use this simple formula to calculate the house edge: House Edge = (Odds Against Success minus House Odds) x Probability of Success. =BINOMDIST (A1;A2;A3;FALSE) The CELL WITH. Number of slots on the wheel: 37 (Single-zero) 38 (Double-zero) 39 (Triple-zero) other. The cumulative distribution for the normal distribution is defined by a mathematical formula, which in R can be obtained with the function pnorm. 34 + 2*0. To find the percentage of a determined probability, simply convert the resulting number by 100. In summary, the conversation discusses the probability of a specific number appearing multiple times on a roulette wheel in a fixed number of spins. Roulette Probabilities Calculator. The odds in roulette indicate your chances of winning a bet. , Is the following a probability model? What. The winning number is determined by real physical variables, like wheel and ball properties, spin spins etc. Step 1 - Enter the Probability of success. The probabilities after several rounds of playing have to be combined. Conditional probabilities or the conditional probability of an event A given the event B is the probability of A given that B is already true. Example (The probability of Red) The probability of the ball landing in Red is. Also, there are 18 red numbers and one green single zero, which means there are 19 ways to lose. 60, from the table. There is a 20/38 probability of losing your initial bet of $1. Divide the number of winning scenarios by the total number of outcomes. 35 + 3*0. Russian roulette is a game of chance in which one or more of the six chambers of a revolver are filled with cartridges, the chamber is rotated at random, and the gun is fired. Add all of these numbers together So for the first coin game, there is a 0. 66. com The essence of the Martingale roulette game system is as follows: we bet on an even chance of roulette (red-black, even-odd), for example, on "red": we bet on roulette at $ 1; if you lose, we double the bet and bet $ 2. That does jibe with what I get in my spreadsheet. Now recalculate the probability. 7% expected of a random bet. 11 + 4*0. The ball does not fall into any green slots_ Probability C. Whether you’re a newbie to sports betting or a regular at the track, our odds convertor and calculation tool makes it easy to understand any betting system and accurately calculate your potential profits no matter where you bet. In one possible bet, the player bets $1 on a single number. Answer: To solve this problem, let's first look at the probability formula. 66. Will anadrol show on a drug test, hip thrust unilatéral avec haltères. Spins. Roulette, Baccarat, Blackjack, Poker, Lottery and Sport Bets. Putting this together with the fact that a + b =1 gives a =6/11 and b =5/11. The probability that the gambler will lose all n bets is q n. 00 bet Success Percentage of (13-24) = Probability of (13-24) x 100% Success Percentage of (13-24) = 31. Step 5 - Calculate variance of Bernoulli distribution. In its most general case, probability can be. Unit 7 Probability. First captured by the WayBack Machine ( web. Then we subtract probability from 1. The strategy is based on increasing your bet after a loss. This version of the formula is helpful to see because it also works when we have an infinite sample space. Since it measures the mean, it should come as no. Roulette pay-outs odds are worked out in the form of x to 1, meaning you will win x pound for every pound you have bet. Just as one die has six outcomes and two dice have 6 2 = 36 outcomes, the probability experiment of rolling three dice has 6 3 = 216 outcomes. 2. It's simple to calculate this for amounts up to 18: If I start with 1 $ my probability is 1/37 1 / 37. Is the roulette calculator probability formula accurate enough that we should take it seriously? It is important to keep in mind that the number of pockets on a roulette wheel does not change from spin to spin. your book suggests. The insurance applications of expected value are detailed in the following video. Learn how to build a roulette wheel simulator in Excel. Schlesinger says the risk of ruin from this formula is an overestimate and my own. 5n q n = 0. The probability of the outcome $36 is 1/38. We will look at some of the possible View PDF FORMULA ROULETTE (*) Quote di partecipazione a persona a settimana: A) Partenza 17 o 18 luglio: €uro 820,oo B) Partenza 24 o 25 luglio: €uro 820€uro 820€uro. Roulette odds are the indicator of the winning probability in the game. The mBit casino beats all brick aA Statistical Analysis of the Roulette Martingale System: Examples, Formulas and Simulations with R. Hence, determining the “ Ball Number ” will lead us to calculate the probability of winning the lottery. g. The American Roulette wheel has an extra slot, 00, which decreases the odds of winning. Use the binomial probability formula to find the probability of x=5 successes given the probability p=1/5 of successes on a single trial. The odds vary with the type of bet. You can bet anywhere from $1 to $100 on each spin. DIST returns the probability of a given number of sample successes, given the sample size, population successes, and population size. Empirical Probability Formula: P(E) = f/n. The calculation will be as follows; ($11 x . For a coin toss, e. How to calculate the probability of a roulette game? The probability is 18/37 and will take the -2 value with 20/37 probability. Expression as a percentage (%) - Probability is calculated as (Event / Outcomes) * 100. (3) (b) Find the expected value of X, E. Martingale is definitely one of the most widely known and most successful roulette strategies (for some it is the best roulette strategy), and it is very simple to apply. If you can bet $1$ dollar and win with a probability of $dfrac{1}{38}$ in a game of roulette. But it's not intuitive (seems low, seems like it should be >50%), and it doesn't jibe with the formula: 1 - (ways to win / total ways) ^ trials = 1 - (36/37)^37 = 64%. The. $> 105$ dollars) if you currently have $105$ dollars, and thus can make $105$ bets on the wheel? 1 – (1/18 + 1/18) = 8/9 = 0. But the probably of 33 consecutive blacks is such a low %, you could bet your life it wouldnt happen. Q: Find the probability of winning in American-style roulette when betting on the first six numbers, 1… A: Number of wheels in American-style roulette =38 Bet consists of 6 numbers Q: A jar on your desk contains fourteen black, nine red, thirteen yellow, and four green jellybeans. 2 Answers. Free Roulette Calculator - Calculates the probability for different bets on a roulette wheel including expected return on a monetary bet. It is the median skip calculated by the Fundamental Formula of Gambling. If we roll n dice then there are 6 n outcomes. In fact, as we will see, we win before we lose with probability at most 1 37648. 0270. The difference is that it is offered in the comfort of your home. the probability of winning 2 times 8. Recognize many other calculators that are available at probabilitycalculator. Plinko Probability - PhET Interactive SimulationsBlackjack payout side bet, roulette probability formula. Example (PageIndex{5}): House Edge in Roulette. For example, the house edge is 2. 3. 7% in single-zero roulette games. 35. The payouts never change. A casino has an edge over anyone who plays roulette (generally 5. Imagine two people in different cities throwing a coin: the outcome of each toss is entirely independent of the other. More concretely, it's the sum of outcomes weighed by their probability. Below is a practical example of how you can calculate the expected value of any given game using American roulette probability values. For an underdog moneyline to break-even win probability Where A1 contains the moneyline odds (like +140) =1-A1/(A1+100) When this gets evaluated with our example number, you get the following:. The type of roulette has a big impact on the roulette strategy probability. But there's also a fourth- implied probability - that is also useful when evaluating a bet or checking how likely an outcome is. P (x): Probability of value. Las Vegas roulette has 38 numbers, 0 and 00 which are green and 1 to 36, half them being red and half of them being black. If you chose correctly, the payout would be 2 – 1. P (A) = T otal number of outcomesnumber of f avorable outcomes to A. Logically, the answer to that challenge is p = ½ = 0. Get the winner of the electronic raffle with RAND, INDEX, MATCH and MAX functions. The sequence itself is cumulative. The player always bet on red, because of the. First ,break the odds into 2 separate events: the odds of drawing a white marble (11) and the odds of drawing a marble of a different color (9). 67 percent. For example, the expected number of goals for the soccer team would be calculated as: μ = 0*0. The outcome is independent of prior outcomes, right? It does not matter how many times in a row black (or red) comes up prior, the outcome is still random and 50/50. For each outcome, multiply its probability by its payout 4. Therefore if we take the. Study with Quizlet and memorize flashcards containing terms like If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct. It is considered a large-coverage combined bets roulette strategy. In the roulette experiment, select the 18-number bet. Eventually the ball will drop into one of the numbered slots. 7) (2 – 1) Probability = 0. With the martingale betting system, one win will yield a net profit because you always bet more than you've lost. (equally likely) outcomes. 89% chance of guessing the winning number. The main game is played with a wheel and colored pockets with alternating black and red. Since 5 of the 6 chambers are empty and each has an equal chance of containing the bullet, we get p=5/6. It follows that the higher the probability of an event, the more certain it is that the event will occur. Find the probability of green occurring on two consecutive plays on a roulette wheel. 64864862 in 100 binomial experiments is: BSD = 4. If we take the French roulette wheel, having 37 numbers, and we place a. Relation of the Birthday Paradox to roulette. A simple formula for calculating odds from probability is O = P / (1 - P). Someone mentioned that he guessed the correct number five times in a row, and said that this was surprising because the probability of this happening was $$left(frac{1}{38} ight)^5$$ This is true if you only play the game $5$ times. What are the odds we win 100 dollars before losing 100 dollars? Most folks would think that since . The limit of this expression as n → ∞ n → ∞ then represents the probability that you will never win. The results showed that the probability increased with the change in bet amount which meant. In probability, independent events are entirely disjointed events: the probability of one occurring (or not) does not influence the others. , and is analogous to the one in Fortune’s Formula: Kelly % = edge/odds. spin MISS HIT HIT=1 HIT>1 *MISS = miss all spins *HIT=1 = hit. One thing that makes roulette so popular with gamblers is the game’s transparency. 00242 = 0. This idea generalizes further for more dice. A simple formula for calculating odds from probability is O = P / (1 - P). 4747 0. Therefore, if E (X) = µ, we have E (X − µ) = E (X) − E (µ) = µ − µ = 0. Unit 8 Counting, permutations, and combinations. The numerical values are written in scientific notations. 7%. The variance is the probability-weighted sum of squared distances from the expected value. Remember, to calculate probability when the question includes the word “and”, you multiply. Your formula (1/N)^x does not express the likelihood of any single outcome. The probability of any x value of a discrete distribution is _____. 7%. The slots numbered 0 and 00 are green. Basic strategies The roulette wheel selection method is used for selecting all the individuals for the next generation. The formula for calculating winning odds is. For example, in Roulette, p = 18 38 = 9 19 ≈ . 1 Number "Straight Up": 1/382 Roulette wheel. Suppose that there are two balls spinning at once, and that it is physically possible for two balls to fit into the same slot. Unit 1 Analyzing categorical data. Many roulette wheels have slots numbered 0, 00, and 1 through 36. Use the Poisson distribution to show that if you play 70 times then the approximate probability you will have won more money than you have lost is. The expected value of a difference is the difference of the expected values, and the expected value of a non-random constant is that constant. The house edge largely depends on which type of roulette game you are playing. expected value of a discrete random variable. The following image shows the probability of a dice landing on a certain value on a given roll: Since the dice is equally likely to land on each value, the probability is the same for each value. In the game, a player may choose to place a bet on a single number, various groupings of numbers, the color red or black,. I presented the famous problem known as the Birthday Paradox here: Birthday Paradox: Combinatorics, Probability, Software, Pick 3 Lottery, Roulette. The probability of each pocket is 1/38, so the probability of this event is 4 x 1/38 = 4/38 = 0.