Coin Flip Probability Simulator


An Optimally Fair Coin Toss Tal Moran Moni Naory Gil Segevz Abstract We address one of the foundational problems in cryptography: the bias of coin-ipping pro-tocols. 00 Anticipating Patterns Discrete random variables and their probability distributions a Rolling dice 1999. The LLN works in polling the same way as in the coin flip experiment. H - HEAD, T - TAIL in Python? Submitted by Anuj Singh, on July 31, 2019 Here, we will be simulating the occurrence coin face i. 1) A coin is tossed 1000 times. Instead, a number cube could be used by specifying that the numbers 1, 2, or 3 represent a hit, the number 4 represents a miss, and the numbers 5 and 6 would be ignored. There are 2 possible outcomes, both of which are equally likely. 49$, then you are saying that there is some underlying random process that generates a real number that, loosely speaking, on average tends to be "close" to $0. I have to write some code in Matlab that simulates tossing a coin 150 times. (a) Interpret this probability. c) The probability the uniform will have the same-coloured shorts and shirt is 6 2 or 3 1. If you have a computer, you can simulate coin toss probability with different numbers of coin tosses, the result might be a table like this. Use the basic rules of probability to solve probability problems. The graph that appears "pretends" that after each toss of the coin, you recorded the percent of the tosses that were heads. If you toss a coin, it will come up a head or a tail. Toss a coin twice. It is accepted that the chance of either result occurring is 50-50, and should you flip a coin 100 times, it will land on heads 50 times, and tails 50 times. We sought to provide evidence that the toss of a coin can be. One way to do that in Java is to use the Math. This includes a random number generator, the use of > , < , and = operations with number assignments. Even if we were to simulate this experiment using a computer programme capable of generating many calculations a second it would not be possible. Problem: A coin is biased so that it has 60% chance of landing on heads. 999023438) ^ #attempts. How to similuate a coin flip with probablility p. Includes home and away, bye weeks, bowl schedules, and printable schedules. The probability of event A and B, getting heads on the first and second toss is 1/4. Probability Theory on Coin Toss Space 1 Finite Probability Spaces 2 Random Variables, Distributions, and Expectations 3 Conditional Expectations. The probability for flipping r heads in N coins has exactly the same form as above, if one notes that (1/2) is the probability to flip a head, and (1/2) is the probability to flip a tail (i. We will use the spreadsheetCoin Flip. That may not be a power of 2, but there is still a simple. Not a precise solution, but good enough for many purposes: Flip the coin a large number of times, interpret the result as number in base 2, and take it modulo 6. Method 1 (Naive) A Naive approach is to store the value of factorial in dp[] array and call it directly whenever it is required. Here is the problem: You toss n coins, each showing heads with probability p, independently of other tosses. This survey article is an introduction to a class of stochastic processes called Lévy processes. The results are shown in the tables below: Color of Marble Number of Times Rolled Blue 12 Green 18 Yellow 20 Heads Tails 30 20 Using Cathy's simulation, what is the probability of pulling a blue marble and the coin landing tails up?. You can explore the entire run of coin tosses by moving the slider. Fair Coin Model(See Example 2 above): Flip a fair coin and observe the side that faces up. There’s only one way for it to land on heads, so the probability is ½. Thus, the simulation suggests that there is a 1. The table below shows the results after Sunil tossed the coin 20 times. 021128451380552. Simulate the family having children for 10 repetitions. 50 probability of flipping heads) and a win must include a streak of 4 consecutive heads at any point. Suppose that we toss three coins. The graphic above shows that the probability ranges from about a 20 percent chance of hitting an opponent's ship when you pick a spot in the center of the board to 8 percent in the corner. Flip the three coins at the same time and recorder the number of heads that are revealed; that is 0,1,2, or 3 heads. A simulation of coin tosses. Land the coin on the side. This example shows using the Binomial distribution to predict the probability of heads and tails when throwing a coin. Toggle Main Navigation Or if you just want to simulate the number of 0's or 1's. A random variable is said to have a Binomial Distribution if it is the result of recording the number of successes in n independent Bernoulli trials. Assuming you can toss 100 coins, count the number of heads and record the outcome at one coin toss per second, it shouldn’t take you more than 4. If you do an internet search for "probability of k heads in a row" or "probability of runs in coin toss", you will find many solutions to this problem. Say we’re trying to simulate an unfair coin that we know only lands heads 20% of the time. I flip a coin and it comes up heads. The number of flips (n), the number of heads, the number of tails, the difference between the number of heads and the number of tails, and the proportion of heads are all recorded and displayed. We take a coin from the pile and flip it once; what is the probability of flipping heads? (I. There are three urns. ) the probability that a coin flip will result in heads (set to a default of 0. ” Now I flip a coin ten times, and ten times in a row it comes up heads. Simulating a Biased Coin With a Fair One. The probability of flipping four coins and getting four “heads” is 1 16. Use the beginning portion of the following Brian Aspinall video, Coding a Coin Flipper. Coin Flipper. Edit the code to simulate a probability experiment that involves the fraction 1/3 3. Online virtual coin toss simulation app. In a sport like football, there is a coin toss at the start of the game. Decide if a specified model is consistent with results from a given data-generating process, e. Coin toss, Toss Coin, Cricket Toss Coin, Sports Toss coin, Selection Toss Coin flip a coin coin toss coinflip heads and tails coin online coin flip heads tails coin virtual coin flip flipa heads and tails coin flip simulator coin sorter flip tails online coin toss coin toss simulator coin toss game spinning coin flip a coin for me heads tails. I am trying a simple toin coss simulation, of say 200 coin tosses. Introduction. ” Or “flip a coin. I flip a coin and it comes up heads. Models: We could simulate this even with several types of models. Suppose you want to test this. Here is the problem: You toss n coins, each showing heads with probability p, independently of other tosses. The Coin Toss Simulation task simulates the tossing of a specified number of coins. Here's a seemingly simple problem. In your brown bag you will find: 3 coins 2 dice. I am new to R, I found the theoretical answer but need to learn how to use R for simulation. With an honest coin, the chances of winning or losing are 50% and consequently, coin flipping is used to decide such momentous events like who kicks off in a football game. NFL Week 15 Playoff Implications: The Chances A Coin Flip Will Decide The Postseason. Spin the spinner and tally the results at MathPlayground. * * Coin objects simulate a coin that, when tossed, has an equal * probability of turning up heads or tails. The distribution of the length of Bob's games is shown in the upper histogram. You can easily input the data you want and simulate it then view the probability and credible interval as well. Right now, it says that we have a 50% probability of getting heads. Coin Toss: Simulation of a coin toss allowing the user to input the number of flips. Suppose you want to test this. This is approximately true in reality: about 51% of newborns are male. We can adjust for this by adding an argument called prob, which provides a vector of two probability weights. Coins and Probability Trees Probability using Probability Trees. To make the dilemma of gambler’s ruin a little easier to understand imagine coin flipping with a friend. You can explore the entire run of coin tosses by moving the slider. The table below shows the results after Sunil tossed the coin 20 times. In a nutshell, students flip two coins for six different traits. Simulating a Biased Coin With a Fair One. 4$ and standard deviation $0. Suppose the proba-bility of picking the rst coin is r and the probability of picking the second coin is 1 r. General Tools. Coin toss probability. In brief (since this is a course in algorithms, not probability and statistics), the guiding principle of inferential statistics is that a random sample tends to exhibit the same properties as the. Before you toss coins, roll dice, pick marbles, spin spinners, or draw cards, you need to know how to access the commands at the bottom of the TI-84 Plus Probability Simulation screen, how to seed the random number generator, and what the ESC command does. A single coin flip is an example of an experiment with a binary outcome. coin turned up heads or not: stating this formally, we have P (A|C) = P (A). on row 15 I have cells with =RANDBETWEEN(0,1) to simulate 200 coin tosses across and have this running down 400 rows for 400 simulations. Quickly generate a random dice roll for gambling, roleplaying, or just making a choice. Plinko and the Binomial Distribution A Bernoulli trial is an experiment that results in a success with probability p and a failure with probability 1-p. You can explore the entire run of coin tosses by moving the slider. For the recorded sequence, compute the proportion of the flips which immediately follow a H that result in H. I am trying to better understand the results of logistic regression models and I wanted to apply a logistic regression model on a trivial "fair" coin flip simulation example. Each coin that shows tails is tossed again (once more). Similarly, a board game that has either a spinner or dice deals with the chance of a player either landing on a specific color or rolling either an even or odd number. 5 # Our anticipated probability of a heads. randrange (2). Since the outcome of flipping a coin is independent for each flip, the probability of a head or tail is always 0. Calculate the experimental probabilities. The probability of heads is 0. True or False - The probability of getting heads when flipping a coin is 0. One coin will toss. The time it takes for half of the remaining pennies to be removed is called the half-life. The Probability Simulation application on the TI-84 Plus graphing calculator can simulate tossing from one to three coins at a time. To simulate a dice, with coin toss, we will need to discard 2 M % 6 = r values. " Simulate tossing three coins 10,000 times in R. First series of tosses Second series. Probability. What's the probability of getting at least one head in the course of 5 coin tosses? What's the probability of getting precisely three heads? But what if we failed to discover this formula? Simulation comes to our rescue! Try this yourself. As such, we will build a quick app to. You can use the Coin Tossing manipulative to explore many different chance processes. Stop Dying in Your Martian Simulator. With an honest coin, the chances of winning or losing are 50% and consequently, coin flipping is used to decide such momentous events like who kicks off in a football game. Choose a coin from the dropdown menu at the top of the page and choose the coin you would like to flip. to take by flipping a fair coin Thus, with each computational path, we can associate the probability of taking this path. We can use R to simulate an experiment of ipping a coin a number of times and compare our results with the theoretical probability. 5 or 1/2, as is the theoretical probability of landing on tails. That was flip number 123,435,929 Flip again? Color The Coin! Share The Coin!. I start off with the probability calculations, then run the simulation. Learn more about probability. In this case, the probability of flipping a head or a tail is 1/2. A Bayesian inference could work like this: Let's say we are playing a coin flipping game. Toss results can be viewed as a list of individual outcomes, ratios, or table. A sequence of consecutive events is also called a "run" of events. We can use these to simulate real-life situations. By "fair", we usually mean that it has a 50% chance of landing heads (or "H" for short) and 50% change of landing tail (or "T"). How did ipping one coin versus 20 coins a ect our results in the previous experiment? Probability 13/26. Here are the broad strokes of their research: If the coin is tossed and caught, it has about a 51% chance of landing on the same face it was launched. We start with a simple illustration. You can explore the entire run of coin tosses by moving the slider. Key words: coin toss, probability of heads, rigid body, dynamics equations 1. I am doing a coin toss simulation, simple enough (below is my code) but I want to add one more step to it and not sure how do I go about it: If I get Heads, I stop, but if I get a Tail, I toss again, if I get a head I stop, but again if I get a tail I toss againI keep tossing until I get a head, then I add up all the times I get a head and all the tails. Internet interactive exploration of experimental and theoretical probabilities (coin tossing and spinner) 3. Which outcome is more likely to occur? Outcome1 or Outcome2? Use fractions to explain your reasoning. I am trying to better understand the results of logistic regression models and I wanted to apply a logistic regression model on a trivial "fair" coin flip simulation example. The theoretical probability is what you expect to happen, but it isn't always what actually happens. olette I have most of the code down, just this last part where I need to report the total number of heads and tails. A = first toss is a head, B = second toss is a head. Let’s first solve this and then confirm our calculated probability by simulating 500 dice rolls with a spreadsheet! In this post, we will focus on understanding basic probability concepts and then discover how with spreadsheets, we can actually see whether our calculated … Continue reading "Probabilities & Dice Roll Simulations in Spreadsheets". Last time we talked about independence of a pair of outcomes, but we can easily go on and talk about independence of a longer sequence of outcomes. The default is set to 5. Since the rows are assumed to be independent, you can then compute the probability of seeing the event in any of the 12 rows. The project below involves using a computer simulator to virtually flip multiple coins. An example of this would be a coin toss. What's not so obvious is that the probability of a coin that has come up heads for the past 19 flips also landing heads up on the 20th throw is also 50 per cent. I flip a coin and it comes up heads. Purpose : The purpose of this program is to simulate the tossing of a coin or coins and to display the results in the form of a graph with the probability of heads versus the number of trials. Coin Flip (Python Newbie) I need to write a python program that will flip a coin 100 times and then tell how many times tails and heads were flipped. Flip a fair coin four times and record the results in order. This generator helps you play any offline dice games without the need to carry around anything but your phone. ) the number of games to be played, and 2. You flip a coin. An ideal unbiased coin might not correctly model a real coin, which could be biased slightly one way or another. However, there are still a number of easy ways to simulate this type of experiment. Each player was given $25 (of real money), and 30 minutes in which to place bets on the toss of a loaded coin, which had a 60 per cent chance of coming up heads. Coin toss probability. The probability for. Record your actual ratios after 4, 16, 40 and 100 tosses in the data table provided. INTRODUCTION Coin tossing has been around for as long as coins existed. Every flip of the coin has an “independent probability“, meaning that the probability that the coin will come up heads or tails is only affected by the toss of the coin itself. Key words: coin toss, probability of heads, rigid body, dynamics equations 1. A Monte Carlo simulation is a method of estimating the value of an unknown quantity by making use of the principles of inferential statistics. 2 Author’s Biographical Sketch Dr. Since the coin is fair, each flip has an equal chance of coming up heads or tails, so all 16 possible outcomes tabulated above are equally probable. Then use the applet to test your prediction. A common example is a (fair) raffle in which each ticket has an equally likely chance of winning. If two coins are flipped, it can be two heads, two tails, or a head and a tail. Each outcome has a fixed probability, the same from trial to trial. H - HEAD, T – TAIL in Python? Submitted by Anuj Singh, on July 31, 2019 Here, we will be simulating the occurrence coin face i. This tutorial covers the code for the coin flip simulator that you will use to answer question in HW 1. We express probability as a number between 0 and 1. But over the course of 100 tosses, the probability of getting heads is way more than 50%. It is accepted that the chance of either result occurring is 50-50, and should you flip a coin 100 times, it will land on heads 50 times, and tails 50 times. A single flip of a coin has an uncertain outcome. Again, we start with HH as the target. Lesson 10: Using Simulation to Estimate a Probability Student Outcomes Students learn simulation as a method for estimating probabilities that can be used for problems in which it is difficult to collect data by experimentation or by developing theoretical probability models. In this probability lesson, students use the graphing calculator to simulate tossing a coin. Even young kids can start to understand the difference between a need and a want. If we have a biased coin, i. Two gamblers, A and B, are betting on the tosses of a fair coin. And what it does is it allows us to simulate many coin flips and figure out the proportion that are heads. The coin will be tossed until your desired run in heads is achieved. You can use the Coin Tossing manipulative to explore many different chance processes. An example would be flipping a coin. sample() use the sample() function to sample from a vector of ones (heads) and zeros (tails). It is about physics, the coin, and how the "tosser" is actually throwing it. Are you guaranteed to get four “heads” twice? Explain. That pleasant surprise we feel when our prediction comes true (after some practice) is associated with one bit of surprisal, as defined above. Just copy and paste the code and you're good to go! import random. It uses mathematical notation in a familiar context of flipping coins. I ditto pex. Let's begin by calculating probabilities associated with this game. In a sport like football, there is a coin toss at the start of the game. Start with your program for the Coin Toss Simulation and adjust it to make it about Rolling a 6-sided Die. If faces is a single integer, say 2, a sequence of integers from 1 to faces will be used to denote the faces of a coin; otherwise this character vector just gives the names of each face. This is interpreted as follows: the first child is a girl, the second child is a boy, and the third child is a girl. A coin-tossing simulation By inspecting the histogram of the uniformly distributed random numbers, observe that half of the values are between 0 and 0. It is measured between 0 and 1, inclusive. Coin Toss Probability Calculator. When tossing only one coin at a time, the application keeps track of the number of heads and tails that occur as the coin is repeatedly tossed. Coin Tossing Games Age 14 to 16 Challenge Level: You and I play a game involving successive throws of a fair coin. Coin-ipping protocols allow mutually distrustful parties to generate a common unbiased random bit, guaranteeing that even if one of the parties is malicious, it cannot signi cantly. Using the Probability Simulation program in the TI-84 to simulate a coin toss experiment. Then compare the Actual Ratios with the Predicted Ratios. Coin Tossing Games Set by Dr Susan Pitts, University of Cambridge Statistics Laboratory, for the Summer 1997 NRICH Maths Club Video-conference. Make a Fair Coin from a Biased Coin January 3rd, 2018. More about that in the next bullet point. 6$ represent probabilities, not the value of a random variable. Classical methods are used for games of chance, such as flipping coins, rolling dice, spinning spinners, roulette wheels, or lotteries. Does it simulate the toss of a unbalanced coin with a probability of Heads that is not 0. This function provides a simulation to the process of flipping coins and computes the frequencies for `heads' and `tails'. Can't figure out the answer? ☜ Can't decide? ☜ Do you want fate to decide for you? ☜ Well, then you just have to download the application and find out the answer of fate - throwing a coin (Yes / No)! ☜ Ask your question to the coin; Find out what the probability of a positive or negative result; Cast lots with your friends! Ask fate at any time. The experimental probability of landing on heads is It actually landed on heads more times than we expected. This is shown with the SHAZAM commands:. But of course there are more thrilling possibilities to use a tossed mint. But how can we obtain a probability of exactly 1/3. For the above experiment there were. Flip the coin twice. Use the basic rules of probability to solve probability problems. The program should call a separate function flip()that takes no arguments and returns 0 for tails and 1 for heads. The results for each trial is reflected in a table. 999023438 ^ 710 = 0. The time it takes for half of the remaining pennies to be removed is called the half-life. If heads comes up less than 4000 or more than 6000 times, you die. Internet interactive exploration of experimental and theoretical probabilities (coin tossing and spinner) 3. The Coin Toss Probability Calculator an online tool which shows Coin Toss Probability for the given input. How to similuate a coin flip with probablility p. Rakhshan and H. 2598960 totalshouldbe = 2598960 probabilities = Columns 1 through 3 0. To simulate one billion coin flips, this script took about 6 minutes to run on a original Microsoft Surface Pro, utilizing all cores. What is a simulation? a) Simulation is the process of creating dashboards in excel. 2 CHAPTER 1. I've found a reasonable negative filter is. VCTs on this site are intended to be random, and are generated as follows: Each minute, a random number is fetched (via HTTP) from the web site random. The possibility of winning on each coin flip is 50% and the possibility of losing is 50%. I'm sure there is a way to determine this statistically, but I don’t know how to do that, so, being new to Ruby, I wrote a little Ruby simulation program — essentially a Monte Carlo simulation of the problem — to find the answer. Choose a coin from the dropdown menu at the top of the page and choose the coin you would like to flip. Enter and Run the code at cscircles. The formula to determine probability is dividing the number of ways an event can occur by the total possible outcomes. Flip the coin twice. the coins can have any probability of landing heads between 0 and 1). Asks the user for the chance of a coin landing on heads, the number of trials per experiment, and the number of experiments. The binomial distribution tells us the total number of outcomes of a particular kind (boy birth, coin landing heads, other binary outcomes) given a number of trials and the probability of "success". Flipping coins This exercise requires the bernoulli object from the scipy. Creates an animated plot shsowing results from coin flips and the resulting converence in the probability of a head as the number of flips goes large. When a coin is tossed, there lie two possible outcomes i. What would you tell the student?. Questions are posed regarding the expected. • Include a title. Because we expect that heads is as likely to come up as tails, we model this experiment with the probability distribution specified by S = \{H, T\}, P(H) =. Any ideas on how to simulate a coin flip? Heads or Tails randomly ganerated each time you want a 50-50 chance at something. Quantity A: The probability of getting more heads than tails Quantity B: 1/2. Say we're trying to simulate an unfair coin that we know only lands heads 20% of the time. Predicting a coin toss. However, there are still a number of easy ways to simulate this type of experiment. To explore the probability of getting heads in a coin toss, run an experiment of 30 trials with the partner sitting next to you. You have two coins. INTRODUCTION Coin tossing has been around for as long as coins existed. Now, if you get Sam, there is 0. I start off with the probability calculations, then run the simulation. Make a Fair Coin from a Biased Coin January 3rd, 2018. If you repeat this 100-flip experiment over and over, the relative frequency should vary around 0. For example, given 5 trials per experiment and 20 experiments, the program will flip a coin 5 times and record the results 20 times. If faces is a single integer, say 2, a sequence of integers from 1 to faces will be used to denote the faces of a coin; otherwise this character vector just gives the names of each face. Let us learn more about coin toss probability formula. This form allows you to flip virtual coins based on true randomness, which for many purposes is better than the pseudo-random number algorithms typically used in computer programs. sample() use the sample() function to sample from a vector of ones (heads) and zeros (tails). It's easy to use such a coin to obtain probabilities of the form m/2^n (1/4, 7/8, 5/16, etcetera) by flipping a coin n times. Simulation provides an estimate for the probability that a family of three children would have three boys or three girls by performing three tosses of a fair coin many times. We take a coin from the pile and flip it once; what is the probability of flipping heads? (I. Heads are dominant and tails are recessive. That means that if we flip a coin 100 times, we will get exactly 50 heads. Internet interactive exploration of experimental and theoretical probabilities (coin tossing and spinner) 3. For the old java version, click here ; For the Spanish version, click here ; For the German version, click here; To. Coin flipping is often used as an unbiased way to call sports games, settle personal bets and disputes, or for many other reasons that you would need to decide something on a 50% basis. You want to know the probability of the coin landing on heads. Toggle Main Navigation Or if you just want to simulate the number of 0's or 1's. Instant online coin toss. Toss both coins together to simulate gamete formation (meiosis) and fertilization. You flip a coin. We'll say the particular trial will include 10 consecutive tosses of a fair coin (. 5 If you have a computer, you can simulate coin toss probability with different numbers of coin tosses, the result might be a table like this. It has two arguments and two options. We can adjust for this by adding an argument called prob, which provides a vector of two probability weights. Before I went looking for answers, I wrote a probability simulator to try and figure it out myself. See the included CSV for the computed data. Byju's Coin Toss Probability Calculator is a tool which makes calculations very simple and interesting. Each time you toss the remaining pennies, about half of them are removed. Now let's flip a coin twice in succession. Re: Coin Toss Simulation try this: n <- 3 data. On a mission to transform learning through computational thinking, Shodor is dedicated to the reform and improvement of mathematics and science education through student enrichment. The simplest example is a coin flip. The coin may land and stay on the edge, but this event is so enormously unlikely as to be considered impossible and be disregarded. Online virtual coin toss simulation app. This function provides a simulation to the process of flipping coins and computes the frequencies for heads and tails. Simulation v2. Below is some sample code in R to simulate a fair coin toss in R using the sample function. Re: Coin Toss Simulation try this: n <- 3 data. 5 # Our anticipated probability of a heads. Each sequence of three tosses is called a trial. Each coin that shows tails is tossed again (once more). Starting out with Java: From control structures through objects Chapter 6 Programming Challenges Coin Toss… by kakradetome 6. If you toss a coin ten times, what is the probability of getting three or more “heads” in a row? If an airline overbooks a certain flight, what is the chance more passengers show up than the airplane has seats for? When 67 people get cancer in 250 homes in a small town, could that be due to chance alone, or is polluted. Define X as the random variable "number of heads showing when three coins are tossed. By "fair", we usually mean that it has a 50% chance of landing heads (or "H" for short) and 50% change of landing tail (or "T"). On a mission to transform learning through computational thinking, Shodor is dedicated to the reform and improvement of mathematics and science education through student enrichment. a coin that comes up heads with a probability not equal to \(\frac{1}{2}\), how can we simulate a fair coin? The naive way would be throwing the coin 100 times and if the coin came up heads 60 times, the bias would be 0. 0 X 1022 centuries to generate every permutation. A coin produced by this machine is tossed repeatedly, with successive tosses assumed to be independent. If a fair coin (one with probability of heads equal to 1/2) is flipped a large number of times, the proportion of heads will tend to get closer to 1/2 as the number of tosses increases. Once the toss method has been * called for the first time, however, either heads or * tails (but not. These are two possible outcomes of a toss of a coin. In this activity, you will explore some ideas of probability by using Excel to simulate tossing a coin and throwing a free throw in basketball. Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. An example of this would be a coin toss. Online virtual coin toss simulation app. Self-reflection. Predicting a coin toss. Most of the worksheets on this page align with the Common Core Standards. Gamblers Take Note: The Odds in a Coin Flip Aren’t Quite 50/50 And the odds of spinning a penny are even more skewed in one direction, but which way? Flipping a coin isn't as fair as it seems. You can use the Coin Tossing manipulative to explore many different chance processes. Record your actual ratios after 4, 16, 40 and 100 tosses in the data table provided. The distribution drops off much more quickly than for Bob's games. If this world were reality, our simulation will compute the correct probability of each possible betting outcome. If you toss a fair coin 20 times, what is the chance that you get a run of at least 5 heads at any time? Easy to solve by simulation, and I know the answer already, but I'm trying to create a spreadsheet where I can enter the number of tosses and the length of the run required and get the probability. Some rules that may be useful:. Example 1: A Coin-Flipping Game Suppose you are Offered a chance to play a game in which you repeatedly flip unbiased coin until the difference between the number Of heads tossed and the number of tails tossed is three.