# Simulate Biased Coin With Fair Coin

Using a fair coin, you can simulate a coin with any desired bias. How to Simulate a Fair Coin Toss With a Biased Coin. Algorithm: Let us define an event. T Moreover, since we randomly pick the coin for each ip, all sequences are equally likely. The sample space of a fair coin ip is fH;Tg. Create a model to simulate this biased coin. # However, in this discussion it is worth noting that there is # a somewhat useful statistic that we can produce to compare # the likelihoods of the fair coin hypothesis with that # of the 2/3 biased hypothesis. In reality this is not the case. Produced by Zcash Company, Zcash is the. How can you use it to simulate a fair coin, i. You don't know the bias of the coin, and yet you have to use it to simulate any probability. Simulate 8,000 trials of flipping a fair coin 20 times and 2,000 trials of flipping a biased coin 20 times. ) Given that the first coin has shown head, the conditional probability that the second coin is fair, is. If we see a coin tossed twice and we see 2 heads, we'd like to know if the coin is fair, or at least to be able to determine the probability that the coin is fair. How could you use this coin to simulate the 50/50 odds of a fair coin flip? Hint. The NBA season is just entering the second week, and we've already had plenty of important developments. One way to determine which is the biased coin is to. After 500 flips, with 400 heads, the individual. A completely biased coin with P (H) = 1 has entropy H(x)=1log1 0log0 = 0 bits, where we have used 0log0 = 0 (which is true in the limit lim p0 p log p =0). Biased coins Run an experiment with a fair coin and a biased coin. 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. Two coins are given. “a fair game”: in repeated play you expect to win as much as you observed in repeated ﬂips of a biased coin (with probability p of coming up heads). You are given a biased coin with some unknown chance 0. So the chances of getting a fair coin after you are through the first stage is only 1/3 But if you choose the bias after the first two trials, then the chance of a fair coin is 1/2. 2019s Most Useful Bit-coin Casino USA — (100% Actual Testimonials ) – Best online crypto casino. If we have a biased coin (i. Run the code above several times, noting the p-values for the fair and biased coins. In this language, the question becomes how many steps does it take on average to. Theoretical and experimental probability: Coin flips and die rolls. In this post, we will discuss how to generate fair results from a biased coin which prefer one side of the coin over another, and returns TAILS with p probability and HEADS with (1-p) probability where p != (1-p). In order to ascertain which type of coin we have,. In a biased coin , the probabilty of heads is 0. How can you use it to simulate a fair coin, i. An unfair coin with Pr[H] = 2/3 is flipped. Flip the coin a single time or make it the best of 3, 5, 7, 9 or 101 flips. (a) On the probability scale below, mark with a cross (×) the probability that he gets a head. With the above definition, a fair coin is one for which Bias = 0. To continue with your YouTube experience, please fill out the form below. I submit that such a bias is necessary for random() to funtion correctly as a simulator of the real-world bias acting on the tossing of a single coin. An event is defined as. 5 the less likely we are to get a result. Usually it suffices to simply nominate one outcome heads, the other tails, and flip the coin to decide, but what if one party to. Two coins are given. Write a new function that returns 0 and 1 with 50% probability each. Game B consists of playing with two biased coins. I want to simulate a coin toss game in which 10 coins are tossed. H - HEAD, T - TAIL in Python? Submitted by Anuj Singh, on July 31, 2019 Here, we will be simulating the occurrence coin face i. A wide variety of animal simulate rides options are available to you,. I will flip it repeatedly, and tell you the result. bioalgorithms. Suppose we have a coin that "tries" to be fair. Toss a coin twice. Be Creative. Your proposed computation makes no sense because $0. Save them as fair_flips and biased_flips, respectively. Have you ever flipped a coin as a way of deciding something with another person? The answer is probably yes. 2019s Most Useful Bit-coin Casino USA — (100% Actual Testimonials ) – Best online crypto casino. Suppose all you have is a biased coin that when tossed comes up heads 60% of the time and tails 40% of the time. Introduction: Coin flipping is based on probability. I want to simulate a coin toss game in which 10 coins are tossed. Interview question for Software Engineer. (B) I tossed the coin only 10 times, and even if the coin is fair there is a good chance of tossing a head 6 times. Algorithm: Let us define an event. If the results match, start over, forgetting both results. John von Neumann gave the following procedure: Toss the coin twice. Injuries have already afflicted Zion Williamson, Marvin Bagley, Jrue Holiday, Jeremy Lamb, Nicolas Batum and others. Given an unfair coin, where probability of heads coming up is P and tails is (1-P). Offline Paper Wallet; Since all your coins will have a key in the blockchain, for using the coin, you need to remember the key. My initial idea is that we need to choose appropriate. consists of a single fair coin with the outcome heads corresponding to one state and tails to the other state. Wikipedia also explains the solution to this problem. The art of using a coin toss to simulate the results of an experiment is one form of simulation. Simulate a random coin flip or coin toss to make those hard 50/50 decisions from your mobile Android, iPhone, or Blackberry phone or desktop web browser. In statistics, the question of checking whether a coin is fair is one whose importance lies, firstly, in providing a simple problem on which to illustrate basic ideas of statistical inference and, secondly, in providing a simple problem that can be used to compare various competing methods of statistical inference, including decision theory. Sample of coins will appear if number of repetitions is 20 or less and the number of tosses is at most 325. I suppose that's what they want for a), but one for. But different sequences of random coin tosses give various results. Hello, I have a question about achieving an unbias coin with a bias coin flip for N = 1000 tosses, for a set of I have written code for unknown bias probabilities p = [ 0. One coin has two heads, another coin has two tails, and a third coin is fair. So, if the coin is fair, it has a 50% chance of landing on heads. \probability" is intended to be the probability that the corresponding outcome occurs (see Section 4. In section 2, the theory of the deterministic torque-free coin motion in gravitational field is presented. Flip up to twn coins simultaneously in multiple trials Simulated Experimental Coin-Toss Data. A fair die can obviously simulate a fair coin, so it suffices to show that a fair coin can simulate a biased one. In this simulation, a biased coin assignment (ξ = 0. 2019s Most Useful Bit-coin Casino USA — (100% Actual Testimonials ) – Best online crypto casino. Solution: (We'll worry about simulating the biased coin with the fair coin later, in the Extensions section) The key to finding a solution is to realize that you don't have to flip the biased coin just once, and that you don't have to consider each outcome of each flip. Even if a question doesn’t invoke the coin toss, the way we approach a coin toss problem can carry over to other types of probability questions. I used C++ language for this simulation. But if we got 502 heads, or 497, say, we would not suspect that the coin is biased: this could very easily happen "by chance". Suppose that you're given a fair coin and you would like to simulate the probability distribution of repeatedly flipping a fair (six-sided) die. Hidden Markov Models. H - HEAD, T - TAIL. Complete the TODO in ee201_roller_tb and simulate. Explanation: Whenever we pick the coin biased with p = 1, we always get Heads. identity of a random variable with distribution P (x). Some dice may be biased. One over two is a half, or 50 per cent. Answer: We have one random variable C which denotes the coin chosen (1, 2 and 3, with 1 being the fair coin), two random variables F1 and F2 denoting the face that comes up for the ﬁrst. Each toss is independent of the last. A flipped coin is biased to land on the same side it. distribution of longest runs is not greatly affected by one coin toss unless n is very small, the implication of (2) is that for n tosses of a fair coin the longest run of heads or tails, statistically speaking, tends to be about one longer than the longest run of heads alone. Write a program that simulates coin tossing. An ideal unbiased coin might not correctly model a real coin, which could be biased slightly one way or another. This shows. Save them as fair_flips and biased_flips, respectively. Describe a method to do so exactly where the expected number of fair coin flips you use is a fixed number independent of p. Curiously, no matter what kind of bias you're trying to simulate, it takes, on average, just two tosses to carry out the simulation. I will flip it repeatedly, and tell you the result. An event is defined as. As you can see, it’s pretty flat (note the scale on the left), over a million games, the average never moves more than a fraction of a penny away from zero. Each biased coin has probability of a head 4 5. I am trying to plot the pdf of flipping heads when drawing from a bag of biased coins. Click the coin to flip it--or enter a number and click Auto Flip. Modify ee201_roller to simulate flipping a fair coin. Let's return to the coin-tossing experiment. I don't think the coin is fair. Say we’re trying to simulate an unfair coin that we know only lands heads 20% of the time. 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. distribution of longest runs is not greatly affected by one coin toss unless n is very small, the implication of (2) is that for n tosses of a fair coin the longest run of heads or tails, statistically speaking, tends to be about one longer than the longest run of heads alone. In an actual series of coin tosses, we may get more or less than exactly 50% heads. Mitzenmacher and D. This problem was then extended to vary the head/tail probabilities of the given coins and the coin to simulate. Well, that’s it. Posted on September 12, 2013 by Jonathan Mattingly | Comments Off on Making a biased coin fair Jack and Jill want to use a coin to decide who gets the remaining piece of cake. One of the coins is tossed once, resulting in heads. The unbiased coin with even odds In the case of an unbiased (or fair) coin, we expect the probability of a heads to be. "Count line" can be moved by mouse. (Von Neumann gave an algorithm that simulates a fair coin given access to identical biased coins. And if you spin. According to Wikipedia, a fair coin is “a sequence of independent Bernoulli trials with. Which of the following situations: (1) or (2), will yield a higher probability that two of the four tosses are heads assuming iid? (1) Using a "fair" coin for the tosses (probability of head…. b) What do you think E[X] should be. I know the probability of a changeover is 0. Find the probability of 2 heads in 3 tosses. Write a program to simulate a fair coin given two biased coins. To view the results of this simulation, type the name of the object and then use table() to count up the number of heads and tails. 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. p to be determined later. 10) until the ﬁrst Head comes up. My initial idea is that we need to choose appropriate. Since I am interested in the % of heads flipped, not the number, I simulate 500K flips and group the results into buckets of 100, computing the % of heads in each bucket. The solution remains the same. Now this seems like it's impossible. For each toss of the coin the program should print Heads or Tails. Note that if the random variable is equal to 0. And if you spin. With this biased coin, I found the following relative frequency chart and an average run time of 881 flips. However, for this example we will assume that the probability of heads is unknown (maybe the coin is strange in some way or we are testing whether or not the coin is fair). 5 I should get an output of 0 half of the time, and 1 half of the time. Steve: These relatively small changes build up. Create a biased sample of length 100, having as input the coin vector, and as probabilities probs vector of probabilities. Counterintuitive property of coin tosses. How could you use this coin to simulate the 50/50 odds of a fair coin flip? Hint. Since the actual coin being used is fair and there are 13 + 7 = 20 decisive outcomes which do not require one to start over, the probability of (eventually) getting a H. 5 and deviations are hard to detect “with a naked eye”. Does Toss1 simulate the toss of a fair coin? And if the answer is “no:” a. Most coins may not be perfectly fair but their bias is still very close to 0. In order to ascertain which type of coin we have,. Rakhshan and H. 0 Unported License. That is, simulate the biased coin with a fair coin). How can you use a biased coin to make an unbiased decision? That is to say the coin does not give heads or tales with equal probability. What results would make you suspect that a coin is biased? An excellent opportunity for class discussion. a nonnegative parameter which my be adjusted according to how strongly it is. If the results match, start over, forgetting both results. The sim­ plest model. I would like to choose these arbitrarily to achieve an unbias coin for each. Introduction to Simulation Using R A. How could we guess which coin was more likely?. Pishro-Nik 13. If it's a fair coin, the two possible outcomes, heads and tails, occur with equal probability. null hypothesis that p = 0. One is fair: P(heads)=1/2. COIN_SIMULATION is a MATLAB library which looks at ways of simulating or visualizing the results of many tosses of a fair or biased coin. I will give a simple example of maximum likelihood estimation of the probabilities of a biased coin toss. What results would make you suspect that a coin is biased? An excellent opportunity for class discussion. Experimental versus theoretical probability simulation. Rolling dice The probability of getting a number between 1 to 6 on a roll of a die is 1=6 = 0:1666667. We can easily simulate an unfair coin by changing the probability p. Introduction to Simulation Using MATLAB A. Answer To Use A Coin To Simulate Any Probability There is a straightforward method if the probability is a fraction with a power of 2; a fraction that is of the form x /2 n. Write a program to simulate a fair coin given two biased coins. Counterintuitive property of coin tosses. In sport, coins are tossed to decide which end of the ground a team is to defend, or who is going to go into bat ﬂrst. Your proposed computation makes no sense because$0. The probability that the biased coin will land on a tail is 0. Two coins are given. 1, the values of loss from the steady-state distribution of Dn are compared with simulation results, showing good agreement for p=2/3 and n>50. Precisely, what does this mean? In this Lab, let’s simulate tossing a coin and investigate the precise meaning of LLN. How can you use this potentially biased coin to generate an unbiased result? In particular, how can you do this when you don't know what, if any, the coin's bias is?. If you toss a coin, it will come up a head or a tail. But suppose I might have some weird coin. Predicting a coin toss. Rakhshan and H. The Coin Toss Probability Calculator an online tool which shows Coin Toss Probability for the given input. Using a prior. It focuses on developing a program to simulate a sequence of coin tosses as a means of testing the "goodness" of App Inventor's pseudo random number generator (PRNG). So, we have a coin. If you get HT call it Heads. If the coin is biased, based on the information provided, the probability of it landing on heads is 61%. How does the p-value vary for the fair and biased coins? What happens to the confidence intervals if you increase n from 10 to 100?. Introduction to Simulation Using MATLAB A. I am trying to plot the pdf of flipping heads when drawing from a bag of biased coins. Write a program that simulates coin tossing. Here is a game that works. In sport, coins are tossed to decide which end of the ground a team is to defend, or who is going to go into bat ﬂrst. That is if the coin is fair, first flip may give head or tail second flip may give a head or tail so if we flip a coin 2 times we may get 2 heads or 2 tails or one head and one tail. For example, given 5 trials per experiment and 20 experiments, the program will flip a coin 5 times and record the results 20 times. We toss two fair coins simultaneously and independently. 2015 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3. Toss a fair coin three times But what if the coins are biased (land more on one side than another) or choices are not 50/50. The difference is said to be statistically significant. 10,000 Coins 9,999 Fair Coins (H/T) 1 Biased Coin (H/H) Problem 1. In this case where we had 450 heads out of 1000 coin tosses, we can reject the. This is a binomial probability distribution The probability of exactly 2 heads in 50 coin tosses of a fair coin is 1. What results would make you suspect that a coin is biased? An excellent opportunity for class discussion. 75 Suppose either a fair or biased coin was used to generate a sequence of heads & tails. Nonetheless, Grubb. At the start I think it might be fair coin (event A) or it might be a biased coin that comes up heads with probability 3/4 (event B). But if we got 502 heads, or 497, say, we would not suspect that the coin is biased: this could very easily happen "by chance". If we use a coin with the bias specified by q to conduct a coin flip. Suppose that the probability of getting heads on a single toss is p. Toss a coin twice. So the chances of getting a fair coin after you are through the first stage is only 1/3 But if you choose the bias after the first two trials, then the chance of a fair coin is 1/2. Work out an estimate for the number of times the coin will land on a tail. Simulating a Fair Coin with a Biased Coin. You can copy and paste the source code below or you can download from here. Now that we have written our function, let’s play 50,000 games with a fair coin and see what results: P1_win_prob_weighted_coin_game(50000) 0. Well, that’s it. Lets revise the example, such that. Your proposed computation makes no sense because \$0. 2015 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3. use the function rbinom() to draw numbers from a binomial distribution: theta <- 0. This shows. Suppose all you have is. How can you use a biased coin to make an unbiased decision? That is to say the coin does not give heads or tales with equal probability. something like this: def flip(p): '''this function…. Now that we have written our function, let's play 50,000 games with a fair coin and see what results: P1_win_prob_weighted_coin_game(50000) 0. Create a biased sample of length 100, having as input the coin vector, and as probabilities probs vector of probabilities. You can load a die but you can't bias a coin Andrew Gelman∗ and Deborah Nolan† April 26, 2002 Abstract Dice can be loaded—that is, one can easily alter a die so that the probabilities of landing on the six sides are dramatically unequal. Each biased coin has probability of a head 4 5. Hint: By Considering A Sequence Of Pairs Of Flips Of The Possibly Biased Coin, Find An Event That Has Probability Exactly 1/2. We can use the following command. Game B consists of playing with two biased coins. Theoretical and experimental probability: Coin flips and die rolls. We would also expect the odds to be no better than 2-1, meaning for every one dollar we bet, we should expect to get no more than two dollars in return. The following texts comes from wiki: Toss the coin twice. Since the actual coin being used is fair and there are 13 + 7 = 20 decisive outcomes which do not require one to start over, the probability of (eventually) getting a H. The problem again is that all simulations do not result in a desired outcome. Homework 8 (Not Collected) Problem 1. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two heade. A wide variety of animal simulate rides options are available to you,. This paper provides an introduction and overview to mystery values, which are analogues to eigenvalues that arise in the [KWG10] model of secure multiparty computation. According to a Stanford study, even a fair coin is about 51% likely to land on the same face it started on. Thus the prior belief about fairness of the coin is modified to account for the fact that three heads have come up in a row and thus the coin might not be fair. We can use the given biased coin for fair results by making two calls from biased coin instead of one call. This problem was then extended to vary the head/tail probabilities of the given coins and the coin to simulate. Yes, it is a standard solution as mentioned by Sangram Kapre. Adam's interests are in algebra and theoretical computer science. consists of a single fair coin with the outcome heads corresponding to one state and tails to the other state. For example, if you flip a coin 10 times, and it comes up heads every single time, then you might start to form an opinion that the coin is not fair, and that it is biased towards coming up heads- you might begin to believe that the population of all possible flips of this coin contained more heads than tails. Given that he observes 3 heads before the first tails, find the posterior probability that he picked each coin. Flipping a coin. 24 to estimate a probability of 0. I will give a simple example of maximum likelihood estimation of the probabilities of a biased coin toss. The difference is said to be statistically significant. consists of a single fair coin with the outcome heads corresponding to one state and tails to the other state. Well, that’s it. Injuries have already afflicted Zion Williamson, Marvin Bagley, Jrue Holiday, Jeremy Lamb, Nicolas Batum and others. "Suppose all you have is a coin with an unknown bias, but which has a thin enough edge that it always lands head or tails when tossed, and will land on each of them some of the time. You have two coins in front of you. ! RandomInteger[5] gives an integer from 0 to 5. Even if a question doesn’t invoke the coin toss, the way we approach a coin toss problem can carry over to other types of probability questions. What is the probability of getting exactly 3 Heads in five consecutive flips. John has two coins: one fair coin and one biased coin which lands heads with probability 3/4. A fair coin would be one that is equally likely to land on either heads or tails when tossed - on any given toss, you have exactly a 50% chance of getting either heads or tails. “a fair game”: in repeated play you expect to win as much as you observed in repeated ﬂips of a biased coin (with probability p of coming up heads). 5, then it can be established that the coin is a fair coin. Practice Questions STAT433, Fall 2019 Inverse Transform Method 1. "On average", we would expect to get 500 heads. Two coins are given. Hi everyone. Introduction to Simulation Using R A. Flipping a coin. Alternatively, you can simulate coin flips online and build up a graph of results and p-values. The coin is. Sunday, March 29, 2009. So, if you are looking for the best Electroneum wallet to store your preferred crypto coins in, your search ends here. The expected number of tosses you need to do this is just two! Preliminaries: let's count heads as 1, tails as 0, and we'll write the desired probability of heads in our simulated biased coin as the binary fraction `p = 0. That’s the only principle that we would be using. 5, generate fair results from the biased coin. R: Simulate flipping three fair coins and counting the number of heads X Use your simulation to estimate P(X = 1) an d E(X). Provide screen shots of important blocks and describe how you used them to solve certain programming problems. 1) The mathematical theory of probability assumes that we have a well defined repeatable (in principle) experiment, which has as its outcome a set of well defined, mutually exclusive, events. Homework 8 (Not Collected) Problem 1. 1 85 Simulating ﬂipping a coin Example. This probability is slightly higher than our presupposition of the probability that the coin was fair corresponding to the uniform prior distribution, which was 10%. Updating with evidence 50 xp Updating 50 xp Updating with simulation 100 xp. Simulate 8,000 trials of flipping a fair coin 20 times and 2,000 trials of flipping a biased coin 20 times. Exercise 7 Compare the sum of values in fair_coin and biased_coin. PyMC3 is alpha software that is intended to improve on PyMC2 in the following ways (from GitHub page): Intuitive model specification syntax, for example, x ~ N(0,1) translates to x = Normal(0,1) Powerful sampling algorithms such as Hamiltonian Monte Carlo. Working on some problems using fair coins to simulate biased coins and vice versa. In general, it is assumed that a PTM has a fair coin. Lyzashun can be employed to generate a desired probability distribution even with an unfair coin, as long as the probability of the coin landing on heads is known. Most Settings editors in the Probability Simulation. The obverse (principal side) of a coin typically features a symbol intended to be evocative of stately power, such as the head of a monarch or well-known state representative. R: Simulate flipping three fair coins and counting the number of heads X Use your simulation to estimate P(X = 1) an d E(X). For example, a simple flip of a coin to determine a decision can be manipulated by a person if it is replaced by a coin with. Byju's Coin Toss Probability Calculator is a tool which makes calculations very simple and interesting. (I don't know about the irrational coins case). Examples: In the experiment of flipping a coin, the mutually exclusive outcomes are the coin landing either heads up or tails up. It turns out that Bayesian statistics (and possibly any statistics) can't answer that question. How can you ensure that decisions made with the coin do have a 50:50 chance?. Without doing any math, which do you now think is more likely- that the coin is fair, or that the coin is biased?. expect to observe 450 heads out of 1000 tosses if the coin was fair. But perhaps you're thinking, "why are you telling me to make 10 numbers when I only have to check until I find a group of four consecutive heads?" For one thing, if you're just flipping 10 coins each time, it really doesn't matter because you'll make the computer flip at most 6, and on average 3, extra coins in each trial. The other coin is tossed three times, resulting in two heads. Any ideas on how to simulate a coin flip? Heads or Tails randomly ganerated each time you want a 50-50 chance at something. See Coin Tossing: the Hydrogen Atom of Probability for a simple way to do it. The Coin Toss Probability Calculator an online tool which shows Coin Toss Probability for the given input. An unfair coin with Pr[H] = 2/3 is flipped. And in any case, Gritchka's writeup here explains how to use an unfair coin to simulate a fair one. "Count line" can be moved by mouse. Why not? b. I continue flipping the coin (flip #2, 3, etc. Let's return to the coin-tossing experiment. But perhaps you're thinking, "why are you telling me to make 10 numbers when I only have to check until I find a group of four consecutive heads?" For one thing, if you're just flipping 10 coins each time, it really doesn't matter because you'll make the computer flip at most 6, and on average 3, extra coins in each trial. Models which can be used to explain the results of hidden coin tossing experiments. 0 Unported License. If it's a fair coin, the two possible outcomes, heads and tails, occur with equal probability. Hypothesis Testing 1 Hypothesis Testing Much of classical statistics is concerned with the idea of hypothesis testing. But different sequences of random coin tosses give various results. Now that we have written our function, let's play 50,000 games with a fair coin and see what results: P1_win_prob_weighted_coin_game(50000) 0. John has two coins: one fair coin and one biased coin which lands heads with probability 3/4. Massachusetts Institute of Technology. Flip a coin n times and record the result of each toss. The simulation below computes expectations for the fair and the biased coins simultaneously along the same path, by importance weighting each outcome by the ratio of the fair or biased respective probabilities and the weights used to generate the path. We have one of these coins but do not know whether it is a fair coin or a biased one. How can you use it to simulate a fair coin, i. But suppose the coin is biased so that heads occur only 1/4 of the time, and tails occur 3/4. Coin collector An individual who accumulates coins in a methodical manner. To be more specific, if we flip the coin n times, and have X heads, then the probability of getting a heads in the (n+1)st toss is 1-(X/n). In general, it is assumed that a PTM has a fair coin. Without doing any math, which do you now think is more likely- that the coin is fair, or that the coin is biased?. Which coin is more likely to be the biased coin, the first or the second?. The rule is that we play coin 2 if our capital is a multiple of an integer M and play coin 3 if it. The experiment is based on a well-known construction which simulates a coin with an arbitrary given heads probability s using, on average, two ips of the fair coin. One way to determine which is the biased coin is to. Repeat 2 for tossing a coin 500 times (do not print histogram). Assume a person has three coins in her pocket, and heads are the preferred outcomes.