The Mathematics Of Poker
Ib3c9612/9ae976b1197ec74c78eda88e41db5ab0.jpg' alt='The Mathematics Of Poker' title='The Mathematics Of Poker' />Probability Problems. In a world as crazy as this one, it ought to be easy to find something that happens. Responsive Web Design With Html5 And Css3 Pdf'>Responsive Web Design With Html5 And Css3 Pdf. It isnt. Kevin Mc. Keen. The Orderly Pursuit of Pure Disorder. Discover, January, 1. American Heritage Dictionary defines Probability Theory as the branch of Mathematics that studies the likelihood of occurrence of random events in order to predict the behavior of defined systems. Of course What Is Random Starting with this definition, it would probably be right to conclude that the Probability Theory, being a branch of Mathematics, is an exact, deductive science that studies uncertain quantities related to random events. This might seem to be a strange marriage of mathematical certainty and uncertainty of randomness. On a second thought, though, most people will agree that a newly conceived baby has a 5. Interestingly, a recent book by Marilyn vos Savant dealing with peoples perception of probability and statistics is titled The Power of Logical Thinking. My first problems will be drawn from this book. As with other mathematical problems, its often helpful to experiment with a problem in order to gain an insight as to what the correct answer might be. By necessity, probabilistic experiments require computer simulation of random events. It must sound as an oxymoron a computer i. See, if you can convince yourself that your computer can credibly handle this task also. The Mathematics Of Poker' title='The Mathematics Of Poker' />A knowledgeable reader would, probably, note that this is a program albeit deterministic and not the computer that does the random number simulation. Thats right. Its me and not your computer to blame if the simulation below does not exactly produce random numbers. When you press the Start button below, the program will start random selection. Every second it will pick up one of the three numbers 1, 2, or 3. You can terminate the process anytime by pressing the Stop button. Frequencies of selections appear in the corresponding input boxes. Do they look random
Remark. Actually, the process of selection includes no selection at all. As a mathematician Robert Coveyou from the Oak Ridge National Laboratory has said. The generation of random numbers is too important to be left to chance. Instead, I have a function that is invoked every second. Each time its invoked, it produces one of the three 1, 2, 3 numbers. This is how the function works. I start with an integer seed 0. Poker Variance Calculator for cash games. Displays variance, possible downswings, upswings and probabilities depending on your win rate. Our mission is to further the interests of mathematical research, scholarship and education. Below are interactive bulletin boards prepared by students in my Methods of Teaching Secondary Mathematics class over the past few years. For a larger photo. When a new random number is needed, the seed is replaced with the result of the following operationseed 7. In other words, in order to get a new value of seed, multiply the old value by 7. Now, assume, as in the example above, we need a random selection from the triple 1, 2, 3. That is, we seek a random integer n satisfying 1 n 3. The formula is. n 3 seed9. Taking it step by step, dividing seed by 9. This times 3 gives a real number between 0 and 3. Brackets reduce the latter to the nearest integer which is not greater than the number itself. The result is a nonnegative integer that is less than 3. Adding 1 makes it one of the three 1, 2, or 3. See Seminumerical Algorithms by Donald Knuth for more details. Problems. 10. 0 Prisoners and a Light Bulb. A Fair Game of Chance. A Pair of Probability Games for Beginners. A Proof by Game for a Sum of a Convergent Series. Amoebas Survival. Are Most Triangles ObtuseAspiring Tennis Club Candidate. Average Number of Runs. Average Visibility of Moviegoers. Averaging Raindrops an exercise in geometric probability. Balls of Two Colors. Balls of Two Colors IIBarycentric Coordinates and Geometric Probability. Bear cubs problem. Bear Born on a Tuesday. Benfords Law and Zipfs Law. Bertrands Paradox Java. Birds On a Wire Java. Birthday Coincidence. Book Index Range. Buffons Needle Problem. Buffons Noodle Java. Careless Mailing Clerk. Checkmate Puzzle. Chess Players Truel Java. Chevalier de Mrs Problem. Clubs or no Clubs. Coin Tossing Contest. Crossing a River after a Storm. Determinants in mathbbZ2Diminishing Hopes. Family Size Java. Script. Family Statistics Java. Four Letters. Getting Ahead by Two Points. Given the Probability, Find the Sample Space. Gladiator Game. Hemisphere Coverage. How to Ask an Embarrassing Question. Incidence of Breast Cancer. Integer Rectangle Java. Lewis Carrolls pillow problem Java. Script. Loaded Dice. Loaded Dice IILost Boarding Pass. Lucky Contest Winners. Marking And Breaking Sticks Java. Script. Matching Socks Java. Script. Mathematics and Biology Java. Misuse and Misconception of Statistics. Monty Hall Dilemma. Multiple of 3 out of the Box. Numbered Balls Out Of a Box. Numbers in a Square. Odds and Chances in Horse Race Betting. Overlapping Random Intervals. Parrondo Paradox Java. Paulings joke. Pencils Logo. Points on a Square Grid. Practical Inevitability of Clustering. Practical Inevitability of Empty Spaces. Probabilities in a Painted Cube. Probability la Tristram Shandy. Probability and Infinity. Probability of 2n Beginning with Digit 1Probability of Four Random Integers Having a Common Factor. Probability of a Cube Ending with 1. Probability of Degenerate Random Matrix in Z2Probability of Increasing Sequence. Probability of Two Integers Being Comprime Java. Script. Random Clock Hands Java. Random Intervals with One Dominant. Recollecting Forgotten Digit. Rectangle on a Chessboard Java. Rolling a Die. Semicircle Coverage. Short Runs from an Urn. Sick Child and Doctor. Simpsons paradox. Probability of Divisibility. Probability of Two Integers Being Coprime. Probability of Visiting Grandparents. Probability with Factorials. Sample Probability Problems from AMCShuffling Probability. Simulating Probabilities. Six Numbers, One Inequality. Six Numbers, Two Inequalities. Six Numbers, Three Inequalities. The 2. 01. 6 ARML Competition, Problem 7. Three pancakes problem Java. Script. Three Random Points on a Circle. Two Envelopes Paradox. Two Friends Meeting. Two Solutions One Correct, One Illuminating. An Example. Tying Knots In Brazil. Waiting for an Ace. Weighted Dice Problem Java. Script. What is the Color of the Remaining BallJava. Script. ContactFront pageContentsProbabilityCopyright 1. Alexander Bogomolny. Poker Variance Calculator Pokerdope. This variance calculator and simulator for poker is handy and easy to use. N-Stalker Enterprise Edition. Just enter your winrate, standard deviation and the amount of hands to simulate. Youll most certainly get insightful results. Read below how to use this simulator. Hit Calculate EV, confidence intervals and samples in BB, Best Worst Best and worst run out of 1. Variance in numbers. Detailed sample with downswings. Million hands. Winnings in BB on right axis, current downswing in BB on left axis. Depending on the number of hands displayed, the extent and number of downswings may be underrepresented due to the resolution of the graph. Downswings in numbers. This section will explain how the calculator works and what the numbers and charts mean. Enter the data. Hop over to the Variance Calculator page and enter your winrate, standard deviation and the number of hands you want to simulate. You can ignore the field observed winrate, well get to its purpose later. Once you have entered the data, hit Calculate and the let the Calculator do its magic. The first thing the Variance Calculator does, is to run 2. Itll also calculate the expected winnings over the amount of hands. This number will appear as a rather boring straight and black line in the graph. Thirdly the calculator displays the 7. What you need to know about them is that at any given time your winnings will be within these intervals with a probability of 7. They basically show, how much variance you should expect to see. Variance in numbers. Below the first chart the Variance Calculator compiles a neat list of additional information EV win rate entered above. Standard deviation standard deviation entered above. Hands number of hands entered above. Expected winnings estimated winnings over the simulated amount of hands. Standard deviation after X hands This number shows by how much your actual results will differ from the expected results on average. The first number shows the absolute value, the second translates this number into BB1. Your actual results over the simulated amount of hands will be within this interval 7. The first interval shows absolute numbers, the second translates those into BB1. Same as the above with 9. Meaning 1. 9 out 2. Probability of loss after X hands probability that you will experience negative winnings meaning losses over the amount of hands. Probability of running at or above observed win rate If you entered an observed winrate, this number will show you the probability that you will experience a run at or above this winrate over the amount of hands. Probability of running below observed win rate Same as above probability that you will experience a run below the observed winrate over the amount of hands. Minimum bankroll for less than 5 risk of ruin the bankroll needed to have a risk of ruin of less than 5Detailed sample with downswings. This chart simulates a single run over 1. You can choose how many hands to simulate by moving the slider. Apart from showing a single sample, this graph also shows some insightful information about downswings. The red area shows for any given point, how much the sample is currently away from its previous peak, meaning it tracks downswings. This chart uses two vertical axes. While the sample winnings have their scale on the right axis, the downswing tracker has its scale on the left axis. In this example the simulated player ended up with winnings over 2. Downswings in numbers. The last section of the Variance Calculator sheds some more light on potential downswings. Therefor 1. 00 million hands are simulated and all downswings over this simulation are tracked. Drivers License Parsing Software Development'>Drivers License Parsing Software Development. The first table shows the extents of downswings. It shows how often the simulated player was stuck in a downswing of at least X big blinds. For example 1. 00. BB 3. 1. 7. 7 means the player was in the middle of a downswing of at least 1,0. The second table shows how long downswings last on average. For example 5. Hands 1. For the purpose of these calculations a downswing is defined as any period where the current total winnings are below the maximum previous total winnings. Meaning, by this definition a downswing is not over until the player has fully recovered its losses. In general these simulations underestimate the extent of downswings, but the numbers should still give you a decent idea of the vastness of downswings you should expect. Should you have any questions, encounter any errors or have ideas for improvements, please let me know.