L. While it does not assign value to risk, simple. Calculate your probability of winning W. Excel Formula for Dutch Betting. "In probability theory and intertemporal portfolio choice, the Kelly criterion (or Kelly strategy or Kelly bet), also known as the scientific gambling method, is a formula for bet sizing that leads almost surely to higher wealth compared to any other. Open navigation menuThe Kelly Criterion is comprised of two basic components. John Larry Kelly Jr. Calculates various arbitrage strategies when an arbitrage opportunity exists. The calculator has 3 modes which you can use to do this. Downloadable (with restrictions)! We develop a general framework for applying the Kelly criterion to the stock market. It takes into account the probability. The First Model • You play a sequence of games • If you win a game, you win W dollars for each dollar bet • If you lose, you lose your bet • For each game, • Probability of winning is p • Probability of losing is q =1 –p • You start out. The Real Kelly) for concurrent events. 4. Place a second bet based upon the Kelly of the remaining capital. We implement a Kelly Engine in Excel which lets us look at what happens at the individual level as opposed to just the mean, which Kelly Optimises. xls / . xlsx), PDF File (. Some derivations of "Stock Market Kelly" involve using back-looking numbers such beta to. Markowitz Portfolio Optimization. It's free to sign up and bid on jobs. The Kelly criterion formula is: (bp-q)/b. The Kelly Formula is: Kelly % = W – (1-W)/R where: * Kelly % = percentage of capital to be put into a single trade. In sports betting, this formula is used to decide the optimal amount of money to place in a bet. (For example, if you have a 40% win rate, then enter the number "40", not 0. Nonetheless, the Kelly Criterion is useful primarily for two factors it utilizes: the. Abstract. In relation to sports betting, it’s. Add the odds quoted by the bookmaker in the cell called "Bookmaker Back Odds". Kelly, Jr in 1956. Simply input your betting bankroll, the odds on offer, your assessed probability for that outcome occurring and your Kelly fraction. Kelly Criterion In probability theory, the Kelly Criterion is a. The kelly criterion is a formula used to bet a preset fraction of an account. There's a section in it that uses the Kelly Formula. . Therefore, go to Developer. . Part 3 is the challenging part. 667. the market, lazy man’s gambling at its finest. Kelly Criterion. 647. According to the kelly criterion, you should place a wager of approximately 1. Thorp is famous for his blackjack paperback, Beat the Dealer, where he explores Kelly for gambling. Add this topic to your repo. Using Python, the author mentions in the article that the Kelly Criterion = 0. We also show that. Try out the Kelly Criterion Calculator below, but pay careful attention to heavy favorites (i. Kelly betting can be applied to Blackjack with a high degree of certainty in the calculated probabilities. Choose Data, Data Tools, What-If Analysis, Data Table. Note: FlashGap and OpenTrace are experimental and highly competative. Basicly, the Kelly Criterion is the value how much you should bet on a team, based on your budget, the lounge odds and "your" odds (as in, what do you think the actual odds are). 00 being returned. Kelly showed that $$frac {p cdot (b+1) – 1} {b}$$ optimizes the growth rate of wealth if the game to bet on is repeated for many times, where p is the probability to win the bet and b. Kelly Criterion. He in fact, suggested the Kelly’s Criterion to help the telecom company with long distance telephone noise issues. xlsx","contentType":"file. (1) Outcomes must be mutually exclusive. The Kelly Criterion is a money-management formula that calculates the optimal amount you should bet when there’s a difference between the true odds and the given odds. In this paper the connection between the probability of default and optimal. 00. How to use the Kelly Criterion calculator. The Kelly Criterion is the principle of bank management for value betting. ALGOET, Paul H. O = log (1+. To use the kelly criterion reasonably in trading you will need to follow these steps: Access at least one sample of one hundred trades you have executed. 75; f*= [(b x p) – q] ÷ (b) = [(4 × 0. However, unlike in the previous situation we examined the Kelly Criterion for, there is not a nite number of outcomes of a bet on a security, so, we will useThe Kelly strategy is a safe method and can be used as a general money management system for both betting and investing. b = the decimal odds: 1. This post will serve as the first of a series to discuss the Kelly criterion. Many adages exist: don't bet more than 2% on one trade, don't enter trades that don't have x% upside, never bet on the same stock twice in quick succession, etc. Download PDF Download PDF with Cover Download XML Download Epub. Kelly Criterion - Free download as Excel Spreadsheet (. It just happens to coincide with log-utility. The Kelly criterion tells you the optimum amount to risk when you have an advantage in gambling, sports betting, stock option trading, or investing, such as. Choose the event type – independent events, which refers to several different games; or exclusive outcomes. The famous coin-flipping exercise that many investors use to measure the performance of chance. J. 탐욕의 공식이란 별명이 있다. We've developed a Kelly Criterion formula Excel spreadsheet that you can download here. According to the Kelly criterion your optimal bet is about 5. 62. KK. We’ll be experimenting with the Kelly criterion formula for a practical example. 5%. Note this is 1-loss PercentageOfOdds = 0. Let’s calculate K for our scenario:Job Overview: We are in need of an Excel spreadsheet developer who can create a customized spreadsheet utilizing the Kelly criterion calculation. Download full-text PDF Download full-text PDF Read full-text. Bringing business and financial analysis to the tidyverse. 025 or 2. The goal is still to maximize ;. I introduced the Kelly Formula into Excel and created a spreadsheet with adjustments. I assume that with multiple bets at a correlation of 1 I would divide the Kelly by the number of bets. 29 Losses using Kelly criterion: 119 X . However, in real life this is hardly ever the case that a. Has anyone made the Kelly Criterion Formula for excel? Here is the Formula: f*= (bp-q)/b. Home. Kelly Criterion ruined many bankrolls especially of those who can’t analyse the exact probabilty. On 40. Losing the first bet and winning the second will lose $4 more. Choose the language and bit version you want, and then select Install. Add your current betting balance in the cell called "Current Betting Balance". f* is the fraction of the current wealth to bet (expressed in fraction), b is the net odds received on the bet (e. Kelly Criterion [Kelly 1956] permits the investor to maximise return on investment, geometrically. 800. Developed by John Kelly, who worked at Bell labs, the Kelly Formula was created to help calculate the optimal fraction of capital to allocate on a favorable bet. With this we can calculate the optimal Kelly leverage via f = μ / σ 2 = 0. 설명. The Kelly Criterion is a mathematical formula that helps investors and gamblers calculate what percentage of their money they should allocate to each investment or bet. The Real Kelly). Kelly criterion calculator stocks. 55) / 1. 3%. (Excel format) AFL form guide; American Football. Presentation Transcript. L. Bibliography. If there is a fixed amount of bets the Kelly criterion will be suboptimal, but as the number of bets grows the optimal strategy will asymptotically reach the Kelly criterion. 미국의 수학자 켈리(J. 50%. It was found that the formula, which has a gambling background and helps to determine the optimal bet size, can also help with finding the ideal investment size. The Kelly Criterion bet calculator above comes pre-filled with the simplest example: a game of coin flipping stacked in your favor. 5 to 1 come hell or high water one thousand times we should *expect* make on average: $12,000. 5. ) 2) Reward per Dollar Risked: Enter the amount of capital your strategy, on average, profits. A year ago I mentioned that I use Kelly criterion in my portfolio management and I promised to expand on that. The calculator will tell you whether or not you should be betting and how much to stake. Kelly’ Criterion has an interesting background. 05, 0. The Crypto Wizards platform capitalises on this by pre-scanning aggregated markets across thousands of coins, checking for potential opportunities and presenting these. Download file PDF Read file. Despite expending substantial resources on a formal financial education, I did not encounter the Kelly criterion in business school or the CFA curriculum. Put simply, the Kelly Criterion or Formula is a way to calculate how much of their assets a Forex trader should risk on any given trade in order to maximize the return. Kelly Criterion. Kelly Criterion. On such events, it is recommended that bets be made according to the Kelly strategy. 39 - 5. The formula has a number of applications, one of which is sports betting. 75 in addition to your stake of $57. 52. The Kelly criterion is a money-management formula of passionate interest (and controversy) to card players, sports bettors, investors, hedge fund managers, and economists. Open navigation menu. ,Has anyone made the Kelly Criterion Formula for excel? Here is the Formula: f*= (bp-q)/b where * f* is the fraction of the current bankroll to. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to. The update enables users of the standard spreadsheet to take advantage of the following features: New custom field added to the Bets worksheet which can be renamed in the Settings sheet. 「kelly criterion賽馬」+1。那就是此前提及的Kellycriterion，很多人稱作凱利公式或凱利方程式。只要是賭徒，. * R = Historical Average Win/Loss ratio. 55, which is 18. Build a new plugin or update an existing Teams message extension or Power Platform connector to increase users' productivity across daily tasks. We then lo. 1. The reason is because in order for the. The left-hand side of the equation, f*, is the percentage of our total wealth that we should put at risk. This guide explains how the Kelly Criterion works and why it’s so good for sports betting. The most common form of value betting calculator. 0% of similar occasions, you would expect to gain $99. The Kelly formula is : Kelly % = W – (1-W)/R. Download RFP Vendor Template - Excel. This includes an experiment where players could bet on a coin that would land on head 60% of the time, for an even money bet. RFP Vendor Template - Excel. R: Number of streaks in the series. 0 – 1 = 4; p = 0. The main advantage is being able to use quantitative functions with the tidyverse functions including purrr, dplyr, tidyr,. Choose Data, Data Tools, What-If Analysis, Data Table. the market, lazy man’s gambling at its finest. We will show why that holds, but. If the sum of all position sizes is 1, weight. It helps calculate the optimal amount one should place on a bet or an investment. Difficile ma non impossibile generare una vincita. In such a case, the Kelly criterion suggests that if one were to go over 20% repeatedly on a low. obj. Dutchformula = (funds / ((funds/odds1)+ (funds/odds2)+ (funds/odds3))) *. To do so, create a Dabble account and download the App. The Kelly Criterion is a relatively simple math equation to determine the percentage of your bankroll you should bet on any given circumstance, assuming you have an advantage. Esempio pratico e concreto: il 29 aprile si giocherà nel campionato russo il bigmatch tra Zenit San Pietroburgo e CSKA Mosca in cui è inutile negare l' equilibrio e l' incertezza. Kelly in his famous article on the information rate, has proven to optimize the growth of an investors’ wealth if one follows the. Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe. 4%. Note that if the formula is absolutely strictly applied, one would literally never make. ,Calculates Kelly stakes for bets on up to either 15 simultaneous betting events or 15 mutually exclusive outcomes of a single event. Follow these steps to determine your optimal bet stake using the Kelly Criterion:1. , Can the Kelly Formula be generated in Excel?Search for jobs related to Kelly criterion calculator or hire on the world's largest freelancing marketplace with 23m+ jobs. 5% and Ralph Vince Optimal f = 0. This strategy allows you to determine the size of the rates depending on the bank and previous results. This post provides an introduction. using excel and Brownian motion. In essence, the Kelly Criterion calculates the proportion of your own funds to bet on an outcome whose odds are higher than expected, so that your own funds grow exponentially. Trading Price Based Charts Instead of Time Based Charts 1 reply. ” Kelly MultiplierBelow is an explanation of how to apply the generalised Kelly Criterion to betting: Step - 1: List all possible outcomes for the entire set of bets. It helps identify your trading weaknesses, strengths, and areas of improvement. will take. This fraction should be equal to the difference between non-default probability ( p) and default probability ( q ). 00 – 1) f* =0. Thorp: Beat the Dealer. Download full answer. The spreadsheet compares your betting performance to the hypothetical results had you strictly followed the four staking plans. Over the years we've done stuff like Dutching, hedging, Kelly Criterion, max-consecutive losses, and other formulas,. The Kelly Criterion If everytime we trade we force ourselves to trade 2. 77 = $91. How to use the Kelly Criterion to decide how much of your. The Kelly Criterion is a formula that produces the long-run optimal bet size, given the odds. 1, 2. 5. * f* is the fraction of the current bankroll to wager; * b is the. However, until recently application of the Kelly criterion to multivariate portfolios has seen little analysis. KELLY CRITERION | Ed Thorp | Optimal Position Sizing For Stock TradingThe Kelly Criterion calculation was created by Ed Thorp and made specifically to beat t. a. Aside from the 'HealthyWealthyWiseProject' headline in the front row, the. Link tải Excel 2016. It is a simple…F = ( (1. Browse Figures. " Kelly Criterion for Optimal Credit Allocation ," JRFM, MDPI, vol. 0 (Criterio di Kelly) Che cosa è il criterio di Kelly? "Il criterio di Kelly, o strategia di Kelly o formula di Kelly, o puntata di Kelly, è una formula utilizzata per determinare la quota di un capitale da investire in una determinata scommessa. Kelly Criterion gambling is especially popular in sports betting and can potentially help you become a successful bettor. 403. The basic concept of Real Kelly is discussed here The Real Kelly. [content_control] {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"Kelly Bet Calculator. The Kelly Criterion is a method by which you can used your assessed probability of an event occurring in conjunction with the odds for the event and your bankroll, to work out how much to wager on the event to maximise your value. The equation tells you exactly how much to bet on each “hand” so that you can survive to keep playing. Mode 1: You know the true probability of an outcome and the soft bookmaker odds. Kelly represents the limit to the range of rational investments. This work presents a disciplined convex programming framework for Kelly criterion in portfolio optimization based on exponential cone programming. The Kelly Criterion bet calculator above comes pre-filled with the simplest example: a game of coin flipping stacked in your favor. It. The Kelly Criterion was. The great thing about the formula is that it’s flexible enough to work where information or skills can give you an advantage by estimating the outcome probabilities. The theory was developed by John L Kelly (pictured left) out of the information theory work of Claude Shannon. This is the accompanying article to my previous post covering a python implementation of The Real Kelly Criterion for independent concurrent outcomes. So: 4 The Kelly Criterion 4. It takes into account the probability of winning, the amount of the potential payout, and the size of the bankroll or investment capital. Many well known investors use it, including Warren Buffett and Bill Gross. It's free to sign up and bid on jobs. In its simplest possible form, the Kelly Criterion states that, on an even money bet, the percentage of the bankroll to bet is: (Win probability x 2) - 1. Kelly Criterion Calculator is a tool for finding the optimal investment size to maximize profits on repeated investments. The Kelly Criterion. The Kelly Criterion is a popular staking method which suggests that your stake should be proportional to the perceived edge. 20 or 20%. Kelly Criterion is a variable staking plan with the goal of maximizing bankroll growth by finding the optimal bet size for each wager. k. at Bell Labs, is a strategy for the optimal sizing of bets in the repeated bets scenario in his seminal paper¹. The Kelly criterion is a way to optimise an unlimited sequence of bets under the following circumstances: a probability p of winning each bet, a loss of a fraction a of the sum bet, a gain of a fraction b of the sum bet, and a fraction f of the current fortune as the sum bet. Calculating the Kelly stake. Focusing, like Kelly, on simple intuitive versions of the expected log criteria, he suggested that it had superior long run properties. b = the decimal odds – 1. obj. By supplying an arbitrary probability distribution modeling the future price movement of a set of stocks, the Kelly fraction for investing each stock can be calculated by inverting a matrix involving only first and second moments. Under few conditions, using Monte Carlo simulations with different scenarios we prove that the Kelly criterion beats any other approach in many aspects. Kelly Criterion – Part 2 – Derivation. Could you provide more. p = the probability of your bet selection winning (being correct). The goal was to figure out the best ways to manage signal-noise issues in long-distance telephone. Part 1 of this series provides an introduction to the Kelly criterion along with a worked example. Versions. B = the Decimal odds -1 P = the probability of success Q = the probability of failure (i. The main requirement to getting the biggest profits is you must have the mathematical edge over the house. where. 50) =. To emphasize this connection, we refer to this optimal allocation as the Kelly criterion henceforth. This gives us a Sharpe Ratio of S = 0. Object moved to here. According to the Kelly criterion your optimal bet is about 5. Edward O. By supplying an arbitrary probability distribution modeling the future price movement of a set of stocks, the Kelly fraction for investing each stock can be calculated by inverting a matrix involving only first and second moments. The higher the volatility, the larger values. These two factors are then input into the Kelly Criterion equation. There has to be a minimum of two legs in your bet to be classified as an. Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or. The Kelly criterion is well known among the gamblers as a formula to calculate the optimal bet size in games with a positive expected return. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a bet. The Annals of. Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. To install Microsoft 365 in a different language, or to install the 64-bit version, select the link Other options. The generalised Kelly Criterion (a. In my book, I described a very simple and elegant formula for determining the optimal asset allocation among N assets: F=C -1 *M (1) where F is a Nx1 vector indicating the fraction of the equity to be allocated to each asset, C is the covariance matrix, and M is the mean vector for the excess returns. 3% more than what you lost. The formula is: (bp – q)/b = f. 124 = 0. In this article I. Add your expected win probability for the selection you have chosen in the cell called “Win Probability”, using values between 0% and 100%. B=2-1=1. Kelly. It is a formula that maximizes your profits and guides your better management. The Kelly Criterion is a formula used to determine the optimal size of your bets based on your edge and bankroll. Copilot will help identify trends, propose what-if scenarios, suggest ideas for improving your business, and will even build everything into an easy-to-read dashboard. Works best when used in retrospect. The criterion is most often used in sports gambling and certain investment related. Our Kelly Criterion calculator makes it easy to calculate the ideal size of your bets for any given. The Kelly Criterion requires there are no other rules other than the Kelly Criterion. Use this if you have a crystal ball that tells you the true probabilities. 5%. First thing to note: growth rate is always sloping down at k = 1 = α. Hence, the Kelly criterion can be very risky in the short term. pdf), Text File (. The formula was developed by Kelly while working at the AT&T Bell. Usually, the bigger your edge on the odds the more you should bet but Kelly also takes into account the real chance of that bet winning and Kelly would advise a smaller bet for a 5% edge at even money (2. 25; q = 0. 124 2 = 5. (Scientist, Bell Labs). 1% x 63. 00. as. Add the odds quoted by the. and the second part is the optimization of that strategy through Kelly criterion. The excel template can be downloaded here real_kelly-mutually_exclusive_outcomes-. Make sure that all other workbooks are closed, because otherwise, the next few steps could take a LONG time. There are two basic components to the Kelly Criterion. He in fact, suggested the Kelly’s Criterion to help the telecom company with long distance telephone noise issues. It was proposed by John Kelly in the 50’s who at that point was working for AT&T’s Bell Laboratories. The main disadvantage of the Kelly criterion is that its suggested wagers may be very large. R = Historical Average Win/Loss ratio. Kelly Criterion can be used in either discrete finance or continuous finance applications. b = net odds. . The Kelly Criterion uses the analogy of a crooked gambler who has control of a private wire (this theory is from the 1950s hence. At the bottom of the app, tap Search and then input "AusSportsBetting" as the. Price-based Vs. The basic concept of Real Kelly is discussed here The Real Kelly. Methods similar to those already described can be used to maximizeKelly Criterion Formula. Further, suppose that on each trial the win probability is p 0 and pb — q > 0 so the game is advantageous to player A. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Make sure that all other workbooks are closed, because otherwise, the next few steps could take a LONG time. 4), and; p is the probability of a win. We briefly introduce the Kelly criterion. Kelly, Jr in 1956. The Kelly Criterion is a strategy that can be used in several. Still, this simulation provides insight into how the Kelly Criterion might perform when used on the stock market. Bringing business and financial analysis to the tidyverse. Revisiting the Kelly Criterion Part 2: Fractional Kelly Another common complaint about the Kelly Criterion is how to manage multiple edges on concurrent bets. The first of these is the probability of a positive outcome, or a winning trade. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected. To calculate the optimal bet size use Kelly's criterion . If you bet twice Kelly (even with a profitable system), you are mathematically guaranteed a ruin, no matter how much money you have initially. The Kelly Criterion is a method of analyzing your odds and assigning a number to those odds. W = Historical winning percentage of a trading system. Let Excel learn your. Mode 1: You know the true probability of an outcome and the soft bookmaker odds. forms of gambling, including sports betting. Kelly criterion can generate an optimal bidding fraction (MacLean et al. There are now platforms that exist to aggregate finding the best pricing. Your 'odds offered' are '2 to 1' (so enter 2 ). This is Kellys Equation. Latane (1959, 1978) introduced log utility as an investment criterion to the finance world independent of Kelly’s work. 6 Profit = 1 Loss = 1 #Betting percentage for the differnet scenarios a = kelly (PercentageOfOdds,Profit,Loss) b = a/2 # Half Kelly c = a*2 # Double Kelly # Creating the monte carlo simulation with the for statements Saving all results in a list before changing. Thus the Kelly leverage says that for a 100,000 USD portfolio we should borrow an additional 401,000 USD to have a total portfolio value of 501,000 USD. The fraction of wealth allocated to each asset is known as the Kelly Portfolio which optimizes the long term compound growth rate of total wealth. p = probability of winning. k. If W remains constant K increases as the trade’s Win/Loss ratio (R) improves. 04. Kelly Criterion mathematical equation takes into account. Thorpe also has a very interesting technical review (Thorp, 2008) and (Cover, 1999), like Kelly in its original paper, describes the interesting connections with information theory. b = 5. But on those occasions when you lose, you will lose your stake of $57. The formula has a number of applications, one of which is sports betting. In the previous section we propose a trading model based on options, which can be summarized as follows. - GitHub - BettingIsCool/real_kelly-independent_concurrent_outcomes-: The generalised. Extending Kelly a bit further (like Ed Thorp, author of two math bibles for the investor/bettor Beat the Dealer and Beat the Market, has done) we can do a bit of hand-waving and make it work for the stock market. Kelly’ Criterion has an interesting background. I am able to generate the same Ralph Vince Optimal f by maximizing the TWR function in Excel which is 3. Excel 2016 Free Download for Windows 10/7/11/8 is the name of the rearmost fixed interpretation of Microsoft’s popular and extremely important spreadsheet application. Excel is an extremely powerful program that can be used for various betting related situations and none more so than calculating the Kelly criterion. Toll Free US: 1. Asymptotic Optimality and Asymptotic Equipartition Properties of Log-Optimum Investment. Kelly Criterion Calculator. It is a formula used to determine the optimal size of a series of bets in sports or investment. resource for various forms of investing too, as its primary. Variance is formula kelly criterion exampleEl Kelly Criterion Calculator Excel es una hoja de cálculo que te ayuda a calcular el tamaño de la posición óptima para cada operación. Kelly himself was an interesting character: a chain smoking Texan who used to be a fighter pilot in the Navy during World War 2, he was also brilliant researcher. One topic you won't find much about on the Web is Kelly himself. We are going to minimize the function so low values, i. The purpose of this study is to address the critical issue of optimal credit allocation. " GitHub is where people build software. Hence, the Kelly criterion can be very risky in the short term. The worksheet tracks your bets and provides in-depth performance data as well as a profit graph. The Real Kelly). Here: b is the decimal odds of an event -1; p is the probability of success; q is the probability of failure (which can be calculated by 1-p). 33). Explore math with our beautiful, free online graphing calculator. We've developed a Kelly Criterion formula Excel spreadsheet that you can download here. The Kelly Criterion is a formula used to determine the optimal size of your bets based on your edge and bankroll. The First Model, con’t • You bet some percentage, f, of your bankroll on the first game --- You bet fB • After the first game you have B 1 depending on whether you win or lose • You then bet the same percentage f of your new bankroll on the second game --- You bet fB 1Kelly Criterion Calculator is a tool for finding the optimal investment size to maximize profits on repeated investments. 45) – 0. 凱利公式、凱利方程、凱利判據、凱利策略（英語： Kelly criterion 、 Kelly strategy 、 Kelly bet ），是一種根据赌博赢或输的概率，计算出每次下注的资金占所有赌本的最佳比例的公式 ，由約翰·拉里·凱利於1956年在《 貝爾系統技術期刊 （ 英语 ： Bell. 25%. b is your potential winnings, in decimal odds b is simply the odds minus one. to the point. pdf from BIZ 101 at National University of Singapore. 6, and its probability of losing is 0. Where can I find an Excel example of the Kelly criterion as . In the Data Table dialog, click in the Column Input Cell edit box; click on any empty cell outside of the area of your table; and then choose OK. I came across it almost by accident, in William Poundstone’s delightful book Fortune’s Formula.