Kelly criterion excel download. (1) Outcomes must be mutually exclusive. Kelly criterion excel download

 
 (1) Outcomes must be mutually exclusiveKelly criterion excel download 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

These calculators let you explore the United States income distribution, or size up job offers and area demographics in different states and cities. Suppose we have initial capital X 0 and we want to determine the optimal betting fraction f to invest each year in S&P 500 stocks. The Kelly Criterion is a formula that produces the long-run optimal bet size, given the odds. The Kelly Formula is: Kelly % = W – (1-W)/R where: * Kelly % = percentage of capital to be put into a single trade. 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. I came across it almost by accident, in William Poundstone’s delightful book Fortune’s Formula. You can read more about how it works in this Kelly Criterion Wikipedia article. Bringing business and financial analysis to the tidyverse. The formula is therefore suggesting that 20% of the portfolio be stake 20% of your bankroll. 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). The Kelly criterion is a money management principle that beats any other approach in many respects. The algorithm will work for markets like ‘Liverpool To Win The EPL’, but will not work for markets like ‘Liverpool Top-4’. Essentially this method takes into account both the probability of a given team or player winning and the value of the odds offered in relation to that probability. 0600. Chapter 2 presents some of the earlier studies of applications of the Kelly criterion and also clarifies more in depth what the Kelly criterion is and how it works. Works best when used in retrospect. rate of wealth. 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. In the one asset two valued payo case, the optimal Kelly wager is the edge (expected return) divided by the odds. This guide explains how the Kelly Criterion works and why it’s so good for sports betting. Kelly betting can be applied to Blackjack with a high degree of certainty in the calculated probabilities. Kelly Criterion - Free download as Excel Spreadsheet (. The Kelly Criterion, in theory, attempts to maximize the growth of your bankroll and this can be applied to any game no matter how much variance said game has. The tidyquant package provides a convenient wrapper to various xts, zoo, quantmod, TTR and PerformanceAnalytics package functions and returns the objects in the tidy tibble format. The reason is because in order for the. Unsurprisingly, the volatility or variance in the evolution of the bankroll is greatest for full-Kelly and least for eighth-Kelly. In my recent article The Real Kelly – an #excel implementation for mutually exclusive outcomes I described how to use excel to find optimal bet sizes for a set of mutually exclusive outcomes applying the generalised Kelly Criterion (a. XLTools Add-In for MS Excel 2016, 2013, 2010, and 2017 provides a set of tools for data manipulation, automation, and version control. The calculator will tell you whether or not you should be betting and how much to stake. 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. ; Click Save to copy the download to your computer for installation at a later time; IT professional resources IT professional working in managed. In sports betting, this formula is used to decide the optimal amount of money to place in a bet. The formula was derived by J. Scribd is the world's largest social reading and publishing site. Mode 2: You know the sharp bookmaker odds and soft bookmaker odds. Sportsbook Pricing and Informed Bettors in the Early and Late Season in the NBA by Rodney Paul, Andrew Weinbach and Brad Humphreys (2013) The Kelly Criterion in Applied Portfolio Selection. Practical Implementation of the Kelly Criterion: Optimal Growth Rate, Number of Trades, and Rebalancing Frequency for Equity Portfolios - Free download as PDF File (. Download full-text PDF. What is the Kelly Criterion? The Kelly criterion is a simple formula that calculates the proportion of your balance to wager on a particular gamble. 00. In the hope of. Unlike our standard Excel betting tracker, this worksheet calculates recommended stakes using four different staking plans: level stakes, percentage stakes, square root stakes and the Kelly criterion. The Kelly Criterion is to bet a predetermined fraction of assets, and it can seem counterintuitive. The basic concept of Real Kelly is discussed here The Real Kelly. They can sometimes be used as criteria to create simple OR logic criteria. So: 4 The Kelly Criterion 4. e. 29 Losses using Kelly criterion: 119 X . 09. Kelly Criterion. - Free download of the 'Optimal F for MQL5 (per Ralph Vince)' library by 'ToneGarot' for MetaTrader 5 in the MQL5 Code Base, 2018. For more Valuation-related content, visit or write to. You can read more about how it works in this Kelly Criterion Wikipedia article. The Kelly Criterion; Other Topics. This formula determines the optimal % of your account that you can bet to get the most profitable outcome in the long run. The purpose of the Kelly Criterion is to help you define the optimal stake amount based on your available funds and the edge you believe you have over the bookmaker. k. Has anyone made the Kelly Criterion Formula for excel? Here is the Formula: f*= (bp-q)/b. 5 Conclusion The Kelly Criterion can be utilized to find the optimal bet size for a wager. It’s free and easy to use. Open the official website and download the software. As explained here, the formula to calculate the Kelly stake is: (BP-Q)/B Where B is the odds you are getting -1 (because we're using decimal odds), P is the likelihood of the bet winning and Q is the probability of losing (or 1 – P). This is Kellys Equation. ,Calculates Kelly stakes for bets on up to either 15 simultaneous betting events or 15 mutually exclusive outcomes of a single event. 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. We then lo. 35 = 0. Then click the centre align button to ensure all data is displayed in the centre of their cells. The formula is: (bp – q)/b = f. The equation tells you exactly how much to bet on each “hand” so that you can survive to keep playing. 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. On 40. In such a case, the Kelly criterion suggests that if one were to go over 20% repeatedly on a low. 0 sperando che possa essere utile per realizzare un profitto ed andare a cassa. This strategy allows you to determine the size of the rates depending on the bank and previous. . The Real Kelly). 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). 33). The true probability may lie between 40% and 60%, or even 20% and 80%. Although it may appear confusing, it’s actually pretty simple. 14 (9), pages 1-16, September. 4. Simply input your betting bankroll, the odds on offer, your assessed probability for that outcome occurring and your Kelly fraction. The Kelly criterion, which was first introduced by John R. 025 or 2. Kelly’s formula is: f = bp – (1-p) / b. 탐욕의 공식이란 별명이 있다. It is a formula that maximizes your profits and guides your better management. 250. Here’s a modified version of the Kelly formula that advantage blackjack bettors use: f = a/v. According to the kelly criterion, you should place a wager of approximately 1. a. 034 or 3. John Larry Kelly Jr. , 2011), which can maximize the long-tern expected log. 25%. f = fraction of current bankroll to bet. 28% on each bet. 62 Using this model you win nearly the same amount as kelly criterion. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a bet. 75 in addition to your stake of $57. R: Number of streaks in the series. L. the market, lazy man’s gambling at its finest. COVER, 1988. Jan 11 21, 15:44 GMT. Download our free and easy-to-use Kelly Criterion Calculator by downloading this excel file! All you need to do is choose which column you want to use (depending whether you want to input your odds in fractions, decimal or american format) and follow the instructions provided! How to create your own Kelly. 55×1-0. Created in 1956 by a Bell Labs scientist, the Kelly criterion is a formula for sizing bets or. ” 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. ) 2) Reward per Dollar Risked: Enter the amount of capital your strategy, on average, profits. It can seem counterintuitive in real time. 025 or 2. For example, a number of papers in MacLean, Thorp and Ziemba (2011) use Kelly principles to assist in asset allocation. The sum of positive trade amounts divided by the sum of negative trade amounts. The formula calculates the ideal sum you should stake on any bet, helping minimise your risk and maximise your profits in the long term. 2 and your odds are. KELLY CRITERION | Ed Thorp | Optimal Position Sizing For Stock TradingThe Kelly Criterion calculation was created by Ed Thorp and made specifically to beat t. Still, this simulation provides insight into how the Kelly Criterion might perform when used on the stock market. 0% x 56. The Kelly Criterion. With sports betting, however, you may feel the probability of an outcome is 50%, but you do not know that with certainty. Most only know a simplified version. P – odds of winning. Applying the formula to forex. Applying the formula to forex trading looks like this: Position size % = Winning trade % - ( (1- Winning trade %) / Risk-reward ratio )The odds are 60/40 in your favour so only betting $1 is likely too conservative. Build a new plugin or update an existing Teams message extension or Power Platform connector to increase users' productivity across daily tasks. How to use the Kelly Criterion to decide how much of your. In this article I. The formula is as follows: f = the fraction of the bankroll to bet. Calculates Kelly criterion utility for a given bankroll (expressed in percent terms) and Kelly multiplier. Using the Kelly Criterion, you can now work out how much of your bankroll to bet on Lucky Punter. xlsx), PDF File (. The Kelly Criterion formula allows bettors to maximize profits from a particular bankroll, based on the value the bet holds. You need to input the probability (according to your own assessment) that your selection will win. 70% of 1 = 0. It is widely applied to sports betting and casino gambling. Download Kelly Criterion Calculator. It can seem counterintuitive in real time. Explore math with our beautiful, free online graphing calculator. There are two basic components to the Kelly Criterion. 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. John Larry Kelly Jr. The Kelly Criterion is a strategy that can be used in several. First thing to note: growth rate is always sloping down at k = 1 = α. At the bottom of the app, tap Search and then input "AusSportsBetting" as the. Mode 1: You know the true probability of an outcome and the soft bookmaker odds. en la década de 1950 mientras trabajaba en los Laboratorios Bell. forms of gambling, including sports betting. We've developed a Kelly Criterion formula Excel spreadsheet that you can download here. It is a simple formula that calculates the proportion of your balance to wager on a particular gamble. Further, suppose that on each trial the win probability is p > 0 and pb - q > 0 so the game is advantageous to player A. b = net odds. The Kelly Criterion. It doesn’t take asymmetric utility into account. Kelly Jr. On the Data tab, in the Sort & Filter group, click Advanced. 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. Download Excel 2016 - Tải Excel 2016 về máy tính. Which I assume you can not. Try out the Kelly Criterion Calculator below, but pay careful attention to heavy favorites (i. txt) or read online for free. 25) – 0. 4%. Here is the Download link for you – Memu Play Website. 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. Though the question affiliated with Kelly criterion is simple, the Kelly criterion has already created the spark in the cross of finance and mathematics. 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. Kelly criterion allows you find out the fraction f* of your bankroll that you should bet if the odds of a bet and the probability of its success are known such as to maximize the logarithmic growth rate of your account. We won’t lie to you. The Kelly Criterion 2. If you’re serious in your ambition to build a sports betting model, just know this, it can be difficult work. Hence, the Kelly criterion can be very risky in the short term. " Kelly Criterion for Optimal Credit Allocation ," JRFM, MDPI, vol. The Kelly criterion is a money-management formula of passionate interest (and controversy) to card players, sports bettors, investors, hedge fund managers, and economists. However, in real life this is hardly ever the case that a. The criterion is most often used in sports gambling and certain investment related. com 152 4. 4% x 52. The Real Kelly). 2151 32 St. 00. Therefore, your probability is . The Kelly Criterion formula is: (BP - Q) / B. 1. We will show why that holds, but. Following this formula, it’s calculated that you stake 80% of your bankroll on the proposed bet. We are going to minimize the function so low values, i. We briefly introduce the Kelly criterion. Aside from the 'HealthyWealthyWiseProject' headline in the front row, the. Therefore, go to Developer. 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. You are here: Home >> Beginner’s Guide >> The Kelly Criterion Once a decision is has been made to wager money on an event, the next decision is to choose how much of your account balance to wager. kelly criterion excel; multi kelly calculator excel;Excel is an extremely powerful program that can be used for various betting related situations and none more so than calculating the Kelly criterion. 1. nancial problems involving the Kelly criterion. In another example, you may have a perceived edge of 55% (0. The Kelly Criterion is a formula that produces the long-run optimal bet size, given the odds. Football betting stats & predictions | OddsWizz. The Kelly formula or criterion is best known as a bet optimisation tool. xlsx","path":"Kelly Bet Calculator. ,Open a new Excel spreadsheet and create the following headers: Betting Bankroll, Kelly Staking Fraction, 1 (outcome 1), 2 (outcome 2), Odds 1, Odds 2,. Kelly Jr. 설명. 4 Free Photo Resizer is a powerful photo manipulation program that combines an intuitive user interface with a range of innovative real-time tools which enables ultra-fast, lossless resizing & converting of pictures - even for large image files. Since our goal is to apply the Kelly criterion on stocks, a similar result for a continuous distribution is relevant (Thorp 2006). 5. How to use the Kelly Criterion calculator. In currency pair trading, the Kelly criterion can be applied to determine the optimal position size based on the trader’s past performance. We then lo. to the point. It is possible. Bettors can also modify the Kelly formula to suit their needs and tolerance to risk. In this video, you will learn how to maximize account growth by defining optimal position size using a fractional Kelly Criterion approach and minimizing you. 40) / 1 = 0. 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 actual formula is: ( (Decimal Odds -1)* (Probability of Success)) – (Probability of Failure )/ (Decimal Odds – 1) The Kelly Criterion is a formula used to bet a preset fraction of an account. That's because the Kelly bet is always proportional to the size of the account. 52. It. Our Kelly Criterion calculator makes it easy to calculate the ideal size of your bets for any given. is the fraction optimising the growth. 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. Kelly Criterion maximizes the wealth in the long-run. Click Install Office to begin the Excel download process. L. xlsx","contentType":"file. The Kelly criterion only defines the “optimal” bet to maximize return. , This Kelly Criterion Bet Calculator takes your inputs on odds, bankroll and payouts to deliver your Kelly Criterion optimized bet size. rate of wealth. Kelly Criteria was developed in 1956 by John L. Interesting, if you’ll note, is that if a user were to win $40,000, the bankroll would then draw down to $3,960,000, making the new highest bet only $39,600. According to the Kelly criterion your optimal bet is about 5. Here are the steps that you have to follow in order to use our Kelly Criterion Calculator: Add your current betting balance in the cell called “Current Betting Balance”. It takes into account the probability. Gain of Positive Outcome: Enter the potential gain of a positive outcome. These are bets where there is no one-to-one correspondence between the bets and the possible outcomes of the game. It takes into account the probability of winning, the amount of the potential payout, and the size of the bankroll or investment capital. e. 5%. 1. 1, 2. 403. 5. The main disadvantage of the Kelly criterion is that its suggested wagers may be very large. 37436% to be more precise but I need help with how the author generates the Kelly Criterion of 2. Download full-text PDF. In relation to sports betting, it’s. As usual, you can also solve this problem with a VBA macro. which gives you the optimal amount to bet ( f*) given the probability of. The odds in the bet multiply for every additional leg you add to the accumulator. The strategy is prevalent and is used as a revered staking plan among stock. past trading performance, 13 10,000 1 14 10,000 1 The Inputs to the Kelly Criterion are as fol 15 12,000 1 16 4,000 1 W = The winning probability facto 17 5,000 1. A good introduction to the subject can be found in Wikipedia. In detail the algorithm will find optimal bet sizes for a set of concurrent singles and/or 'round robin' combinations of parlays or teasers. Again, this is a straight forward calculation: simply multiply the opposing. 75] ÷ 4 = 0. . Theoretically, the Kelly criterion states that the optimal strategy is to allocate a fraction of available capital to each borrower. 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. Now, instead of 5%, assuming you lost 10% and your capital becomes 90000, now in order to recover 10000 or 10% of your original capital, you have to earn back 11. The method is based on a mathematical formula designed to enhance expected returns while reducing the risk involved. Excel and briefly R are used to show how the Kelly criterion is effective. After each bet a gambler loses or doubles the money at跳到 How To Make Your Own Kelly Calculator In Excel? - Creating your own Kelly staking calculator in an Excel spreadsheet is fairly simple. I assume that with multiple bets at zero correlation placed simultaneously that I would bet the full Kelly per bet made. Income Calculators. . . obj. There's a section in it that uses the Kelly Formula. - Free Excel Help. This article will explain usage of an excel implementation applying the Real Kelly Criterion to concurrent events. When the download is complete, open the file, and Microsoft will automatically install the entire collection of Microsoft 365 apps to your computer. Calculate your probability of winning W. For example, in the screen below, cell F4 contains this formula: = SUM ( SUMIFS (C3:C7,B3:B7,{"red","gold"})) Translation: SUM sales where the color is "red" OR "gold". Moneyline odds given the criterion formula spreadsheet calculates the wager Creating a plan when i realized that the formula does it is not a return. One thing that complicates the matter is that short term results can vary widely from the long term. Toll Free Canada: 1. Download full-text PDF Download full-text PDF Read full-text. The formula was invented in 1956 by John Larry Kelly, Jr. Click a cell in the list range. 32 = $101. Kelly Criterion. Calculate the relationship between risk and return R. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. The basic concept of Real Kelly is discussed here The Real Kelly. For the gambler/investor with average luck bankroll and a fixed bet size, the expected bankroll growth after one. Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe. 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. ,This Kelly criterion calculator determines a stake based on the odds. 04. The Kelly Criterion is a method of analyzing your odds and assigning a number to those odds. * R = Historical Average Win/Loss ratio. is the author of the Kelly criterion formula from 1956. In detail the algorithm will find optimal bet sizes for. ” is published by TongTanapat. Feel free to download the model using this link: Kelly Criterion Capital Allocator. 1. Here, we determine our ideal bet size (f) by dividing our edge by the game’s variance. [content_control] {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"Kelly Bet Calculator. 1-p)The excel template can be downloaded here real_kelly-independent_concurrent_outcomes- Please note that the worksheet supports singles & parlays up to 6 selections . You're now. 1 Main Idea In the gambling game we just described, the gambling probability and payo per bet do not change, and thus, from an intuitive stand-point, it would make sense that an optimal solution would bet the same fraction, f, of your money for every trial. This value is. p is the probability of the bet winning. Determine the bet amount according to the Kelly criterion using the formula:بله. Vancouver. 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. Make your sports betting experience easier with. The Kelly Formula is: Kelly % = W – (1-W)/R where: * Kelly % = percentage of capital to be put into a single trade. There are now platforms that exist to aggregate finding the best pricing. 01. 0% = 6. 28% on each bet. * R =. while reducing volatility. Chapter 4 concludes and sums up what we find in our simulations. . Using the example, click any cell in the list range A6:C10. It results in the maximum expected rate of bankroll growth, and is the optimal strategy for money management in betting games. The left-hand side of the equation, f*, is the percentage of our total wealth that we should put at risk. 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. Given all these pieces of information, the maximum win, specifically on BitRocket, is $40,000 per game. The excel template can be downloaded here real_kelly-mutually_exclusive_outcomes- Please note (1) Outcomes must be mutually exclusive (= EXACTLY one outcome will happen). Y si bien la fórmula en sí misma puede ser un poco complicada, Excel ha simplificado su aplicación con su hoja de cálculo de Kelly Criterion. 75; f*= [(b x p) – q] ÷ (b) = [(4 × 0. blogspot. Note: FlashGap and OpenTrace are experimental and highly competative. " So, using his equation(s), I created this library for the Geometric Mean version of Optimal f. Applying the formula to forex trading looks like this: Position size % = Winning trade % - ( (1- Winning trade %) / Risk-reward ratio ) 4 The Kelly Criterion 4. Bayesian statistics, health economics and random stuff by Gianluca Baio. xlsx (15. 40. We've developed a Kelly Criterion formula Excel spreadsheet that you can download here. Chances are, you just typed "Kelly formula" or "Kelly criterion" into a search engine. Furthermore, many believe that the Kelly Criteria has the tendency to be overly aggressive. Determine mathematic equation. . 켈리는 벨 연구소에서 근무하던 연구원이었는데, 어떤 전송 채널이 가질 수. View Test Prep - 05. This is where the Kelly formula comes into play: K = ( PxB – (1–P) ) / B. Predicting a borrower’s probability of default. The Kelly criterion is an excellent tool for assessing the qualitative shape of risk versus reward and understanding the boundaries of rational bets. 55) on a specific spread or total priced at -110 (american odds). The Kelly criterion is a theoretical formula for obtaining the best return when repeatedly investing money. The formula is as follows: Where: K % = The. Providing vendors with a thorough RFP can help foster a successful. Using the Kelly Criterion with Your Portfolio. where. The Kelly criterion formula is: (bp-q)/b. RFP Vendor Template - Excel. It can seem counterintuitive in real time. Assuming the anticipated wager has odds of 3. 70. * f* is the fraction of the current bankroll to wager; * b is the odds received on the wager; * p is the probability of winning; * q is the probability of losing, which is 1 − p. This leads us to the optimal betting amount called the kelley criterion: f∗ = pb − qa ab f ∗ = p b − q a a b. 5. O=MP(O) with P(x) being a probability measure and f a fraction of capital invested. 00, with a winning probability of 0. Il segreto del criterio Kelly è una formula che può sembrare complessa e dal difficile: (Q x P-1) / (Q-1); Q sta per quota e P sta per probabilità. 35 * 0. The Kelly Criterion uses the analogy of a crooked gambler who has control of a private wire (this theory is from the 1950s hence. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is. 1. * W = Historical winning percentage of a trading system. MT4 Position Size Calculator Excel Spreadsheets 28 replies. The worksheet tracks your bets and provides in-depth performance data as well as a profit graph. One very important criteria, your trading system must have a Positive Expectancy and a minimum of 100 historical trades (see the Expectancy Tool). But on those occasions when you lose, you will lose your stake of $57. 1. Kelly Criterion Excel Spreadsheet. C. the market, lazy man’s gambling at its finest. Then how did Kelly Criterion calculate the optimal ratio? Kelly Criterion considers the winning probability and the odds. a. Microsoft Excel 2016 es el software de hoja de cálculo que forma parte del conjunto de herramientas de productividad que obtienes al descargar Office 2016 o Microsoft Office 365. Uploaded file has aOnline Calculators. When the odds are 1:1 (a=1 and b=1), the optimal betting size becomes f∗ = p − q f ∗ = p − q.