It is named after him, and it is a mathematical formula that calculates the optimal position size for an investment, given the investor's probability of success and the payoff ratio of the investment. 1. More than 100 million people use GitHub to discover, fork, and contribute to over 330 million projects. As discussed, that’s pretty much the case with 50/50 leagues, but not at all the case in heads-up leagues. In other words, the Kelly Criterion takes into account both the size of your advantage (I. The Kelly Criterion. at Bell Labs in 1956. If only one of them is in your favor, it must more than offset the other, i. If you check out Wikipedia or Investopedia, you’ll see formulas like this: f ∗ = p − 1 − p b − 1 f ∗ = p − 1 − p b − 1. a. This value should be a number between 0 and 100. If the bias were lesser at a 55% chance, the Kelly percentage would be 10%. Heuristic proofs of the Kelly criterion are straightforward. The strategy is to maximize long run wealth of the investor by maximizing the period by period expected utility of wealth with a logarithmic utility function. Most importantly the criterion gives motivation to decide between investments with identical expected value but different risk of default. 38% = $53). If you bet more than 10%, you’re taking on too much risk. Enter. The picture above has 2 simulations of betting at 20%, 50%, and 75% and 4 at the Kelly Criterion amount. However,. The formula is therefore suggesting that 20% of the portfolio be stake 20% of your bankroll. However, in order to reach that conclusion, we must wager with a flat betting plan for a large number of bets. I’m a professional trader and former quant and I don’t know a single actual pro who uses anything like Kelly to size bets. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to. 3 is the profit rate if I win an investment, p = 0. 0. Theoretically, however, the Kelly Criterion could go much higher than 100% and be calling for 200%, 300%, 500% allocation (i. We need to maximize E (G) = (1 + (O-1) * X) p * (1 - X) 1-p - 1 with respect to X, subject to X lying on the unit interval [0,1]. John Larry Kelly, Jr. 2. q = (1 – 0. Based on the Kelly criterion, K% = (1 × 0. The Kelly Criterion is a mathematical formula created by John L. Generally, the Kelly criterion is a formula that maximizes the expected value of the logarithm of wealth that is equivalent to maximizing the expected long-term growth rate. 48the Kelly criterion. 54 p = 0. We advise you to set it at 0. The Kelly Criteria is popular with many professional punters, but as mentioned above, the main problem is to. Kelly)가 1956년에 발표한 공식. 124 = 0. This paper shows the theoretical framework of the Kelly criterion as a portfolio optimization method. The first credit allocation system is the adaptive Kelly strategy (‘Kelly Strategy’). Kelly Criterion. 36: Understanding the Kelly Criterion. Therefore you would stake 10% of your. We also show that. He gives lectures to various institutions including The World Bank, Carnegie Mellon, and billion-dollar hedge funds. (2009) show the Kelly criterion to de ne an investment strategy that ensures the survival of agents following this strategy and yields global evolutionary stability. 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. Kelly also gives you a 50+% chance of ending up a millionaire, and a 11% chance of ending up a billionaire! 1. e. There is a 60% chance of a winning a coin flip. Let’s calculate K for our scenario:ity”). For example, if you think the fair odds of an outcome are 2. We compare and contrast three types of utility theories:According to Kelly formula, optimal size of your stake would be: Stake = ( (2. Mochkovitch. The conclusion is: Kelly Criterion is the numerical expression of the attitude of the gaming company to a certain result of the game. This equation is not analytically solvable, but may be approximated as a quadratic programming problem as described in a paper by Vasily Nekrasov. If the dice bias were less, at 53%, the Kelly criterion recommends staking 6%. However, it can be complicated to use if you are not used to it. This is all the information we need in order to use the Kelly formula (p = 40% and r = 3). The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to. The Kelly criterion calculator is a powerful tool for managing your money when gambling or investing. It can seem counterintuitive in real time. Kelly Criterion • Developed by John Kelly, a physicist at Bell Labs – 1956 paper “A New Interpretation of Information Rate” published in the Bell System Technical Journal • Original title “Information Theory and Gambling” – Used Information Theory to show how a gambler with inside information should bet4 hours ago · Gaming Today is licensed and regulated to operate in AR, AZ, CO, CT, DC, IA, IL, IN, KS, LA, MA, MD, MI, NH, NV, NJ, NY, OH, OR, PA, TN, VA, WV & WY. Given all these pieces of information, the maximum win, specifically on BitRocket, is $40,000 per game. PK. While most calculators compute the Kelly Criterion in terms of odds and edges. 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 useHow to Use the Kelly Criterion. 60) / 4 = 0. 10. 00 – 1) f* =0. Its mathematical foundation provides individuals with a systematic approach to determining appropriate bet sizes, allowing for the balancing of risk and reward. The Kelly Criterion, fundamentally, computes the optimal stake or position size for a given event, hinging on four factors: the equity balance, expected return from a successful outcome, probability of success, and probability of failure. Abstract: 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 investing. 01, we need to borrow an additional 105,460 USD in order to increase our account size to 631,510. We develop a general framework to apply the Kelly criterion to the stock market data, and consequently, to portfolio optimization. How to use the Kelly Criterion calculator. Kelly in 1956. I therefore recommend using the more sophisticated generalised Kelly Criterion wherever possible as it is superior to the simplified Kelly Criterion. But what happens when one uses profit-factor on the last 6. where 𝑓∗ is the Kelly Fraction - the optimal amount you invest in your risky asset while the rest sits in a hypothetical risk-free asset (e. It is the only formula I’ve seen that comes with a mathematical proof explaining why it can deliver higher long-term returns than any alternative. Um den Kelly Formel Rechner zu benutzen brauchen Sie nur die angebotene Quote und die Wahrscheinlichkeit in das Formular einzugeben. It is suboptimal in the long run. 6%) and a standard deviation of 9%. with constant bets. 091 500:1 odds 0. The famous Kelly betting criterion (Kelly, 1956), which maximizes a logarithmic utility function, is widely used to choose s. The performance of the model are hence studied as a function of the input capital state under the assumption that the latter belongs to the set of. Thorp is famous for his blackjack paperback, Beat the Dealer, where he explores Kelly for gambling. In this case, the Kelly criterion betting strategy suggests that if you wager over 20% of your bank continuously on 1, 2. This is how the simplified Kelly looks. The growth rate is reduced less significantly in comparison. The Kelly Criterion gives an optimal result for betting based on the probability of winning a bet and how much you receive for winning. 2. You win $100 if the dice shows up as a 1, 2, or 3. Below 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. Conclusion. 71% of your capital, or $57. The Investopedia definition is P- [ (1-P)/winLossRatio], where P is the probability of a. Predicting a borrower’s probability of default is a key requirement of any credit allocation system but turning it into labeled classes leads to problems in performance measurement. The criterion helps: investors optimize portfolio. Follow these steps to determine your optimal bet stake using the Kelly Criterion:1. I. Kelly suggests maximizing the expected value of the logarithm of our money, so we want to maximize p. For example, in the game we're playing, when you put up equal amounts of money, you want to bet (2p-1) of your bankroll, where p is your chance of winning (here, 55%. ity”). Rechner und Wettwerkzeuge. s = b * (o / f. He devoted four years of his life in the US Navy as a pilot and served in the World War II. This is the well-known "Kelly Formula" (aka 'Kelly Criterion. This shows that according to the Kelly Criterion formula, you should stake 25% of the amounts you have set for betting. 025. The Kelly criterion indicates that the fraction that should be wagered to maximize compounded return over the long run equals: F = PW – (PL/W) where. where: K – optimal % risk. F = Kelly criterion fraction of capital to bet. The kelly criterion is a theory that measures the long-term growth of capital. 5 per game forever, while the second bettor (red line) utilizes the Kelly criterion and bets 5. Rechner und Wettwerkzeuge. Following this formula, it’s calculated that you stake 80% of your bankroll on the proposed bet. ” Invented in the 1950s by a Bell Labs researcher named J. One was the 'square root' plan whereby a base bet is established, say $20, and each bet you place is $20 plus the square root of any. The first credit allocation system is the adaptive Kelly strategy (‘Kelly Strategy’). You lose $100 if the dice shows up as a 4, 5 or 6. 66. 0. The author initiated the practical application of the Kelly criterion by using it for card counting in. While the criterion has its limitations, its core principles have found. I have a coin that lands heads 60% of the time and tails 40% of the time. That means 55 (the percentage probability you think your bet will win) minus 45 (the percentage probability you think your bet will lose) will give you 10. Enter the probability (%), which represents the likelihood of winning the bet. The Kelly Criterion is most often used by card counters. Kelly ≠ Goal Kelly = Limit. Full Kelly has an interesting property: there is an X% chance of your bankroll dropping to X% of what you started with 5. 2 Holding Period Returns The work of Ralph Vince extends the Kelly criterion from the scenario involving afinding optimal weight using Kelly criterion. 개요 [편집] 미국 의 수학자 켈리 (J. The formula has a number of applications, one of which is sports betting. Kelly system betting provides an objective answer on how to make your bankroll grow as fast as possible. Profit-factor is a nice matrix for using as fractional-size. Kelly's result is, in its simplest sense, a solution to an optimization problem which maximizes logarithmic utility and was originally applied to a technical problem in information theory (Kelly 1956; Kim 2008). Strategy 2 gains 8% with probability q, and loses 5% with probability 1-q, where q = 0. 2. 01, we need to borrow an additional 105,460 USD in order to increase our account size to 631,510. Thus: f = ( (1 × 0. Jacot. After backtesting this, say it gerates 60% win. A 50% chance of a 50% drawdown is a lot to stomach. You have $1,000 with you. Because the Kelly Criterion seeks to calculate the optimum stake for any value bet so as to maximise that value as well as maximise the growth of your betting bankroll. 5% of wealth. 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. You have to remember that the basic Kelly Criterion formula is meant to optimize bets for black-and-white, independent outcomes. e. In particular, it maximizes the expected growth rate and the median of the terminal wealth. 53. B – payout on the bet. The benchmark for new traders to move on from paper trading is a win rate of 75% and a profit factor of 2, so an average win of say $1 and average loss of -$1. The Kelly strategy is a safe method and can be used as a general money management system for both betting and investing. The algorithm’s resilience is enhanced by several premium distribution policies over partially. import pandas as pd import numpy as np import matplotlib. Unterstützt EW, Dead Heats, Regel 4. You need to input the probability (according to your own assessment) that your selection will win. The Kelly wager is positive iff the expected value b p − (1 − p) is positive. 36. From the framework described in Section 2, we know that the Kelly criterion k(p) is the optimal value of f. Kelly betting can be applied to Blackjack with a high degree of certainty in the calculated probabilities. E. The Kelly bet is popular among big investors, including Berkshire Hathaway's Warren. 71% of your capital, or $57. It was first used by gamblers in the betting industry before its application was extended to investing. But that was not my point. In the third event on the Belmont program, you find an angle play that has a 15 percent strike rate and 8-1 average winning odds. If Bronzetti’s odds were 1. 0102 = 1. You must scale the Kelly output so that the amount you bet is equal to the potential loss. This paper examines how the Kelly criterion, a strategy for maximizing the expected log-growth of capital through informed betting, can be applied to non-mutually exclusive bets. They will just be on different scales, but their peaks will occur in the same place. 1 Introduction Kelly (1956) considered the question of how a gambler with an edge should act in order to maximize his bankroll growth. edge2 edge2+σ2 = σ2 market σ2 market+σ2. The Kelly Criterion is a formula which accepts known probabilities and payoffs as inputs and outputs the proportion of total wealth to bet in order to achieve the maximum growth rate. 5. This announced the discovery of favorable card counting systems for blackjack. A divergence in attitude towards this theory illustrates the disconnect between academicians and practitioners, and the necessity of closer collaboration between the two circles. ple and correct procedure to apply the Kelly strategy for the general case. In this paper, we provide a new approach to apply-ing the Kelly criterion to stock market investments. Here are five tips to help you use the Kelly sports betting strategy more effectively. 65. The Kelly criterion: How to size bets. In relation to sports betting, it’s. Most sources provide coverage only…The optimal allocation given in Proposition 1 coincides with the Kelly criterion (Kelly 1956; Thorp 1971) in probability theory and the portfolio choice literature. I can run backtest simulations to get a sense of historical "edge" and "odds". 00. It doesn’t take asymmetric utility into account. For short straddles and strangles, I imagine you would use the probability of the price remaining between the two strikes until expiration. 35 = 0. Calculate your probability. This paper examines how the Kelly criterion, a strategy for maximizing the expected log-growth of capital through informed betting, can be applied to non. 33 or . In one sense it is widely known: the basic "i. Thorp extended the Kelly Criterion logic and developed an adapted model to. e. Of course we cannot do that. This paper presents a model to address the uncertainty inherent in replacement problems, whereby a firm must select between mutually exclusive projects of unequal lifespans by applying the Kelly criterion (which is not well known to the engineering economics community) within a binomial lattice option-pricing environment. Beachten Sie bitte, dass Sie das Komma sowohl bei der Wahrscheinlichkeit als auch. These two factors are then input into the Kelly Criterion equation. The basic formula for the Kelly Criterion is given by: -> f^* is the optimal fraction of the bankroll to bet; -> b is the net odds received on the wager (i. The famous coin-flipping exercise that many investors use to measure the performance of chance. You get the only answer one can reasonably expect: if. which gives you the optimal amount to bet ( f*) given the probability of. The Kelly Criterion is a method of analyzing your odds and assigning a number to those odds. The Kelly Criterion How to Use the Kelly Criterion. You shouldn't count on serious success with a bankroll of $10-20. As far as I understand the Kelly criterion, it's about maximizing the expected logarithmic returns - which computes as $$frac{1}{n}sum_{t=1}^{n} log(frac{wealth_t}{wealth_{t-1}})$$ This correctly weighs losses, since summing in log-space is equivalent to multiplying in regular-space: even just one complete loss bankrupts my. Kelly Jr. The idea was derived from an American scientist John L. Let gt = Xt / Xt − 1 be the gain obtained after the t -th bet. Computing and following an exact decision tree increases earnings by $6. In the one asset two valued payo case, the optimal Kelly wager is the edge (expected return) divided by the odds. It is suboptimal in the long run. 02%. The formula is: Kelly fraction = edge / odds. scientific gambling method ), is an effective strategy in every sense of the word. was born in Corsicana, Texas on December 26, 1923. The calculus is rather simple. Risking 2% does not mean buying with 2% of capital. But in a horse race, how do you decide which set of outcomes are favorable to bet on? It's tricky, because these wagers are mutually exclusive i. 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. It was proposed by John Kelly in the 50’s who at that point was working for AT&T’s Bell Laboratories. The Kelly Criterion is a bet-sizing technique which balances both risk and reward for the advantage gambler. Wettrechner und Quotenrechner - Überprüfen Sie Ihre potenziellen Gewinne auf den Akkumulatoren mit unserem Wettrechner, Quotenrechner, Akkumulator berechnen, Lucky 15, Each Way, Doubles, Trebles und mehr. Here, the formula is F = W – [ (1-W) / R] W = Probability of success. If we’re high-frequency traders, we may want to think twice before betting on this game. If they allow the customer to bet too big in the start they might be able to win and wipe them out in one go, but forcing customers to use small bets ensures that profit approaches the expected value, which for all games is tilted in the casino's favor. e the value available) and the size of your bankroll, so as to minimise risk and. In your example, you propose to reach a specific rate of return. e. ROTANDO and EDWARD O. 36 n. Kelly Criterion (kCrit) = ((odds - 1) * (1 - winP)) / (odds - 1) 'odds' is the Decimal form of the American odds after conversion. This paper presents a model to address the uncertainty inherent in replacement problems, whereby a firm must select between mutually exclusive projects of unequal lifespans by applying the Kelly criterion (which is not well known to the engineering economics community) within a binomial lattice option-pricing environment. f * is the fraction of the current bankroll to wager, i. The formula is as follows: Where: K % = The. 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. W T statistics Half Kelly Full Kelly Double Kelly T riple Kelly Mean ( W T ) 1. obj. The Kelly criterion maximizes the expected value of the logarithm of wealth (the expectation value of a function is given by the sum, over all possible outcomes, of the probability of each particular outcome multiplied by the value of the function in the event of that outcome). Library "FunctionKellyCriterion" Kelly criterion methods. The use case of the Kelly criterion is to determine the optimal size of your capital to put at risk, where the profit you're expecting to make is linearly related to that size. With hand waving and basic math you can also use it to help guide your investment decisions. P – odds of winning. I therefore recommend using the more sophisticated generalised Kelly Criterion wherever possible as it is superior to the simplified Kelly Criterion. rate of wealth. In most gambling scenarios, and some investing scenarios under some simplifying assumptions, the Kelly strategy will do better than any. The Kelly Criterion is a mathematical formula used to determine the optimal amount to bet based on the edge you have over the sportsbook. Bet calculator and free betting calculators to determine payouts. 05. Kelly came up with a betting system which optimizes bankroll growth based upon known odds and a definite payout. When investors maximize their relative wealth, the Kelly criterion is. 10/2. Let’s do the maths. R = Historical Average Win/Loss ratio. From Wikipedia, the free encyclopedia. . The Kelly criterion: exploiting favorable bets and the stock market In many ways this is my favorite topic to talk about. Conclusion. how much to bet; b is the net odds received on the. The Kelly Criterion is defined as ( from Wikipedia ): For simple bets with two outcomes, one involving losing the entire amount bet, and the other involving winning the bet amount multiplied by the payoff odds, the Kelly bet is: where: f * is the fraction of the current bankroll to wager, i. So you first need to decide your bankroll size and the length of time you’ll be using the Kelly method. Maybe we’d rather not have optimal growth. You can find these same numbers in the image above, and the Kelly Criterion Formula expresses it as follows: (0. B=2-1=1. With this we can calculate the optimal Kelly leverage via f = μ / σ 2 = 0. Keep in mind that this is a high percentage and the ideal amount you should bet is 3% of your bankroll or less. In his post on the Kelly criterion, Zvi notes that full Kelly is only correct if you know your edge and can handle the swings. The Kelly’s formula is : Kelly % = W – (1-W)/R where: Kelly % = percentage of capital to be put into a single trade. 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 same principle would work for any investment with an expectation of being profitable. He came of age during World War II and spent four years as a flyer for the Naval Air Force. The Kelly criterion is a formula used to determine the optimal size of a series of bets in order to maximize wealth. 4. While the Kelly Criterion calculator defaults the multiplier to 1, you’re encouraged to adjust the multiplier based on your preferences. 077 / 0. At +100 52. The win probability (P) is calculated as the. Thorp later applied this formula to the Blackjack poker and then to the global financial markets. Step - 2: Calculate the probability of each outcome. 05. 52 -1 = 0. For standard Kelly betting, set the fractional Kelly betting value to 1. 6 ⋅ 1. Let’s say we wager x. The Kelly Criterion is a powerful tool that can help sports bettors maximize their profits and minimize their risks. 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. 5 if you want to wager 50% of the stake recommended by the Kelly. Use our Kelly Criterion Calculator to determine the optimal amount for a series of wagers. significant leverage) or more for a position. 75 -x) +2x = 5. It does not use caution or assign value to risk. you can win. 890. The formula is as follows: f = the fraction of the bankroll to bet. 1, 2. Since the variance in heads up will always be 1 than the formula is easily applicable to HU SNGs. This gives a win probability (P) of 0. Results. 1 chance of winning -- kelly & net odds around 0. f ∗ = p (b + 1) − 1 b. 6) = 0. 10, you can calculate your edge as 2. This formula determines the optimal % of your account that you can bet to get the most profitable outcome in the long run. , which relates to the long-term growth of capital. Kelly Criterion Example. The Kelly Criterion (a. The Kelly criterion can easily be extended to uneven payoff games. Sie geht auf den Wissenschaftler John Larry Kelly jr. An. It is one of the few betting strategies. Thorp used the Kelly Portfolio to produce 20%. Assume a quarter Kelly stake on 2 wagers at +100 odds with a 55% chance of winning. This type of situation is common in horse racing, where. 3 – [ (1 – 0. The formula is therefore suggesting that 20% of the portfolio be stake 20% of your bankroll. The simplified Kelly Criterion has some potential flaws and can give some head-scratching results which are explained in the article above. The below formula is for multiple games at the same time. We also know from the graph that if𝑥𝑥≠0. This value should be in decimal format (e. It is widely applied to sports betting and casino gambling. The Kelly criterion for the stock market. Gruss Betting Assistant has a spreadsheet functionality that lets you place bets using your own variables and information from the live market, which is what we've used here to not only. so basically Kelly is exactly what I wrote above, and then then exp/log and end up maximizing the mean of the $log(1 + f u)$ in the exponential. Effectively manage your bankroll with this sports betting tool. Gain of Positive Outcome: Enter the potential gain of a positive outcome. Another problem with the Kelly criterion is it sees as the goal maximizing a particular function of terminal wealth. 25%. 80 the investment at least doubles, with 0. It can then tell you the optimal amount you should invest in each trade, given the strategy and your personal forex trading record. 6) = 0. The only way a player can ever gain an edge over the casino in blackjack is through the use of basic strategy and card counting. 077 / 0. And the most common method they use to figure that out is the Kelly criterion. 4 = 1. , which relates to the long-term growth of capital. 33% of your bank roll, or 8. The multiplier is normally set to 50%, for an aggressive betting strategy set it to 100%. Wettrechner und Quotenrechner - Überprüfen Sie Ihre potenziellen Gewinne auf den Akkumulatoren mit unserem Wettrechner, Quotenrechner, Akkumulator berechnen, Lucky 15, Each Way, Doubles, Trebles und mehr. 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. Kelly came up with a betting system which optimizes bankroll growth based upon known odds and a definite payout. A key thing that they miss, is that the log is only defined if. The left-hand side of the equation, f*, is the percentage of our total wealth that we should put at risk. Which has a 40% chance if they match would have continued going exactly as before, since. Kelly criterion staking approach aims to maximize your winning and protect your capital in losing runs. To emphasize this connection, we refer to this optimal allocation as the Kelly criterion henceforth. The calculator will tell you whether or not you should be betting and how much to stake. By using the Kelly criterion formula, you can make informed decisions about the optimal size of your bets or investments to maximize long-term growth. I'm trying to figure out the best way to scale my bets and I've come across the standard Kelly Criterion posts and while it seems logically to be the best there is another bet scaling practice that appears to outperform the Kelly. To arrive at the final number, you first have to take a look at your last 50 trades. Hence, the Kelly criterion can be very risky in the short term. The strategy maximizes the entropy and with probability one outperforms any other strategy asymptotically [3]. In general, the Kelly strategy gets an expected value of 100 ⋅ 1. Kelly studied at the University of Texas at Austin and earned a PhD in Physics in 1953. I intuitively think about probability in terms of r, not b. Add the odds quoted by the. This leads us to the optimal betting amount called the kelley criterion: f∗ = pb − qa ab f ∗ = p b − q a a b. For example, if you have $10,000 in your trading account, you can risk up to $670 per trade to optimize your account growth. The equity balance. There is a 60% chance of a winning a coin flip. Disclosure. the Kelly Criterion to the stock market. The role of Kelly value in game result prediction. R: Number of streaks in the series. and the second part is the optimization of that strategy through Kelly criterion. The Kelly strategy puts 60% of its money down, instead. 4450% on each, and the expected growth is 0. Thorp. pyplot as plt import decimal as d # Probablility of winning. Chopra and Ziemba (1993), reprinted in Section 2 of this The Kelly Criterion is a formula used to bet a preset fraction of an account. Introduction to Kelly Criterion Kelly’s formula is a theoretical benchmark for deciding the appropriate position size when investing, trading or gambling. I risk 2k. Suppose player A wins b units for every unit wager. According to the Kelly criterion, the probability of getting a return of -5 or less in this example is only 5. Kelly Criterion mathematical equation takes into account. This betting method was originally developed in the 1950s and was quickly applied to gambling and financial investing. 45)/ (2. W = Dollars won per dollar wagered (i.