# Kelly Calculator

The Kelly Criterion is a famous formula developed by its name-sake John Kelly Jr and is used by many a handicapper and blackjack player. It is an effective way to manage your bankroll and keep you in check.

There is more information below on how to use the tool.

The top sportsbooks below offer great odds to get the best out of your betting strategy.

## More Information

## Inputs

**Event Type Selector:**

Either simultaneous independent events (as in several distinct games) or mutually exclusive outcomes (as in a single event that can have one of several winners, e.g., a horse race or the American Idol competition).**# Events/Outcomes:**

The number of either simultaneous independent events or mutually exclusive outcomes.**Consecutive Series:**

The number of times that this set of bets is to be *sequentially* repeated. This is included in order to determine expected and median bankrolls over multiple trials. (For example, if the user expects that every Sunday he’ll have 5 betting opportunities and wanted to determine bankroll expectations over the course of a 17-week NFL season, he’d set “# Independent Events” to 5 and “Consecutive Series” to 17).**Kelly Multiplier:**

The true Kelly multiplier such that 1 implies full Kelly, 0.5 implies half Kelly, 0 implies total risk aversion, and 8 implies total risk neutrality. Note that because this is the “true” Kelly multiplier, the n-Kelly stake will not necessarily be n×full Kelly stake. (Mathematically speaking, the utility function for a Kelly multiplier of ?>0 is U(x;?)=(^{?}/_{(?-1)})*x^{1 – 1/?} for ??1, and U(x;?)=log_{e}(x) for ?=1. This implies ^{dU}/_{dx}=x^{-1/?} for all ? > 0). Currently, this is only implemented for independent events, for mutually exclusive events, the Kelly multiplier is hard coded to a value of 1.**Starting Bankroll:**

The starting bankroll prior to the first bet being made. A value of “1” or “100%” will yield outcome stakes and expected profit/growth as percentages, while any other input will be treated as a dollar figure yielding outcomes and single period expectations in dollar terms. If dollar input is used then the number of decimal places in the input determine the number of decimal places in teh output (so a starting bankroll of “$10,000” would yield whole dollar outputs, while a starting bankroll of “$10,000.000” would yield output precision to a tenth of a penny).**US/Decimal Odds Selector:**

Indicates whether input for the n^{th} bet will be in US or decimal odds.**US/Decimal Odds:**

Odds for the n^{th} bet. For any given bet, decimal odds = edge + 1.**Win Probability/Edge Odds Selector:**

Indicates whether input for the n^{th} bet will be as win probability or edge.**Win Probability/Edge:**

Win probability/edge for the n^{th} bet. Inputs are in percentage terms, so a value of “5” would correspond to 5%. The sum of win probabilities for all mutually exclusive events may not total to more than 100%. For any given bet, edge = decimal odds – 1.**Calculate Kelly:**

Calculates Kelly stakes and expectations. Note that every additional variable increases calculation time by a factor of 4, so processing times for a large number of variables can be quite long.

## Outputs-Inputs

**Stakes:**

The text area displays the Kelly-optimal stakes for singles and parlays of constituent bets (for mutually exclusive events optimal parlays sizes will always be zero and so are not displayed). Stake output format will be as specified in “Starting Bankroll” text box. Stake sizes may be edited (in all tabs except the “All” tab) so expectations may be recalculated for a user specified set of (suboptimal) stakes.

## Outputs

**Expected Profit/Growth:**

These boxes display expected profit and growth (format as specified in the “Starting Bankroll” text box) from a single set of bets. (To be precise, expected profit corresponds to the arithmetic average profit per set of bets were the set repeated an infinite number of times with bet size held to a constant dollar amount, and expected growth corresponds to the geometric average growth per set of bets were the set repeated an infinite number of times with bet size held to a constant percent of bankroll).**Expected Bankroll/Median Bankroll:**

These boxes display the expected mean and median bankrolls after a number of series of bets equivalent to the value in the “Consecutive Series” text box.**Calculate Expectations:**

This button calculates expectations after the user has made modifications to stake sizes in the above text area.

## Example

Let’s say you’re confronted with 5 bets on football sides at -110, all of which you expect to win 55% of the time, and you wanted to calculate the growth maximizing optimal bet sizes and expectations. You also wanted to determined both your expected and most likely bankroll after 17 weeks betting similar opportunities. You start off with a bankroll of $15,000.

Set the event type selector to independent events, the # of events to “5”, consecutive series to “17”, starting bankroll to $15,000.00 (the two places after the decimal point will yield results to the nearest penny). The US Odds on all 5 bets would be -110 and the win probability would be 55%.

After clicking the “Calculate Kelly” button, you see that the optimal bet size for each of the 5 singles would be $657.93, for each of the 10 2-team parlays would be $38.29, for each of the 10 3-team parlays it would be $2.23, for each of the 5 4-team parlays it would be $0.13, and for the 5-team parlay it would be $0.01.

We see that this corresponds to expected profit of $207.39 and expected growth of $103.70. After repeating these bets each week over the course of a 17-week NFL season, you’d expect a bankroll of $18,943.85. Half the time your bankroll would be greater than $16,863.89, and half the time it would be less than $16,863.89.

If you decided you didn’t want to bet any parlays of more than 2 teams, you’d set the stake sizes to zero for each parlay of 3 or more teams, and click the “Calculate Expectations” button. We see that this reduces expected profit by $3.66, expected growth by $0.04, expected bankroll after 17 weeks by $77.20, and median bankroll after 17 weeks by $0.74. It’s left for each user to make hiw own determination as to whether he deems the reduction in number of bets placed worth the reduction in expectation.

## Kelly Criterion Calculator

**Results**

## Featured Sportsbooks

## Kelly Criterion Calculator

The Kelly Criterion helps you calculate the optimal amount you should wager when there is a difference between the true odds and the given odds. **A mathematician called John Kelly Jr. developed it during his time at AT&T’s Bell Laboratories in Texas**, and it was later used for blackjack and card counting. It can help sports bettors manage their bankrolls effectively, but it is fiendishly complex, so this Kelly calculator does the hard work for you.

## What is the Kelly Criterion?

Kelly developed a formula that helps you determine the bet size you should place in proportion to your bankroll and the perceived edge. The formula is f* = (bp – q) / b. Within this formula, the f is the fraction of your bankroll that you should bet, b represents the decimal odds, p refers to the probability of winning and q is the probability of losing. You can use it to decide how much of your bankroll to stake on a particular wager once you gain an understanding of the estimated winning percentage it carries

## Advantages of Using This Kelly Criterion Calculator

The Kelly calculator is one of our most popular bet calculators, because it makes a complex mathematical equation easy to understand. This sports betting calculator works out your ideal stake for 15 different bet options on simultaneous events, or 15 mutually exclusive outcomes of a single event. It allows sports bettors to manage their bankrolls in an optimal fashion. When used correctly, this Kelly calculator for odds and stake percentages can maximize your expected bankroll growth. It gives you an advantage over fellow sports bettors and **helps you find success at sports wagering in the long term**.

## How to Use the Kelly Calculator

Follow these steps to determine your optimal bet stake using the Kelly Criterion:**1.** Choose the event type – independent events, which refers to several different games; or exclusive outcomes, which refers to a single event that could yield various different winners, such as a horse race.**2.** Enter the number of events or exclusive outcomes, up to a maximum of 15.**3.** Enter the consecutive series, which refers to the number of times you will place this sequence of bets. For example, if you expect to place 5 bets per weekend throughout a 17-week NFL season, you would set “Independent Events” to 5 and Consecutive Series to 17.**4.** Choose the Kelly Multiplier. This is where you can enter a fractional Kelly or a Kelly multiplier. For standard Kelly Criterion betting, simply enter 1. A more conservative option would be a fraction, such as 0.5, whereas a bolder option would be anything above 1.**5.** Enter your starting bankroll. You can enter a monetary figure, such as $1,000, or a percentage, such as 1% or 100%, to inform you how much of your bankroll you should bet in relation to the amount you wish to win.**6.** Choose either US odds or decimal odds for the Kelly Criterion.**7.** Enter the odds for each bet option and the Kelly calculator will tell you the implied win probability, or the edge.**8.** Click “Calculate” to see the results.

The Kelly Criterion Calculator will then tell you the optimal stake for each single bet and for parlays. You will learn your expected profit and growth after the first betting set, and after consecutive betting sets. You can also learn the ideal bet size for parlays, which is helpful for anyone serious about using proper bet amounts and probability strategy.

## An Example

Let’s say you plan to bet on four different teams to cover the spread at odds of -110 each weekend over the course of the 17-week NFL regular season. You have a bankroll of $1,000 for the season, and you want to use the standard Kelly Criterion, with US odds as opposed to decimal odds. **You would then enter the following into the Kelly Criterion Calculator:• Event Type: Independent Events• Number: 4• Consecutive Series: 17• Kelly Multiplier: 1• US Odds of -110 in each of the four boxes that appear, and you will see that the probability is 55%**

You will then receive your Kelly Criterion results after you hit “Calculate”. In this example, you would see that the optimal size stake for each single bet would be $186. It also recommends two-team parlays featuring the various picks at $3 each. If you do not wish to place certain parlays, you can change the bet amount to $0 for each of them. In this example, you would expect to earn $11 in profit after the first betting set, and growth of $6. After 17 consecutive betting sets, you would have an expected bankroll of $1,205 and a median bankroll of $1,098, according to the Kelly Criterion bet cal.

## Who Should Use the Kelly Criterion Calculator

All sports bettors and casino bettors should consider using the Kelly Criterion before deciding how much to bet on each pick. **It is great for horse racing fans, as you can enter the number of horses in the race and the odds on each runner, and it will tell you an implied probability and the amount you should ideally bet on your chosen horse or horses**. The Kelly Criterion is also really useful for all sports bettors, from novices to pros.

The Kelly Criterion brings a much more sophisticated level of strategy to choosing your bet size each time, rather than simply risking different amounts each weekend. It leaves less to chance and represents a more methodical approach to proceedings. However, it can be complicated to work it all out yourself. You have to convert US odds to decimal odds, and work out the probability yourself. This can take up lots of your time, which could be better spent making astute betting picks and finding the best available odds. It also leaves more scope for errors to creep in, so it is best to leave the hard work to our calculator rather than leaving it to chance. You will then be presented with the ideal wagering strategy and probability of success over the course of the season.