Freeplay Value Calculator

Determines the risk-free real dollar profit that may be obtained from betting and hedging a freeplay of given size.

Inputs

  • Freeplay Size: The freeplay notional size in dollars
  • Freeplay Line: The line at which the freeplay is bet (US or decicmal)
  • Hedge Line: The line at which the freeplay is hedged

Outputs

  • Hedge Bet: The dollar amount wagered on the hedge to extract risk-free value
  • $ Profit: The risk-free profit in real dollars obtained from the freepla bet and hedge
  • % Profit: Dollar profit as percent of freeplay notional size.

Example:

Let's say that a book offers you a $200 freeplay which you bet at +200 and hedge -215, You'd enter $200 into the "Freeplay Size" box, +200 into the "Freeplay Line" box, and -215 into the "Hedge Line" box.

When you click "Calculate" you see that the proper amount for the hedge bet would be $273.02 and your locked-in profit would be $126.98. This means that you would have captured 63.49% of the notional ($200) value of the freeplay.

Now compare that to the same $200 freeplay, bet at -110 (entered into the "Freeplay Line" box) and hedged at +120 (entered into the "Hedge Line" box). After clicking "Calculate" you see that the proper hedge bet under these circumstances would be $82.64 and the locked-in profit would then be $99.17. This means that you would have captured 49.59% of the notional value of freeplay.

The conclusion which could then be drawn from this is that betting a freeplay at +200, and hedging at -215 would be a better usage of the freeplay than betting at -110 and hedging at +120.

Multivariate Kelly Calculator

Calculates Kelly stakes for bets on up to either 15 simultaneous events or 15 mutually exclusive outcomes of a single event.

Inputs/Outputs

  • 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 ∞ 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 κ>0 is U(x;κ)=(1-1/κ)*x(1 - 1/κ) for κ&ne1;, and U(x;κ)=loge(x) for κ=1. This implies dU/dx=x(-1/κ) for all κ > 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 nth bet will be in US or decimal odds.
  • US/Decimal Odds:
    Odds for the n bet. The decimal odds on any given bet may not be less than the edge on that bet plus 1.
  • Win Probability/Edge Odds Selector:
    Indicates whether input for the nth bet will be as win probability or edge. For any given bet the following inequality must hold: 1 < decimal odds ≥ edge + 1.
  • Win Probability/Edge:
    Win probability/edge for the nth 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 the following inequality must hold: -100% ≥ 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.

Parlay Calculator

Calculates fair parlay odds.

Inputs

  • Odds Offered: The odds on which the parlay in question is offered (only necessary to detrmine premiums)
  • Line Set: The line set charged in cents (-110/-110 => 20 cents) Select "user" to define markets per bet (only necessary to determine mathematical odds and premium)
  • Number of Games: Number of distinct underlying bets represented by parlay
  • Game N Line: Line offered on straight bet# n (also enter line on opposite side of market if "user" selected for "Line Set")

Outputs

  • Mathematical Odds: The theoretical odds that would imply zero vig on the parlay
  • True Parlay Odds: The odds implied by the underlying bets
  • Premium Paid Over Mathematical Odds: Total vig charged on parlay (negative number would imply player edge)
  • Premium Paid Over True Parlay Odds: The additional amount paid by player as percentage of parlay amount over and above that implied by the underlying bets (a negative number would imply the parlay was offered at a discount)

One Variable Poisson Calculator

Calculates win probabilities and odds for Poisson-style proposition bets based upon an underlying win percentage

Inputs

  • Expected Average: The number of expected occurrences of the event (any positive number)
  • Proposition: The number of occurrences specified in the terms of the bet (any non-negative integer or integer plus a half)

Outputs

  • Odds of: Describes bet terms
  • Percentage: Probability of bet winning
  • Money Line: Fair odds (zero-vig) on bet

Example:

Let's say a book is offering up a prop bet on an event you to believe to be Poisson -- let's say the number of 3-point attempts made by the Knicks in a particular game. The line is over 15.5 -105 under 15.5 -115.

You think that the based on historical averages the expected number of Knicks 3pt attempts is actually 15.2. Is the under bet positive expectation?

Solution:
  • Select "One Variable" radio button
  • Enter 15.2 into "Expected Average" text box
  • Enter 15.5 into "Proposition" text box
  • Click "Calculate"
  • We see that the probability of hitting the under ("Less than 15½") is 54.7611%, corresponding to a fair money line of -121.05
  • Since you'd only be laying -115 on the bet your edge would be positive. (How positive? Your edge would be 54.7611% * 100/115 - 45.2389% = 2.3794%)

Two Variable Poisson Calculator

Inputs

  • Event A Expectation: The number of expected occurrences of the first event (any positive number)
  • Event B Expectation: The number of expected occurrences of the second event (any positive number)
  • Spread: The number of occurrences of event A added to or subtracted from event A occurrence total for comparison to event B (any integer or integer plus a half)

Outputs

  • Odds of: Describes bet terms
  • Percentage: Probability of bet winning
  • Money Line: Fair odds (zero-vig) on bet

Example:

Let's say a book is offering up a prop bet on a combination of events, each one of which you to believe to be Poisson and independent -- let's say the number of 3-point attempts made by the Knicks in a particular game versus the number of 3-point attempts made by the Nets in a different game. The line is Nets -1½ -110, Knicks +1½ -110.

You think that the based on historical averages the expected number of Knicks 3pt attempts is 15.2, and the expected number of Nets 3pt attempts is 17.0. Is the Nets -1½ bet positive expectation?

Solution:
  • Select "Two Variable" radio button
  • Enter 15.2 into "Event A Expectation" text box
  • Enter 17.0 into "Event B Expectation" text box
  • Enter 1.5 into "Spread" text box
  • Click "Calculate"
  • We see that the probability of hitting the Nets -1½ ("A +1½ < B") is 52.0527%, corresponding to a fair money line of -108.56
  • Since you'd have to lay -110 on the bet your edge would be negative. (How negative? Your edge would be 52.0527% * 100/110 - 47.9473% = -0.6267%)

Reverse Bet Calculator

Calculates maximum win/risk amounts and situational results on a reverse bet.

Inputs

  • Reverse Type: Denotes whether reverse bet is of type If Win Only (implying pushes terminate the remainder of the given IF bet) or Action (implying pushes do not terminate the remainder of the given IF bet).
  • Notional Bet: Notional dollar amount of reverse bet
  • Number of Games: Number of games included in reverse bet
  • Game N: Line on event# N and event results (WIN, PUSH, or LOSS).

Outputs

  • Max Win: Maximum possible dollar win on reverse bet
  • Total Risk: Maximum possible dollar loss on reverse bet
  • Situational Result: Profit or loss on reverse bet given actual event results

Round Robin Calculator

Calculates maximum win/risk amounts and situational results on a round robin bet.

Inputs

  • Notional Bet: Notional dollar amount of round robin bet
  • Number of Games: Number of games included in round robin bet
  • Parlay Size: Number of games included in parlays and whether that number constitutes a maximum (At Most) or an exact figure (Exact).
  • Game N Line/Result: Line on event# N and event results (WIN, PUSH, or LOSS).

Outputs

  • Max Win: Maximum possible dollar win on round robin bet
  • Total Risk: Maximum possible dollar loss on round robin bet
  • Situational Result: Profit or loss on round robin bet given actual event results

Scalp Value Calculator

Calculates total value attained (positive or negative) from a completed multiway scalp and calculates bet size on each outcome to fully smooth results

Inputs

  • Number of Outcomes: Number of distinct possible outcomes non-push outcomes of the event (the number of horses in the race)
  • Outcome 1 Bet: The bet to be placed on the first outcome
  • Outcome N Line: The line offered on event# N

Outputs

  • Outcome N Bet: The bet that would need to be placed on event# N to fully smooth results (i.e., so that the monetary result from each of the possible outcomes are equivalent)
  • Total Bet: The sum of all bets placed on all outcomes
  • $ Profit: Dollar profit (or loss) from completing scalp
  • % Profit: Profit (or loss) as percent of total bet (if all bets take place at the same book this negative number would corresponds to the vig charged by that book)

Streak Calculator

Determines the probability of losing a streak of a given number of wagers over the course of a series of wagers of specified length.

Inputs

  • Series Length: The size of the streak of lost wagers
  • Streak Length: The size of the streak in number of wagers
  • Loss Probability: The probability of losing any given wager

Output

  • Streak Probability: The probability of a streak of losses of length specified in the "Streak Length" text box occuring over a series of wagers as specified in the "Series Length" text box.

Example

Q: If you place 500 wagers per betting season, each losing with probability 46%, what is the likelihood of losing 10 or more wagers in a row at some point during the season?

A: Enter 500 in the "Series Length" text box, "10" in the "Streak Length" text box, and 47% in the "Loss Probability" text box. Clicking "Calculate" we see that over a stretch of 500 wagers, a bettor who wins with probability 54% has a 10.677% probability of losing 10 or bets in a row.