Linear Interpolation Calculator

This calculator will determine the missing coordinate of a data point when the coordinates of two surrounding data points are known.
Fill in values for x1, y1, x3, y3, and then either x2 or y2 (but not both).
If x2 is known, then either (x1 < x2 < x3) or (x1 > x2 > x3) must be true.
If y2 is known, then either (y1 < y2 < y3) or (y1 > y2 > y3) must be true.

x1 =	y1 =
x2 =	y2 =
x3 =	y3 =

Example

You discover an 8/5 Jacks or Better game with a progressive jackpot for getting a Royal Flush, and you want to determine how large the jackpot needs to be in order for the game to be a break-even game. You analyzed the return of the game using a 4,000-coin Royal Flush, which is 97.2984%. You also analyzed the game using a 10,000-coin Royal Flush, and the return for that paytable was 100.8229%. It is now possible to estimate the value that the Royal Flush needs to be by using the following values:

x1 = 4,000	y1 = 0.972984
x2 = (blank)	y2 = 1.000000
x3 = 10,000	y3 = 1.008229

This calculates a value of 8,599 coins. Due to the nature of video poker - the fact that strategy is involved - the return is not going to be exactly 100% with 8599 coins; it is actually 99.9590%. Using this new number we can interpolate again by using the following values:

x1 = 8,599	y1 = 0.999590
x2 = (blank)	y2 = 1.000000
x3 = 10,000	y3 = 1.008229

Which gives a value of 8,665 coins. Analyzing the paytable with a Royal Flush worth 8,665 coins gives a return of 99.9996%. The actual break-even point is 8,666 coins, which returns 100.0002%. Using interpolation to estimate the correct number of coins can reduce the number of times you need to analyze the paytable, as opposed to guessing or trial-and-error. There are many other uses for linear interpolation.