Enter the discount rate, probability of success, and the value of the reward into the calculator to determine the Gittins Index.

Gittins Index Formula

The following formula is used to calculate the Gittins Index.

GI = (r + sqrt((r^2) + 4*r*(1 - p)*v)) / (2*(1 - p))


  • GI is the Gittins Index
  • r is the discount rate (decimal)
  • p is the probability of success (decimal)
  • v is the value of the reward

To calculate the Gittins Index, add the discount rate to the square root of the sum of the square of the discount rate and four times the product of the discount rate, the complement of the probability of success, and the value of the reward. Divide this sum by twice the complement of the probability of success.

What is a Gittins Index?

A Gittins Index is a numerical value used in decision theory and operations research to determine the optimal strategy in a multi-armed bandit problem. It is named after John C. Gittins, who developed the concept. The Gittins Index helps to decide which project or task to pursue when resources are limited and the outcomes are uncertain. It balances the potential reward from a project against the opportunity cost of not pursuing other projects. The project with the highest Gittins Index is considered the most valuable to pursue.

How to Calculate Gittins Index?

The following steps outline how to calculate the Gittins Index.

  1. First, determine the discount rate (r).
  2. Next, determine the probability of success (p).
  3. Next, determine the value of the reward (v).
  4. Next, gather the formula from above = GI = (r + sqrt((r^2) + 4*r*(1 – p)*v)) / (2*(1 – p)).
  5. Finally, calculate the Gittins Index.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

discount rate (r) = 0.05

probability of success (p) = 0.8

value of the reward (v) = 10