Multi Armed Bandit Allocation Calculator

Work out multi armed bandit allocation instantly with clear inputs, formula shown and shareable results.

About Multi Armed Bandit Allocation Calculator

An epsilon-greedy bandit sends a fixed exploration share uniformly across all arms and the remainder to the current leader. Regret is what exploration costs: the conversions an oracle that always played the best arm would have won, minus what the bandit actually earns. Compared with a fixed A/B split, a bandit cuts regret sharply because losing arms stop receiving half the traffic.

Formula

Epsilon-greedy allocation

explore traffic = total x epsilon, split evenly across arms; exploit traffic = total - explore, all to the leader; regret = oracle conversions - expected conversions

Worked example

With the default values below, Multi Armed Bandit Allocation Calculator returns Traffic served by the best arm of 92,500. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number of armsaccepts 2–100: 4
Total traffic to allocateminimum 1: 100,000
Best arm conversion rateaccepts 0.01–100 %: 12 %
Traffic reserved for explorationaccepts 0.1–100 %: 10 %

Results

Traffic served by the best arm: 92,500
Exploration traffic per arm: 2,500
Expected conversions: 11,775
Conversions lost to exploration (regret): 225

Step by step

1Values used
2Epsilon-greedy allocation
3Traffic served by the best arm= 92,500
4Exploration traffic per arm= 2,500
5Expected conversions= 11,775
6Conversions lost to exploration (regret)= 225

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

When is a bandit better than an A/B test?

When the goal is to maximise reward during the experiment rather than to obtain a clean unbiased estimate of each arm's effect. Bandits complicate statistical inference.

Why do bandits struggle with delayed conversions?

The allocation update needs feedback. If conversions arrive days later, the bandit reallocates on incomplete data and can lock onto an arm that only looks good early.