When betting on Primedice you have the opportunity to win a jackpot by rolling the number 77.77 twice in a row. The jackpot prize is an amount of bitcoin which steadily increases until the jackpot is won. When the jackpot is not won for some time the prize can get very large, to the point where betting on Primedice is statistically expected to be profitable.

Below we calculate

• Your chance of winning the jackpot.
• How high the jackpot needs to be for positive expected value betting?
• Optimal betting strategy to profit off the jackpot.

## What’s the probability of hitting the jackpot?

There are 10,000 possible numbers you can roll from 00.00 to 99.99.

77.77 is only 1 of those so you have a 1 in 10,000 chance of rolling it, which is a 0.0001% chance. You have to multiply that to roll it twice, so you get

`0.0001 * 0.0001 = 0.00000001`

or another way to put it, the number of expected rolls.

`10,000 x 10,000 = 100,000,000`

That’s a 1 in 100,000,000 chance!

## When does the jackpot make Primedice betting profitable?

TLDR; It needs to be over 10,000฿ to be profitable to bet for, which will never happen.

Oh well, we have better news about the Nitrogen dice jackpot which does sometimes get so big you can bet for it profitably, and you have a better chance of winning it, as we detailed in our mathematically profitable dice betting blog.

The Primedice jackpot becomes profitable when the amount you will win from hitting the jackpot exceeds the expected losses from the rolls required to hit the jackpot. The share of the jackpot you will win is either 1%, 10% or 100%, depending on the size of your bet. Your expected losses from each dice roll are the size of your bet multiplied by Primedice’s edge of 1%. So the jackpot is profitable when:

`jackpot × share > expected_rolls_to_hit_jackpot × bet × 0.01`

The share of the jackpot you will win is:

Nakul Shah

Author

In 2016, I worked on my first client to help write a white paper for a crypto and blockchain project they were building, and started delving deeper into blockchain and distributed ledger technology.

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