# Range

Win if the number is in your chosen range.

Range is a game where players bet on the outcome of a randomly generated number between 1 and 100. Players bet on whether the generated number will fall within that range or outside of it. Range offers players the flexibility of adjusting their odds of winning.

- First move is to select an integer, say N, from the range [5, 95]. You can either bet that the output will fall in the range [1, N] (roll under) or [N, 100] (roll over). Note that the output is always an integer between 1 and 100.
- The probability of winning, P, is given by

$P =
\begin{cases}
\frac{N}{100} &\quad\text{if rolling under }N\\
\frac{100-N}{100} &\quad\text{if rolling over }N \\
\end{cases}.$

- The house edge is 2% in Range. So the payout multipliers in case of winning are given by

$\text{Payout Multiplier} =
\begin{cases}
\frac{98}{N} &\quad\text{if rolling under }N\\
\frac{98}{100-N} &\quad\text{if rolling over }N \\
\end{cases}.$

- For example, if the player selects the range [1, 50], the payout multiplier will be x1.96.

In Range, players have complete control over the odds, allowing to adjust the risk they're taking.

Last modified 1mo ago