Experience Table

From Melvor Idle
Revision as of 21:49, 24 March 2021 by Auron956 (talk | contribs) (Add anchor for table)

Note: Enabling "Virtual Levels" in the Settings will show the player if they would be on a level higher than 99, even though this gives no benefits.

The experience difference between level [math]\displaystyle{ L-1 }[/math] and level [math]\displaystyle{ L }[/math] is approximately [math]\displaystyle{ \left\lfloor \frac{1}{4} \left( L-1+300\times 2^{\frac{L-1}{7}} \right) \right\rfloor }[/math]. The table below shows this experience difference for each level and also the cumulative experience from level 1 to level [math]\displaystyle{ L }[/math].

The formula to calculate the amount of experience needed to reach level [math]\displaystyle{ L }[/math] is:

[math]\displaystyle{ \text{Experience} = \left \lfloor{\frac{1}{4}\sum_{\ell=1}^{L-1}}\left\lfloor{\ell + 300\cdot2^{\ell/7}}\right\rfloor\right\rfloor }[/math]

If the floor functions are ignored, the resulting summation can be found in closed form to be:

[math]\displaystyle{ \text{Experience} \approx \frac{1}{8} \left( {L}^{2} - L + 600 \, \frac{{2}^{L/7}-2^{1/7}} {{2}^{1/7}-1} \right) }[/math]

The approximation is very accurate, always within 100 experience but usually less than around 10 experience.