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Experience Table: Difference between revisions
Added xp formulas.
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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. | 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. | ||
<math display='inline'>L-1</math> and level <math display='inline'>L</math> is <math display='inline'>\left\lfloor \frac{1}{4} \left( L-1+300 \left\lfloor 2^{\frac{L-1}{7}} \right\rfloor \right) \right\rfloor</math> | |||
The experience difference between level <math display='inline'>L-1</math> and level <math display='inline'>L</math> is <math display='inline'>\left\lfloor \frac{1}{4} \left( L-1+300 \left\lfloor 2^{\frac{L-1}{7}} \right\rfloor \right) \right\rfloor</math>. The table below show this experience difference for each level and also the cumulative experience from level 1 to level <math display='inline'>L</math>. | |||
! Level !! XP !! Difference | ! Level !! XP !! Difference | ||
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| colspan="3" | | | colspan="3" | | ||
|} | |} | ||
The formula needed to calculate the amount of experience needed to reach level L is: | |||
:<math>\mathit{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>\mathit{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. | |||
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