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Experience Table: Difference between revisions
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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. | |||
<onlyinclude>The experience difference between level <math display='inline'>L-1</math> and level <math display='inline'>L</math> is approximately <math display='inline'>\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 display='inline'>L</math>. | |||
{| class="wikitable alternating-rows sticky-header" style="text-align:right;" id="xp_table" <!-- this ID is an anchor for incoming links --> | |||
! Level !! XP !! Difference | ! Level !! XP !! Difference | ||
! rowspan="26" | | ! rowspan="26" | | ||
| Line 137: | Line 136: | ||
| 75 || 1,210,421 || 114,143 | | 75 || 1,210,421 || 114,143 | ||
| colspan="3" | | | colspan="3" | | ||
|} | |}</onlyinclude> | ||
The formula | The formula to calculate the amount of experience needed to reach level <math display='inline'>L</math> is: | ||
:<math>\ | :<math>\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: | If the floor functions are ignored, the resulting summation can be found in closed form to be: | ||
:<math>\ | :<math>\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. | The approximation is very accurate, always within 100 experience but usually less than around 10 experience. | ||
{{Menu}} | {{Menu}} | ||
