# Experience

Experience, commonly abbreviated as exp or xp, is a measure of progress in a certain skill. It is obtained by performing tasks related to that skill. Experience can also be gained through other means, such as quests, the Book of Knowledge from the Surprise Exam random event, a lamp from the genie random event, certain mini-games, and lamps for completing parts of the Achievement Diary.

After gaining a certain amount of experience, players will advance to the next level in that skill, which can result in new abilities, and the chance to try more quests. The amount of experience needed for the next level is approximately 10% more than the last level. For example, 83 experience is required for advancement to level 2, while 91 experience is required for advancement to level 3.

A 10% growth factor may seem slow, but it expands rapidly to a total 13,034,431 experience needed for level 99. Level 85 requires nearly one quarter of the experience needed for Level 99 and Level 92 is nearly the exact halfway mark, requiring 6,517,253 experience. This clearly demonstrates the experience gap that grows rapidly at higher levels.

Each skill has a maximum amount of xp that you can receive: 200,000,000. After reaching this point, no more xp can be gained in that skill.

## Experience table

### Levels 1-99

The experience difference calculation is a function in the form of ${\displaystyle f(x)={\frac {\lfloor x-1+300*2^{\frac {x-1}{7}}\rfloor }{4}}}$,

where x is the level starting from 2.

Level Exp. Exp. Diff Level Exp. Exp. Diff Level Exp. Exp. Diff Level Exp. Exp. Diff
1 0 N/A 26 8,740 898 51 111,945 10,612 76 1,336,443 126,022
2 83 83 27 9,730 990 52 123,660 11,715 77 1,475,581 139,138
3 174 91 28 10,824 1,094 53 136,594 12,934 78 1,629,200 153,619
4 276 102 29 12,031 1,207 54 150,872 14,278 79 1,798,808 169,608
5 388 112 30 13,363 1,332 55 166,636 15,764 80 1,986,068 187,260
6 512 124 31 14,833 1,470 56 184,040 17,404 81 2,192,818 206,750
7 650 138 32 16,456 1,623 57 203,254 19,214 82 2,421,087 228,269
8 801 151 33 18,247 1,791 58 224,466 21,212 83 2,673,114 252,027
9 969 168 34 20,224 1,977 59 247,886 23,420 84 2,951,373 278,259
10 1,154 185 35 22,406 2,182 60 273,742 25,856 85 3,258,594 307,221
11 1,358 204 36 24,815 2,409 61 302,288 28,546 86 3,597,792 339,198
12 1,584 226 37 27,473 2,658 62 333,804 31,516 87 3,972,294 374,502
13 1,833 249 38 30,408 2,935 63 368,599 34,795 88 4,385,776 413,482
14 2,107 274 39 33,648 3,240 64 407,015 38,416 89 4,842,295 456,519
15 2,411 304 40 37,224 3,576 65 449,428 42,413 90 5,346,332 504,037
16 2,746 335 41 41,171 3,947 66 496,254 46,826 91 5,902,831 556,499
17 3,115 369 42 45,529 4,358 67 547,953 51,699 92 6,517,253 614,422
18 3,523 408 43 50,339 4,810 68 605,032 57,079 93 7,195,629 678,376
19 3,973 450 44 55,649 5,310 69 668,051 63,019 94 7,944,614 748,985
20 4,470 497 45 61,512 5,863 70 737,627 69,576 95 8,771,558 826,944
21 5,018 548 46 67,983 6,471 71 814,445 76,818 96 9,684,577 913,019
22 5,624 606 47 75,127 7,144 72 899,257 84,812 97 10,692,629 1,008,052
23 6,291 667 48 83,014 7,887 73 992,895 93,638 98 11,805,606 1,112,977
24 7,028 737 49 91,721 8,707 74 1,096,278 103,383 99 13,034,431 1,228,825
25 7,842 814 50 101,333 9,612 75 1,210,421 114,143

### Virtual levels

Level Exp. Exp. Diff Level Exp. Exp. Diff Level Exp. Exp. Diff
100 14,391,160 1,356,729 109 35,085,654 3,307,711 118 85,539,082 8,064,254
101 15,889,109 1,497,949 110 38,737,661 3,652,007 119 94,442,737 8,903,655
102 17,542,976 1,653,867 111 42,769,801 4,032,140 120 104,273,167 9,830,430
103 19,368,992 1,826,016 112 47,221,641 4,451,840 121 115,126,838 10,853,671
104 21,385,073 2,016,081 113 52,136,869 4,915,228 122 127,110,260 11,983,422
105 23,611,006 2,225,933 114 57,563,718 5,426,849 123 140,341,028 13,230,768
106 26,068,632 2,457,626 115 63,555,443 5,991,725 124 154,948,977 14,607,949
107 28,782,069 2,713,437 116 70,170,840 6,615,397 125 171,077,457 16,128,480
108 31,777,943 2,995,874 117 77,474,828 7,303,988 126 188,884,740 17,807,283
Max 200,000,000 11,115,260

## Formula

The formula needed to calculate the amount of experience needed to reach level L is:

${\displaystyle {\text{Experience}}=\left\lfloor {{\frac {1}{4}}\sum _{x=1}^{L-1}}\left\lfloor {x+300\cdot 2^{\frac {x}{7}}}\right\rfloor \right\rfloor }$

If the floor functions are ignored, the sum is merely a combination of arithmetic and geometric sums, and can thus be further derived into a closed-form continuous function with a positive real variable L (standing for level). The approximation rapidly approaches the original sum asymptotically. The function is as follows:

${\displaystyle {\frac {1}{4}}\left[{\frac {1}{2}}\cdot {L}^{2}-{\frac {1}{2}}\cdot L+300\cdot {\sqrt[{7}]{2}}\cdot {\frac {{2}^{\frac {L-1}{7}}-1}{{2}^{\frac {1}{7}}-1}}\right]+E\left(L\right)}$

Ignoring floor functions will result in an exceedingly minor error term, and as floor of real numbers is taken twice, once from the inner function of sum and once from the total sum, the error term E(L) is strictly bounded:

${\displaystyle 0\leq E\left(L\right)\leq L+1}$

According to these bounds the maximum error at level 99 would only be 100, whereas the actual error, 9.97, is even lower. The aforementioned bounds can be improved, although it is redundant with this low errors.

## Graphs

The experience required for each level can be graphed. Graphing the experience required on a linear scale shows that the experience required is essentially exponential.

Graphing the same data on a logarithmic scale shows that the function deviates from being exponential before around level 10.

## Trivia

Due to the exponential nature of experience needed for each level (for levels above 10):

• to level up 9 more times after levelling up once, it will take 15.25 times the xp needed for the initial level up.
• similarly for 19 more level ups, it will take 59 times the initial xp.
• similarly for 29 more level ups, it will take 176.768 times the initial xp. formula
• the xp needed to level up 11 times is not enough to level up even once 30 levels from now. formula
• After about level 20, where the exponential experience curve fits the best, the amount of total experience doubles every 7 levels. (i.e. Level 85 requires twice as much total experience as level 78, level 92 requires twice as much total experience as level 85, and level 99 requires twice as much total experience as level 92.)

After level 30, the general experience required to level up falls between 9-10% of your current experience. At mid to high levels of 55+, the experience needed to level up falls at around an average of 9.4% of current experience all the way to level 99.