# Treasure Trails/Rewards

 This section or article is incomplete and could do with improvement.Reason: Master clues/ReworkYou can discuss this issue on the talk page or edit this page to improve it.

This page is about the mechanics of how a Treasure Trail's rewards are determined and calculations from this to determine drop chances of each reward.

Most clues operate on a series of drop tables with associated chances to access. They start with an initial table which contains all the rewards common to all levels of trails - sweets, meerkats, god pages, etc - and a chance to enter the clue's rare table, containing all of the clue's specific rewards (some of which may be on subtables within the rare table).

The vocabulary used here can be confusing, so here are a number of definitions of terms used on this page:

• Droptable
A list of things that can be dropped and their associated chances. Can contain another droptable.
• (Droptable) slot
One of the things on the droptable. This may be an item or another droptable.
• Reward spot
A place on the clue reward interface which can contain an item. A clue generates at least 2 of these per reward. Each tier of clue has a minimum number of reward spots it will create, and then it will add 0-2 extra spots randomly.
If the same item is generated for multiple spots, they will combine into one stack (commonly occurs with runes), which may make a clue appear to generate less than it should.
• 1/x
The value given in the column is the x value in the 1/x. So a value of 15 in the column means the chance is 1/15, or 1-in-15.
• x SF
The value in the column has been rounded to x significant figures.
• Roll
Generate a random number in order to choose a droptable slot, or other number needing to be generated randomly. Each number is equally likely to occur, giving rolls a uniform distribution.
• Any text with a dotted underline has hover text with further explanation.

In order to calculate the per-clue chances, one needs to use a binomial distribution, taking the number of trials n to be the average number of reward spots of that clue tier, and p to be the per-spot chance of getting the items, then calculating the probability of receiving greater than zero of the item. In statistics notation:

{\displaystyle {\begin{aligned}X\sim &Bin(average\ reward\ spots,per-spot\ chance)\\&{\text{Find }}P(X>0)\\&=1-P(X=0)\end{aligned}}}

Most spreadsheet programs can do this natively. One can verify these values using a Wolfram Alpha query, such as this for barrows dye from a hard clue; in Microsoft Excel or Google Sheets, this is performed using =1-BINOMDIST(0,5,3/25600,true) (see documentation: Excel, Sheets).

## General mechanism

Each clue tier, when completed, first decides how many rewards are given. This is the minimum amount (2 for easy, 3 for medium, 4 for hard and elite), with the result of a 0-2 roll added. Since it is equally likely to be 0, 1, or 2, the average is 1, so the average number of rewards the clue will give is the minimum plus one.

Once the number of rewards are chosen, the rewards are generated. This is usually a series of rolls:

• The first roll is against the common reward table
• Most of the slots contain the 'common' rewards of the clue (runes, normal staves, normal gear, materials, etc); none of these are clue-specific rewards
• One slot leads to the global table, which contains god pages, meerkats, sweets, etc
• One slot leads to the rare table for that clue
• If the global or rare table is obtained, another roll is performed
• Depending on the result of the second roll, a third (or more) roll may be performed to determine precise rewards

## Global table

The table that all clues can pull rewards from (which includes god pages, meerkat pouches and scrolls, purple sweets, prismatic stars, etc) is positioned in the top level droptable for each clue tier. This means each clue tier has a different chance to access it.

If the clue doesn't generate a reward by the time it reaches its last reward spot, it will give an item from this table.

Biscuits have a cap of 200 - once this cap is met, further biscuit rewards are replaced by purple sweets.

## Easy

Easy clues generate a minimum of 2 reward spots and a maximum of 4, giving an average of 3 rewards.

## Medium

Medium clues generate a minimum of 3 reward spots and a maximum of 5, giving an average of 4 rewards.

The chance of getting each medium-clue-specific item is "around 1/250 per clue". In addition, the 5 animal masks share one droptable slot, as do the male/female variants of elegant clothing (2 per slot) and main-/off-hand briefcases. The pith helmet appears multiple times in the table.

If medium clues behave similarly to the others, one can deduce that there's around 70 slots in the rare table (by counting the rewards) and around 15 in the common table (by using '1/250 per clue' and rounding). However, as the mechanics were not expanded upon in the same way as hards and elites, further analysis will not be done.

## Hard

Hard clue rewards begin with a droptable with 16 slots. One of these enters the hard-clue-specific droptable containing 96 slots; this table is documented below. Of the top level droptable, some of the remaining slots leads to the all clues table, and the remaining 14 are assigned to general reward items (mahogany planks, rune equipment, etc). (Technically the top level table is much larger than 16, but simplifies to very close to 1/16 to access the rare table.)

Hard clues generate a minimum of 4 reward spots and a maximum of 6, giving an average of 5 rewards.

Notes
• All of the following items occupy one droptable slot on the rare table directly; a third roll is not performed
• The items grouped together are grouped for comparison only, they are not grouped in the table itself
Rare table
Item Droptable slots
occupied
Per-reward-spot
(1/x)
Per-clue approx.
(1/x)
Per-clue exact
5 SF
Any god-trimmed rune armour 15 total pieces:

15 102 21 4.78837%
Any specific part 1 1,536 308 0.32510%
Any trimmed rune armour 10 total pieces:

10 154 31 3.2131%
Any specific part 1 1,536 308 0.32510%
Any heraldic rune armour 25 total pieces:

25 61 13 7.8774%
Any specific part 1 1,536 308 0.32510%
Any trimmed dragonhide 4 total pieces:
4 384 77 1.2953%
Any specific part 1 1,536 308 0.32510%
Any enchanted part 3 total pieces:
3 512 103 0.97276%
Any specific part 1 1,536 308 0.32510%
Any vestment part 12 total pieces:

12 128 26 3.846%
Any specific part 1 1,536 308 0.32510%
Any blessed dragonhide 12 total pieces:

12 128 26 3.846%
Any specific part 1 1,536 308 0.32510%
Any cavalier 3 total pieces:
3 512 103 0.97276%
Any specific cavalier 1 1,536 308 0.32510%
Pirate's hat 1 1,536 308 0.32510%
Robin Hood hat 1 1,536 308 0.32510%
Amulet of fury (t) 1 1,536 308 0.32510%
Amulet of glory (t) 1 1,536 308 0.32510%
Top hat 1 1,536 308 0.32510%
Rune cane 1 1,536 308 0.32510%

The remaining 6 droptable slots each lead to a different subtable. These are discussed here and then the chances of each item follow in another table.

The animal mask droptable contains 3 slots, each assigned to an available animal mask (fox, unicorn, black unicorn).
The dragon mask droptable contains 3 slots, each assigned to an available dragon mask (green, blue, red).
3. Sack of effigies
The sack of effigies droptable has 30 slots; one of these is the sack of effigies, and the remaining 29 lead to another droptable. This table has 120 slots; one is the explosive barrel and the remaining 119 are coins (2,500)
4. Backstab table
The backstab droptable has 15 slots; one of these is the backstab cape, and the remaining 14 slots are coins (around 5,000).
5. Dyes
The dyes table has 10 slots; one of these is shadow dye, and the remaining 9 lead to another droptable. This table has 5 slots; one is barrows dye and the remaining 4 are coins (around 10,000)
6. Mega-rare
The 'mega rare' table contains 11 slots.
• The parts of the gilded rune set take 1 slot each (5 total)
• 4 slots are used by each potion set (1 slot each for 15 super energy, 15 super restore, 15 antifire, and 5 super 'sets' [attack, strength, defence])
• 1 slot is a starved ancient effigy (or 2,500 coins if 5 effigies are already owned)
• The final slot leads to another table. This final table has 12 slots, each occupied by a part of third age armour (mage, ranger, warrior sets).
• All of the following items are part of one of the above subtables and are not directly on the rare table; a third (and sometimes fourth) roll is performed to obtain them
Subtables
Item Per-reward-spot
(1/x)
Per-clue approx.
(1/x)
Per-clue exact
5 SF
1,536 308 0.32510%
Any specific mask 4,608 922 0.10846%
1,536 308 0.32510%
Any specific mask 4,608 922 0.10846%
Sack of effigies 46,080 9,216 0.010850%
Coins[hard 1] 5,000 from backstab table 1,646 330 0.30345%
10,000 from dyes table 2,133 427 0.23416%
Backstab cape 23,040 4,608 0.021700%
Barrows dye 8,533 1,707 0.058580%
Any gilded rune 5 total parts:
3,379 676 0.14788%
Any specific gilded 16,896 3,380 0.029589%
Any potion set 4 total options:
15 , 15 , 15 ,
or 5 of each of
4,224 845 0.11832%
Any specific potion set 16,896 3,380 0.029589%
Starved ancient effigy[hard 2] 16,896 3,380 0.029589%
Any third-age part 12 total:

16,896 3,380 0.029589%
Any specific part 202,752 40,551 0.0024660%
Notes
1. ^ Note that coins also occur elsewhere, in the common table.
2. ^ Replaced by 2,500 coins if 5 ancient effigies are already owned

## Elite

 This section or article is incomplete and could do with improvement.Reason: Blood dyesYou can discuss this issue on the talk page or edit this page to improve it.

Elite clue rewards begin with a droptable with 14 slots. One of these enters the clue-specific droptable containing 52 slots; this table is documented below. Of the top level droptable, some of the remaining slots leads to the all clues table, and the remaining 12 are assigned to general reward items (mahogany planks, royal dragonhide, etc). (Technically the top level table is much larger than 14, but simplifies to very close to 1/14 to access the rare table.)

Elite clues generate a minimum of 4 reward spots and a maximum of 6, giving an average of 5 rewards.

Notes
• All of the following items occupy one droptable slot on the rare table directly; a third roll is not performed
• The items grouped together are grouped for comparison only, they are not grouped in the table itself
Rare table
Item Droptable slots
occupied
Per-reward-spot
(1/x)
Per-clue approx.
(1/x)
Per-clue exact
5 SF
Any god-trimmed rune armour 15 total pieces:

15 48.5 10 9.8863%
Any specific part 1 728 146 0.68493%
Any dragonhide god armour 12 total pieces:

12 61 12.5 7.9745%
Any specific part 1 728 146 0.68493%
Any vestment part 6 total pieces:

6 121 25 4.0535%
Any specific part 1 728 146 0.68493%
Any animal staff 5 total pieces:
5 146 30 3.3872%
Any specific staff 1 728 146 0.68493%
Any dragon armour kit 8 total pieces:

8 91 19 5.3751%
Any specific kit 1 728 146 0.68493%
Fury ornament kit 1 728 146 0.68493%

The remaining 5 droptable slots each lead to a subtable. These are discussed here and then the chances of each item follow in another table.

The dragon mask droptable contains 6 slots, each assigned to an available dragon mask (black, frost, bronze, iron, steel, mithril).
2. Effigy
The effigy droptable has 5 slots; one of these is an effigy, and the remaining 4 slots are coins (around 20,000).
3. Prismatic star
The star droptable has 20 slots; one of these is a prismatic star, and the remaining 19 slots are coins (around 20,000).
4. Hard dyes
The 'hard dyes' table (so named as it contains the two dyes also available in hard clues) has 22 slots; one of these is shadow dye, and the remaining 21 lead to another droptable. This table has 11 slots; one is barrows dye and the remaining 10 are coins (around 10,000)
5. Third-age dye
The third-age dye table has 70 slots; one is third-age dye, and the remaining 69 lead to another droptable. This table has 40 slots; 1 is the sack of effigies, and the remaining 39 lead to yet another droptable. This final table has 20 slots; one is the backstab cape and the remaining 19 is a triskelion piece.
6. Mega-rare
The 'mega rare' table contains 51 slots.
• One of these slots leads to a second table containing the 5 slots, each assigned to one of the 5 parts third-age druidic
• The remaining 50 slots also lead to another table; this one contains 3 slots, each assigned to one of the 3 god bows
• All of the following items are part of one of the above subtables and are not directly on the rare table; a third (and sometimes fourth) roll is performed to obtain them
Subtables
Item Per-reward-spot
(1/x)
Per-clue approx.
(1/x)
Per-clue exact
5 SF

728 146 0.68493%
Any specific mask 4,368 874 0.11442%
Coins[elite 1] 20,000 from effigy table 910 182 0.54824%
20,000 from star table 766 154 0.65077%
10,000 from hard dyes table 839 182 0.54824%
Starved ancient effigy[elite 2] 3,640 728 0.13729%
Prismatic large fallen star 14,360 2,912 0.034336%
Barrows dye 8,389 1,678 0.059585%
Third Age dye 50,960 10,192 0.0098112%
Sack of effigies 29,542 5,909 0.016924%
Backstab cape 15,150 3,030 0.032999%
Crystal triskelion fragment[elite 3] 797 160 0.62550%
Any god bow 3 total:
743 149 0.67154%
Any specific bow 2228 446 0.22425%
Any third-age druidic part 5 total:
37,128 7,426 0.013466%
Any specific part 185,640 37,128 0.0026934%
Notes
1. ^ Note that coins also occur elsewhere, in the common table.
2. ^ Replaced by 2,500 coins if 5 ancient effigies are already owned
3. ^ Whichever part is not owned, in order.

## Master

### Obtaining

• Most sources of elite clues have a 1% chance of upgrading to a master clue instead, including monster drops, Treasure chest decoration, etc.
• After completing Pieces of Hate, the Skeletal horror has a 1/12 (8.33%) chance to drop a master clue instead of an elite clue.
• When opening clue reward caskets, the following chances apply to get a master clue:
• Elite: 1/5 (20%)
• Hard: 1/15 (6.66%)
• Medium: 1/30 (3.33%)
• Easy: 1/50 (2%)

### Initial rolls

Master clues always have 6 rolls.

Each roll begins with a 100/1400 chance of accessing the rare table, and will access the common table otherwise. If the rare table is missed, the numerator is increased by 25 up to a maximum of 175/1400. If tier 4 luck is equipped, the denominator is reduced by 1% to 1386. If the roll is sucessful, the numerator reverts to 100.[source needed]

The chances are summarised below:

Missed rolls Next roll chance Next roll chance (T4 luck)
Fraction Percent Fraction Percent
0 100/1400 7.14% 100/1386 7.22%
1 125/1400 8.93% 125/1386 9.02%
2 150/1400 10.71% 150/1386 10.82%
3 175/1400 12.5% 175/1386 12.62%

### Weighted average chance

The overall chance of a rare from a specific slot can be calculated by accounting for the scaling chance. It was later confirmed that this increased rare chance does carry over from one clue to the next.[1] For the sake of some simplicity in the calculation, the original chance of 1/14 is used. Tier 4 luck only adds a 1400/1386 modifier.

Because the increased chance carries over, we have a continuous loop through a system with 4 states.
State 0: your first ever roll, or your roll after a rare roll. Chance of a rare is 4/56 (or 1/14).
State 1: Bad luck mitigation (BLM) step 1. Chance of a rare is 5/56 (or 1.25/14).
State 2: BLM step 2. Chance of a rare is 6/56 (or 1.5/14).
State 3: Maximum BLM. Chance of a rare is 7/56 (or 1.75/14).

These states feed into each other. For example: from state 0 you can return to state 0 by rolling a rare, with a chance of 1/14, or you can reach state 1, with a chance of 13/14. You cannot skip steps, so reaching state 2 and state 3 from state 0 is impossible. This corresponds to the matrix: ${\displaystyle {\begin{bmatrix}4/56&52/56&0&0\\5/56&0&51/56&0\\6/56&0&0&50/56\\7/56&0&0&49/56\end{bmatrix}}}$

Because it is a continuous system we can use the fact that in a long distribution ${\displaystyle v_{\infty }P=v_{\infty }}$ We then solve for the steady state vector ${\displaystyle v}$. We first rewrite the equation, and factor out ${\displaystyle v}$, which leads to the equation: ${\displaystyle v(P-1)=0}$

In matrix multiplication an identity matrix I is the equivalent of 1. So we substitute that in, and we then rewrite the whole equation to: ${\displaystyle {\begin{bmatrix}a&b&c&d\end{bmatrix}}\times \left({\begin{bmatrix}4/56&52/56&0&0\\5/56&0&51/56&0\\6/56&0&0&50/56\\7/56&0&0&49/56\end{bmatrix}}-{\begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{bmatrix}}\right)}$

We can then solve for the variables ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$, and ${\displaystyle d}$, which give us the input to get a weighted average for the chance to roll a rare, given the chance of having different BLM numerators.

This weighted average is ${\displaystyle \left({\dfrac {392}{3663}}\times {\dfrac {4}{56}}\right)+\left({\dfrac {364}{3663}}\times {\dfrac {5}{56}}\right)+\left({\dfrac {357}{3663}}\times {\dfrac {6}{56}}\right)+\left({\dfrac {2550}{3663}}\times {\dfrac {7}{56}}\right)={\dfrac {835}{7326}}}$.

The number of master clues with at least one rare is then simply found by calculating the chance of getting nothing in 6 slots, then subtracting that from one. Thus the chance of a master clue having at least one rare is 51.62%, or 52.14% with tier 4 luck.

### Rewards

If the rare table is successfully rolled, you then roll between 1 and 42 to determine which reward is obtained. Each of the following occupies one slot of this table, giving them a 1/42 (2.38%) chance to be chosen.

The following continue with a 1/42 chance to be chosen, but then do additional rolls to determine specific rewards

### Simplified

While the reward tables above describe the full behaviour, it is usually easier to have a simplified 'flattened' table,as the full behaviour can be represented as just a simple chance.

• From rare table simply multiplies out the above table to be a 'flat' table
• After rare roll uses a 100 numerator
• Overall per clue uses the chances calculated in the #Weighted average chance section above
• Percentages are rounded to 4 significant figures to a minimum of 4 decimal places
Item(s) Chance from rare table Chance after rare roll Overall chance per clue
Normal T4 luck Normal T4 luck
Percent Fraction Percent Fraction Percent Fraction Percent Fraction Percent Fraction

Simple items (each)

2.3810% 1/42 0.1701% 1/588 0.1718% ≈1/582 1.6283% ≈1/61.42 1.6447% ≈1/60.80
1.1905% 1/84 0.08503% 1/1176 0.08589% ≈1/1164 0.8141% ≈1/122.8 0.8223% ≈1/121.6

Glasses (each)

0.7937% 1/126 0.05669% 1/1764 0.05726% ≈1/1746 0.5428% ≈1/184.2 0.5482% ≈1/182.4
Elemental battlestaff 2.3677% ≈1/42.23 0.1691% ≈1/591.3 0.1708% ≈1/585.4 1.6192% ≈1/61.8 1.6356% ≈1/60.8
Orlando Smith's hat 0.01323% 1/7560 0.0009448% 1/105,840 0.0009544% ≈1/104,781 0.009046% ≈1/11,055 0.009137% ≈1/10,944
Shadow dye 0.08503% 1/1176 0.006074% 1/16,464 0.006135% ≈1/16,299 0.05815% ≈1/1720 0.05874% ≈1/1702
Ice dye 0.1208% ≈1/827.5 0.008631% ≈1/11,586 0.008718% ≈1/11,470 0.08264% ≈1/1210 0.08347% ≈1/1198
Barrows dye 0.1554% ≈1/643.7 0.01110% ≈1/9011 0.01121% ≈1/8921 0.1062% ≈1/941 0.1073% ≈1/932
Third Age dye 0.02801% 1/3570 0.002001% 1/49,980 0.002021% ≈1/49480 0.01916% ≈1/5220 0.01935% ≈1/5168
Sack of effigies 0.03922% 1/2550 0.002801% ≈1/35,700 0.002829% ≈1/35,343 0.02682% ≈1/3729 0.02709% ≈1/3692
Backstab cape 0.07712 ≈1/1297 0.005509% ≈1/18,153 0.005565% ≈1/17,971 0.05274% ≈1/1896 0.05328% ≈1/1877
Blood dye 0.02646% 1/3780 0.001890% 1/52920 0.001909% ≈1/52391 0.01809% ≈1/5527 0.01827% ≈1/5472
Ancient effigy 0.4762% 1/210 0.03401% 1/2940 0.03436% ≈1/2911 0.3257% ≈1/307.1 0.3289% ≈1/304

Second-Age armour (each)

0.002646% 1/37,800 0.0001890% 1/529,200 0.0001909% 1/523,908 0.001809% ≈1/55,274 0.001827% ≈1/54,721

Second-Age weapons (each)

0.007937% 1/12,600 0.0005669% 1/176,400 0.0005726% 1/174,636 0.005428% ≈1/18,425 0.005482% ≈1/18,240
Re-roll token (master) (failed dyes) 2.0197% ≈1/49.5 0.1443% ≈1/693.2 0.1457% ≈1/686.2 1.3812% ≈1/72.4 1.3952% ≈1/71.7
Re-roll token (master) (failed Second Age) 1.5167% ≈1/65.93 0.1083% ≈1/923.1 0.1094% ≈1/913.8 1.0372% ≈1/96.4 1.0477% ≈1/95.5
Re-roll token (master) (overall) 3.5353% ≈1/28.3 0.2526% ≈1/395.9 0.2552% ≈1/391.9 2.4184% ≈1/41.3 2.4428% ≈1/40.9
200,000 (failed blood dye) 2.3545% ≈1/42.47 0.1682% ≈1/594.6 0.1699% ≈1/588.7 1.6102% ≈1/62.1 1.6264% ≈1/61.5
500,000 (failed Second Age) 0.8167% ≈1/122.4 0.05833% ≈1/1714 0.05892% ≈1/1697 0.5585% ≈1/179.1 0.5641% ≈1/177.3
Coins (overall) 3.1712% ≈1/31.53 0.2265% ≈1/441.5 0.2288% ≈1/437.1 2.1687% ≈1/46.11 2.31906% ≈1/45.65
Triskelion fragment (failed capes) 2.2366% ≈1/44.71 0.1598% ≈1/625.9 0.1614% ≈1/619.7 1.5295% ≈1/65.38 1.5450% ≈1/64.73
Triskelion fragment (failed effigy) 1.9048% 1/52.5 0.1361% 1/735 0.1374% ≈1/727.7 1.3026% ≈1/76.77 1.3158% ≈1/76
Triskelion fragment (overall) 4.1414% ≈1/24.15 0.2958% ≈1/338.1 0.2988% ≈1/334.7 2.8321% ≈1/35.31 2.8607% ≈1/34.96

## References

All data sourced from the following (now-expired Twitch VODs):

Highlight videos of the above streams are available on YouTube, however they don't contain all the content of the streams:

### Master clues

Master clues rates were released later, via the RuneScape website.

## Update history

The update history project is a work-in-progress – not all updates to this topic may be covered below. See here for how to help out!
• patch 26 February 2018 (Update):.
• Several existing Treasure Trail rewards such as hats, masks and shirts have been made available in F2P.
• Tweaks have been made to existing Treasure Trail drop tables, such as removing low-value seeds elite and improving coin values when failing to roll on certain rare rewards.
1. ^ Mod Shauny. Discord - Clue Chasers FC. 4 July 2019. "If for example (...) on the last 2 rolls you get 2 'bad tables' you carry over a +50 to the start of the next clue."*