Trophy-taker's

Trophy-taker's

Description?
3% chance per rank a slain creature will add zero kills to its Slayer assignment; 2% chance per rank it will add 2 kills.
Release date	25 January 2016 (Update)
Gizmo type	Weapon, Armour
Maximum rank	5

Trophy-taker's is an Invention perk that has a chance for each kill on a Slayer assignment to count as either 2 kills or zero. The perk only affects assignments given by Slayer Masters and not normal or Special slayer contracts obtained from Markus outside of the Slayer Tower.

On average, trophy-taker's works out to be a net increase in assignment length. If however you do fewer kills than assigned you will receive fewer slayer points for completing the task.

Change in task length

Rank	No KC	Double KC	Avg change
0	0%	0%	±0.00%
1	3%	2%	+1.01%
2	6%	4%	+2.04%
3	9%	6%	+3.09%
4	12%	8%	+4.17%
5	15%	10%	+5.26%

When the perk doubles kill count, it prompts the message "Trophy-taker's perk: this kill has added double to your Slayer task tally." When a kill does not count, it prompts, "Trophy-taker's perk: this kill did not contribute to your Slayer task tally."

Calculation

The effect of trophy-taker's on task length can be summarised as follows (where $R$ is the rank of the perk):

• Chance of a kill counting 0: $R\times 3\%$
• Chance of a kill counting 2: $R\times 2\%$
• Chance of a kill counting 1 (as normal): $100\%-R\times 5\%$

This can be combined to give the gross effect of the perk:
$100\%-R\times 3\%+R\times 2\%=100\%-R\times 1\%$
i.e. a 1% per rank task length increase. For example, with rank 5 trophy-taker's, a task of 100 will, on average, have 5 remaining after 100 kills.

However, trophy-taker's will also work on the additional kills generated by the perk - from the example above, the 5 remaining on the task will also get a 5% increase, and so on. This means the net effect calculation is infinite, and best represented as a series:

$Increase = \sum_{n=1}^\infty (0.01R)^n$

This converges when $|R|<100$, which is true for all of our possible values. If you substitute in the possible rank values (1–5), you will get the results in the above table.

Sources

Material		Rarity	Perk ranks with X materials
			1	2	3	4	5
	Crystal parts	Common	0	1	1–2	1–3	1–4
	Spiked parts	Common	0	1	1–2	1–3	1–4
	Powerful components	Uncommon	1	1–2	1–3	1–5	1–5
	Variable components	Uncommon	1	1–2	1–3	1–5	1–5

Suggested gizmos

Gizmo layout	Possible perks
	Trophy-taker's 1–5 Genocidal Other possible perks: Flanking Fatiguing Committed Bulwark Blunted Taunting Junk Food
	Trophy-taker's 1–5 Bulwark 1–3 Other possible perks: Genocidal

Trivia

• • Even though the patch notes on 22 February 2016 implied that this perk works with Slayer contracts, this is not the case.