birdhouse run

Bronze Dagger Crabbing

The Gemstone Crab finally lets me do what I always wanted to do: hit big crabs without having to worry about other people. It has really low requirements too; as long as you can get to western Varlamore, you can hit the big crab.

How long would it take to get to 99 attack/strength, from level 1, with just a bronze dagger?

How often can you hit the crab?

You can hit the crab continuously until it burrows away, which happens after 1000 ticks (10 minutes) of hitting the crab. After it burrows away, there is approximately 28 ticks (16.8s, which I timed myself) until it respawns in its other location.

A bronze dagger can hit once every four ticks (2.4s). That means you get an uninterrupted set of 250 hits per crab rotation. In total, including the downtime, you can hit the crab 24.32 times per minute.

How hard can you hit the crab?

How much damage you do depends on your accuracy and your max hit, so we need to find those out. The wiki has a useful guide on how max hit works.

Let's call max hit h. Thankfully at level 1 we don't have access to potions, prayers, or void armour, so the calculation is made much easier. We do have a few options on how to use the dagger — it can be used with stab, lunge, or slash (ignoring the defensive "block" option). Stab gives a +3 bonus to attack level, while lunge and slash give a +3 bonus to strength level. The dagger has a +4 to hit when stabbing and lunging, and a +2 when slashing. For this reason, we'll never want to slash — we'll only ever want to stab or lunge depending on whether we want to get the attack xp and bonus or the strength xp and bonus. Also, the bronze dagger has a strength bonus of +3 (regardless of style).

Let s be your strength, and k be your attack style (k = 1 for lunge, and k=0 for stab). That gives:

h(s,k)=0.5+(s+8+3k)64+3640

which is linear in s.

How likely are you to hit the crab?

The crab has very poor defences, but poor defence is not no defence. Let the chance-to-hit be p[0,1], and the player's attack level be a. The attack roll pa is:

pa(a,k)=(a+8+3(1k))(4+64)

and the defence roll pd of the crab is a constant 640 based on its level 1 defence stat and lack of defence bonuses. p then depends on whether pa is greater or less than pd.

p(a,k)={1640+22(pa(a,k)+1)pa(a,k)>640pa(a,k)2(640+1)

This is surprisingly complicated.

Anyway, it's of interest to us to know what level a tips us from the first case into the second. When our attack style is lunge, pa(a,1)>640 when a=2. When our attack style is stab, pa is always more than 640. So unless we are lunging at level 1, we will always be using the former case.

How hard do you hit the crab, on average?

The average damage per hit d(a,s,k) is:

d(a,s,k)=p(a,k)(h(s,k)2+1h(s,k)+1)

How should we level to maximise crab damage?

As you can see, the average damage depends on both your attack and your strength level. If we stand there at level one strength, stabbing away with the bronze dagger, the damage per hit at each level is capped at h(1,0)=1, no matter our level. Clearly, we should level strength as well as attack. On the other hand, upgrading our attack will also increase our DPS. If we stand there at level one attack, lunging away with the bronze dagger, the damage per hit will increase but the chance-to-hit will be capped at p(1,1)=0.48, which is also terrible.

It is, however, apparently not that terrible. I wrote a simple dynamic programming algorithm to figure out the best choice of levelling, and you should lunge until 99 strength, and then switch to attack.

How long do you spend at each strength level?

From the wiki, the amount of experience required to reach level L from level L1 is:

(L1)=14L1+300·2L17.

Strength xp is four times the damage dealt, so our xp per minute is

xp/min=24.32×d(1,s,1)×4

So to get the time in minutes spent at level L, we just divide the former by the latter.

How long do you spend at each attack level?

Attack xp is gained in the same way as strength xp, so

xp/min=24.32×d(a,99,0)×4.

Also the crab has reduced xp rates

The crab has a 87.5% rate of xp gain, so we need to multiply any results we get by that.

Results

It takes just over 2 minutes to get your first strength level. It takes, to decent approximation, 1.5e0.083s minutes to get through any given strength level s. In total, you'll be hitting the crab for strength xp for 61769 minutes, or just under 43 days. About every ten levels, starting at level 4, you'll spend a bit less time on that level than the level before as your max hit goes up.

And then you have to do the attack levels!

You spend just under 30 seconds on your first level. There are no stepped increases to your damage output, so you never have any levels which are faster than the level before. The number of minutes per level is very well approximated by 0.21e0.097a. You'll spend just over 20 days doing attack training.

In total, you'd spend 63 days there.

If you instead just go to 95 in both, you'd only need to spend 43 and a half days, and you could use the rest for other activities.