User:Siddhant/Tangling Grasp Hit Calculation

[edit] Defining the Problem

[edit] Grasp + Claws

We have a 50% chance of hitting a person for 3 damage. Upon hitting the person, we grasp the person. Further claw hits will land at 60% probability, with a 20% chance of missing and losing the grip, and a 20% of missing and retaining the grip. We need to find the average damage inflicted on the person on a long run.

[edit] Grasp + Bite

We have a 50% chance of hitting a person for 3 damage. Upon hitting the person, we grasp the person. Further bites will land at 40% probability, infilicting 4 damage. We also have a 30% chance of missing and losing the grip, and a 30% of missing and retaining the grip. We need to find the average damage inflicted on the person on a long run.

[edit] Solving the Problem

We have two states, State 1 being the lack of tangling grasp and State 2 having tangling grasp active. We calculate the probability of staying in a state for n number of hits, and find the value to which it tends to.

[edit] Grasp + Claws

[edit] Grasp + Bite

[edit] Emperic Testing

This simple C# program was run multiple times to verify the above calculated values. The results were as expected.

Random r = new Random();
int hits = 0;
for (int i=0; i<Convert.ToInt32(textBox1.Text); i++)
{
	int nextRnd = r.Next(0,100);
	if (state == 1)
	{
		if (nextRnd < 50)
		{
			state = 2;
			hits += 3;
		}
	}
	else if (state == 2)
	{
		if (nextRnd < 60)
		{
			state = 2;
			hits += 3;
		}
		else if (nextRnd >= 60 && nextRnd < 80)
		{
			state = 2;
		}
		else if (nextRnd >= 80)
		{
			state = 1;
		}
	}
}
textBox2.Text = hits.ToString();

[edit] Conclusion

As we can see, the probability of Grasp + Claws tends an average DPS of 1.71429.
On the other hand, the probability of Grasp + Bite tends to an average DPS of 1.5625.

Thus, it's better to use claws to grasp and keep clawing.

[edit] Result for all Combinations

Well, I decided to go the full monty and finish all the possible combinations of Tangling Grasp and n skills. They are compiled here. The xls on which I did all the calculations will be put up on my site soon.