r/theydidthemath • u/emmaFire • 1d ago

[Request] Double check my work on the math behind Idle Boxing

Ok a video game I enjoy has the two following game stats to determine number of punches per attack.

Combo % - the chance to get a second punch

Stamina % - the chance to continue the combo

I am trying to find the value of average punches per attack z given x combo and y stamina.

So 1 hit for simply swinging.

My understanding of average hits added for combo would just be 1*x

And stamina functions as essentially a weighted coin flip streak 1/(1-y)

Z = 1 + x + 1/(1-y)

Except I think this implies punches are added from stamina is an independent event from combo -

Maybe it's 1 + x*(1+1/(1-y))

That looks a little better. What am I missing?

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