Do I need a win streak?
Python 3, 35 bytes

lambda w,n,p:-min(0,(w-p*n)//(1-p))

Try it online!
-4 bytes thanks to pajonk
Some simple math: if \$X\$ is the number of wins we need, then we have:
\$\frac{W+X}{N+X}\geq P\$
\$W+X\geq PN+PX\$
\$X-PX\geq PN-W\$
\$X(1-P)\geq PN-W\$
Since \$P&lt;1\$, then \$1-P&gt;0\$, so we can divide from both sides without division by zero or flipping the sign.
\$X\geq\frac{PN-W}{1-P}\$