We can solve this problem by writing down how much each person drinks as an infinite sum. $$ $$ I drink $\frac{1}{2}$ of the pint, then $\frac{1}{8}$, then $\frac{1}{32}$ and so on. Generally, this is $$ N_{\text{me}} = \sum_{k=0}^{\infty} \frac{1}{2^{2k + 1}}. $$ Likewise, you drink $\frac{1}{4}$ of the pint, then $\frac{1}{16}$, then $\frac{1}{64}$ and so on. Mathematically, this is $$ N_{\text{you}} = \sum_{k=0}^{\infty} \frac{1}{2^{2k + 2}} = \frac{1}{2} \sum_{k=0}^{\infty} \frac{1}{2^{2k + 1}}. $$ We do not need to evaluate these sums. We simply need to see that you drink half as much as me. From this, we can see that I drink $\frac{2}{3}$ of the pint and you drink $\frac{1}{3}$. So, the answer is $$ N_{\text{me}} = \frac{2}{3}. $$