$$\frac{2}{1}(\frac{1}{6}+\frac{1}{2})-1=F(1)$$
$F=\frac{1}{3}\approx 0.333333333$
$$2\left(\frac{1}{6}+\frac{1}{2}\right)-1=F\times 1$$
$$2\left(\frac{1}{6}+\frac{3}{6}\right)-1=F\times 1$$
$$2\times \frac{1+3}{6}-1=F\times 1$$
$$2\times \frac{4}{6}-1=F\times 1$$
$$2\times \frac{2}{3}-1=F\times 1$$
$$\frac{2\times 2}{3}-1=F\times 1$$
$$\frac{4}{3}-1=F\times 1$$
$$\frac{4}{3}-\frac{3}{3}=F\times 1$$
$$\frac{4-3}{3}=F\times 1$$
$$\frac{1}{3}=F\times 1$$
$$F\times 1=\frac{1}{3}$$
$$F=\frac{1}{3}$$
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