Complaining about the payouts

In this context, the p -value is the probability that a casino visitor would win 1 or fewer games on the slot machine in 8 games. This can be computed with the binomial distribution , assuming the slot machines are working as intended:

$\begin{aligned} p &= \binom{8}{0} \left(\frac{1}{5}\right)^0 \left(\frac{4}{5}\right)^8 + \binom{8}{1} \left(\frac{1}{5}\right)^1 \left(\frac{4}{5}\right)^7 \\ \\ &\approx \boxed{0.503}. \end{aligned}$

If the slot machine is working, then any customer would essentially have a $\frac{1}{2}$ chance to get the same payout in 8 games. Estelle can't really prove that the slot machine is broken!