The best strategy seen above was:

1) Flip a coin until \(max(P(\text{Cheater}|Heads=h),P(\text{Fair}|Heads=h)) \geq \max(\text{Threshold},\text{Random})\) and \( \text{number of flips} \geq n\)

2) If \(P(\text{Cheater} > P(\text{Fair}|Heads=h)\), choose "Cheater". If \(P(\text{Cheater} \leq P(\text{Fair}|Heads=h)\), choose "Fair"

where \(h\) is the number of times the coin flips heads, Threshold is set by the user (i.e., \(0.5 \leq \text{Threshold} < 1\), in my case \(\text{Threshold}=0.8\)), Random is a randomly generated number (\(0 \leq \text{Random} < 1\)), and \(n\) is a user set number of flips (in my case, \(n=12\))