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I thought the bonus had a lower house edge... when I was playing it to clear, I just bet the bonus.
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You are correct, the bonus has a lower house edge but i believe a higher variance.
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The normal game has a 3.37% house edge but because you are able to fold bad hands this means the element of risk is 2.01% so you will lose less compared to the pair plus bonus bet.
Read this for a full explanation:
http://wizardofodds.com/gambling/houseadv.html