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I don't know how the house edge is actually implemented at dice sites (anyone care to explain?)
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It is very simple, the site just set your probability to win to make your EV always be (1- House edge %)*bet size.
For example if you are playing a x2 bet in a 0.5% edge site, you will win the bet if the roll is under 49.75. (1-0.5% = 49.75%*2)
But if you are playing in a 1% edge site, you will win the bet if the roll is under 49.5. (1-1% = 49.5%*2)