Re: looking for a bigger edge
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but the turn card is going to increase hero's equity far more often than it will decrease hero's equity in a 3-way pot.
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I suspect that only 2,9 and A increase value of his hand assuming he doesn't know if they drawing to overcards or to straight or simply have pocket pair. All other cards decrease his valued, cards from T to K as well as 3 and 4 decrease his value a bit (3-5%) and 8 or 7 decrease his value greatly.
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a hand that's losing will need to add twice as many outs, or obviously take the lead in order to decrease his equity. that means a pair will have to add a flush draw or a gut shot (and even a pair and gut shot will have less equity). if you consider the overall range of hands, I don't think it's possible for his equity to decrease on the turn, no matter what slides off
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