[turaho]

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The reason is that you may take it down right there.

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I think you have a 0% chance of all three opponents folding to a single turn bet.

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If you miss on the river you're likely beaten, so a bet allows you a bit of fold equity right now. You've been the aggressor, so you have that edge.

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If you don't hit on the river, you're absolutely beaten, unless you think all your opponents (including the one who bet into you as the preflop raiser) can't beat K high. Betting this turn also means inevitably betting the river and hoping everyone else folds since your hand has little showdown value.

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With this many players in, I'd prefer to bet it and either take it down or build a bigger pot for myself should I hit the hand. The free card play is a great tool, but I think in this particular situation you have great equity with plenty of opponents who will pay you off.

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You have 8 clean outs to the nuts (four aces, four nines). Your overcards are worth about 3 outs. 11 outs gives us a little less than 25% pot equity. So even if you bet and all players call, your bet is not even EV neutral.

In a situation like this, I would take the free card every time. At nano-limits, opponents take the craziest hands to show down. There's no way you're winning this hand unless you hit on the river.