[Ribbo]

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KK7 you can give a free card with K7 in hand. K77 you cannot give a free card with K7 in hand. The difference should be apparant.

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What do you mean by this? Seems like the opposite is true.

Flop KK7, an opponent with a K can have as many as 9 outs to beat K7.

Flop K77, an opponent can have 2 outs with a a pocket pair greater than 7, 3 if they have A7 and we don't have an A, or 5 if they have pocket pair + A7, or they can have KK and have us crushed.

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On a flop like K77, pocket pairs 88 through QQ can beat you on the turn. They cannot on a KK7 flop, indeed you want them to catch up.