If I have
T7 and the flop is
T 3 K, how many outs would I have?
Would it be 2 out (2xT), or 5 outs (2xT, 3x7), or some other number?
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Board K T 3
You have T 7
Some people call an out a card to improve and others a card to improve and likely be ahead.
Middle pair is likely ahead and you don't need any outs.
If you are behind to a pair of kings then you have 5 outs.
If you are in the pot with T 7 then no reason to put your opponent on KK or TT as if so you should not even be in the pot and you have a blocker on the T. KT maybe but again you have blocker on the T so not likely.
The definition of an out is a currently unseen card, which if dealt will improve a player's hand such that it is likely to win. This last part: "likely to win" makes the term somewhat subjective, as determining which hands are likely to win in a given situation takes a varying degree of skill depending on the situation. It is not uncommon to refer to any card which improves your hand (without improving every other player's hand) as an out.
With that aside, in your specific example you have flopped middle pair with
T7 on a
KT3 board. The only cards which can improve your hand are a T or a 7, so as you proposed, many people would consider that you have 5 outs.
However, depending on your opponent's hand, some of these outs might be "dirty", such that they improve your hand, but you still lose to your opponent's better hand. For example if your opponent has
AT, then your T is a dirty out, as even hitting it will not be enough for you to have the best hand (unless you also hit a 7 for a runner-runner boat).