My favourite training video up to this day is by Joe Hachem and it is called: "Odds, Outs and Probabilities".

The feature that most helped me in understanding some things like "bad beats" or wrong calculation of pot odds, was the section regarding "hidden" outs. I think that most of us inexperienced players tend to forget these.

Being a mathematician myself, the calculation part was rather easy for me, though in order to be accurate, you need to know the facts. So the concept of "hidden" outs and the concept of "discounted" outs were the actual "ghost in the machine" for me. I think that it will help me improve my game and be more accurate in my calculations regarding whether it is worth to follow a hand or throw it right away.

Recently I lost my seat at a tournament in this way:

I was holding J10. Flop was QJ10, giving me two pair and the last opponent in the game was holding KQ. I thought his outs were the two remaining Queens, the three remaining Kings, and the eight remaining Aces and Nines. Thus he had 13 outs at the flop and all the rest were mine including the remaining two Jacks and two Tens, that gave me a monster. The colors were not an issue at this hand.

Alas, turn was a Three, improving my odds a great deal more, but the river was another Three, giving my opponent two pairs, namely Queens and Threes who were a stronger hand than my Jacks and Tens. THAT I never had in mind as "outs". Although the probability of the same card appearing in turn AND river is relatively small*,  in this case it made a huge difference.

What do you think about it?

*It actually is 10(1/49 x 1/4