The skill card is the last card on the flop in hold'em, more commonly referred to as fifth street or the river card. Calling it the skill card is something players do when multiple hands are turned over, and someone basically needs to get lucky. In order to win, the player behind must hit one of his outs to win the pot. Usually the outs are outnumbered by the cards that can come that favor the leader.
Let's take a look at that math though, because sometimes the expectation of that decent skill card can be surprisingly weak or strong. Since you know at this point there are six known cards to you including the two hole cards and the four community cards, that leaves forty-six unknown cards. Your job is to know how many of those 46 cards will help you, how many will not help you, and in some cases, how many will help you AND your opponent.
Let's take for example if you have an open-ended straight draw where you are holding T9 and the board shows J82. That means any queen or seven is going to make your straight and very likely the best hand. Since there are 4 queens and 4 sevens left unseen in the deck you have 8 help cards of the 46 left. You only get one chance to hit your card so that equates to 8 divided into 46 equals 0.1739 or 17.4% of the time, you will hit your card. To convert that to odds just take 100 divided by the percentile, then subtract 1. Use that number as a ratio to 1. So in this example it is 100 / 17.4 which equals 5.747 then subtract 1 and you come with 4.747 or in odds terms 4.75: 1.
Now let's take an example where the Skill Card has a much higher chance of appearing on the river. Remember in hold'em that if two players go to the river, they usually have some kind of hand, which means that on many of these showdown confrontations, a lot of outs may overlap for both players. You are holding JcTc And your opponent is holding KcQc, the community cards are 9c8dAc and the Jh. Now you definitely have some outs here as you ponder shoving all-in. You feel any Ten, Seven, Queen or club will win, in case he calls you with presumably, top pair. But those outs are absolutely overlapping as any club is going to make him a better flush and a Ten will make him the nut Broadway straight.
In this situation you are playing for him not to hit a card, because in fact you are a clear favorite here. Let's take a look at his "Skill Card" chances though as they are now more significant than you may have thought before he turned over his hole cards. There are 7 clubs left in the deck, 3 non-club Tens, and 3 Kings.
So let's say everything goes in and turned up before the skill card shows. He then sees he actually has 13 outs, not the 18 he might have hoped for because 2 more clubs are gone and the 3 remaining queens will not help you, not him. Even so 13 help cards divided into 44 unseen cards left is a 29.55% chance of hitting. Now you might think that sounds good for you, and over the long term those are excellent odds. However, if you get into a huge pot or tournament situations where a lot is riding on this hand, his 30% can be a huge short term loser for you.
So in the end, beware the skill card and watch for duplicate outs by envisioning why your opponent is STILL in the hand and what kind of hand he could be holding that may very well be close to your hole cards too.