What are the odds of cutting a "ten" card in cribbage?

What are the odds of cutting a "ten" count card (10, jack, queen, or king) playing 4-handed?

Odds on cutting a ten-card

Here's one way to look at it. In each suit of 13 cards there are four ten-cards. (10, J, Q, K). So the odds of any randomly-chosen card being a ten-card are 4 in 13, or roughly 1 in 3. Dealing out the hands does not change the distribution of ten-cards, so the chances of cutting a ten-card remain the same after the deal as before: 1 in 3.