And this is a case where the real pronunciation of many words is different from the standard spelling because it's a song sung very casually quoting the words of someone who might not have a lot of education and so it fits his character and (very importantly) the flow of the song better. You wouldn't normally write those words that way but these are song lyrics and that's how they are sung and it wouldn't work well with full standard pronunciation.
You've got to know when to hold 'em
Know when to fold 'em
In the first line he actually gives "You've got to" standard pronunciation, and does not say it as "You gotta" because that fits the rhythm better. But for "hold them" and "fold them" he says "hold 'em" and "fold 'em".
And throughout the song, -ing words all end in -in'. "When you're sittin' at the table." That matches the character and his language better, too.
(He also says "a-starin' out the window".)
These are appropriate contexts for those kind of contractions. Song lyrics can do what they want, especially when quoting speech. But in normal text, in a normal paragraph, you wouldn't do any of that.