To draw a 5th card or not to draw?

My instincts tell me to never take a 5th card.
In this case the count is 0 in a 4/6/8 deck game and my total is 12 to 16, I haven't drawn a 10 yet. My calculations say that I have a less than 3% chance of dodging that bullet ( 4/13 to the 5th power = .00275 ). Drawing 5 cards out of a full suit of cards and not catching a 10 is about 1 in 361, seem like long odds to me. This also doesn't take into account the other cards that will bust the hand depending on exactly what my total is.
It seems sound but without proof it's just a hunch and I'm not comfortable with that. My calculations could very well be dead wrong. But if correct, I suspect that this is closely related to the 5 Card Charlie.
Any help shedding some light on this would be greatly appreciated.

Once you have already drawn twice and have a four-card 12 to 16, your odds of avoiding a 10 on the third draw (fifth card) are (roughly) 9/13. What happened on the previous draws is irrelevant, except for the very slight increase in the ten density for the next draw.

If you flip a coin and get heads four times in a row, do you figure the chance of heads on the fifth flip is 1/2 to the fifth power or just 1/2?

Bottom line: Hit or stand on your hand according to the basic strategy of your holding and the dealer's upcard, and don't worry about how many cards are in your hand.

Don

You don't have to decide on drawing 5 cards the moment you start playing your hand. Each draw is relatively independent based only on the cards still left in the deck, not on the cards you've already drawn.