The importance of redraws

A reasonable rule of thumb when contemplating an all in after the flop is that each out is worth about 4% equity. But, it may be important to keep in mind the redraws that your opponent has. Here are a couple of illustrative cases:

You have T♠9♠, with a flop of 5♥7♠8♠. You're contemplating calling an all in from an opponent.

Discounting your overcard outs entirely it looks like you have 15 outs: any spade, any jack or any 6. So, on the rule of thumb basis, you're actually a favourite on the hand and are delighted to call.

But, the two cases where your opponent has a set, or an overpair are actually quite different. When he has the overpair (assuming that it's not JJ) then if you improve you are practically certain to win the hand (particularly if he doesn't hold a spade). It turns out that in this case you are actually about a 57:43 favourite.

However, when he has a set, the odds are virtually reversed, and solely because of his redraws to a boat. With more than 40% equity it's still probably correct for you to call (unless the all in bet is much bigger than the pot), but don't be tempted to think that the two situations are equivalent.