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Late surrender is probably the least well-known rule of blackjack.  While the four options everyone knows about are hit, stand, double down, and split, there is a fifth option in which you surrender your hand after receiving your inital two cards and after the dealer has checked for blackjack (surrendering before that check is early surrender, which is very very very rarely offered).  The dealer ends your hand, as if you had busted, but instead of the house getting your entire bet, they only get half.

This is a tricky thing.  In a normal hand of blackjack (outside of surrendering), you can lose your bet, retain your bet (push), or double your bet.  You want to surrender only when you will win the hand you have been dealt less than 25% of the time.  Why?  Lets say that probability tells us you will win a certain hand exactly 25% of the time.  So, 25% of the time you double your money, and 75% of the time you lose all your money.  (25% * 2) + (75% * 0) = a 50% return of your money--exactly what surrendering gives you.

In a game of blackjack with standard table rules (dealer hits on soft 17, six decks, you can double after you split), the following are the hands (and the ONLY hands) you will want to surrender on:

A hard 17 when the dealer is showing an ace.
A hard 16 other than a pair of eights when the dealer is showing a 9, a 10, a picture card, or an ace.
A hard 16 that is a pair of eights when the dealer is showing an ace.
A hard 15 when the dealer is showing a 10, a picture card, or an ace.

"Hard" simply means that your hand does not contain an ace--although it might not seem like it, having an ace and a six is a substantially better hand than having a ten and a seven and so you would not want to surrender in the former case.  Similarly, having a pair of eights is better than having a ten and a six, and so you will want to surrender the pair in less situations.

Many casinos will not allow surrender, or if they do, it may only be available in their high roller room.  They might tell you it's to not confuse the average player with uneccesary options, but it's really just to increase the house's chance of winning.  The house will also tell you never to surrender, but they're completely wrong and just trying to take your money anyway, so who are you going to trust, them or me?  I thought so.  On average, surrendering correctly during one full hour of blackjack will save you half of one bet you would've otherwise lost.  It may not seem like a lot, but it adds up.  So, always be sure to ask your friendly dealer if surrender (and other quirky options, like the ability to draw multiple cards after splitting aces) is available at the table.  Even if it's not, it will establish you to the dealer as a player who's worth their salt and make for a better gaming atmosphere.

Oh, and if you get a blank look from your dealer because he doesn't know what surrendering is, I highly suggest you find another table--or preferably another casino.

For more information about blackjack and how to (almost) beat the sytem, see Pyrogenic's excellent writeup under How to improve your chances of winning at blackjack.

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