"Free Ace" Blackjack bet How +EV is this?

[renodoc]

Local casino offers various prize tickets. One of them I highly desire is the "free ace". This allows you to play one hand of blackjack and get one card to go with your ace. Must be after a shuffle.

Obviously a big plus, right? How much of a positive expectation can one expect from this ticket? Thanks math geeks.

[Siegmund]

The exact EV is going to depend on the fine print in the rules. I assumed the following:

6-deck shoe, fleshly shuffled;
They don't actually remove an ace from the deck for you, just play your coupon as 25th ace;
You are allowed ONLY one card (no splits, 2nd hits, etc);
if you get a ten you DO get the 3:2 BJ payoff;
dealer hits soft 17.

I also made the simplifying assumption that dealer's hand was dealt from all 312 cards instead of only the 311 left after you took one - this will introduce errors in the last decimal place.

Under these assumptions, your hand will be:
BJ 4/13ths; 20, 1/13; 19, 1/13, 18, 1/13, 17, 1/13, 16 or worse, 5/13.
Dealers hand will be: 17, 13.3%; 18, 14.1%; 19, 13.6%; 20, 18.1%, 21 12.2% including 4.7% BJs; bust 28.6%.

You lose 40.1% of the time (4.75% of your 21s, 12.2% of your 20s, ..., 71.4% of your <17s);
You push 4.5% of the time (18.1% of your 20s, 13.6% of your 19s...)
You win a single bet 26.1% of the time (69.6% of your 20s, 56.1% of your 19s, ... 28.6% of your <17s);
You win a 3:2 bet 29.3% of the time (95.3% of your 21s)

For an overall expectation of -.401+.261+.439=.299 units with standard deviation 1.11 units.

If your 21s don't count as blackjacks, that cuts the EV in half. Changes in the other rules only mess around with the last digit. Yes, a very nice comp indeed, if the table limits are high and you expect to play there enough to get several of these to even out the variance a bit.

[renodoc]

Excellent.

Its actually a single deck. I believe I can play the hand as I would any other: double down on any two cards, and split if I catch an ace (one card hit only). Other assumptions seem correct.

[pzhon]

As quoted on the Wizard of Odds (http://wizardofodds.com/askthewizard/blackjack-weirdrules.html):

<ul type="square">Our local casino hands out promotional coupons, which act as a first-card ace in blackjack. ... Do you know the overall expectation of having an ace as your first card?

According to Stanford Wong's 'Basic Blackjack' he says the player's edge given the first card is an ace is 50.5% (page 124). [/list]

[Siegmund]

If you're really allowed to do anything you want (hitting soft 16s, etc) after starting with an ace, as opposed to just getting "an ace and one card", I can certainly believe there'd be a large increase beyond 30%.

I should have been clearer in my post that changing THAT assumption made a big difference.

[Abbaddabba]

How do you get this "free ace"?

Do you have to be playing at the table for a given length of time?

Depending on what the conditions are, that could easily be exploited, unless they put an extremely low max wager on the free ace hand.

[renodoc]

You get a random card per day. Some of them are crap, but the table games cards are the best. Some of them will match your bet. The amount of the bet is stated on the card also. Some of the free ace cards are only for a $5 bet. The one I got yesterday was for $50. (Dealer was kind enough to drop a ten on me when I played it)

[Skipbidder]

[ QUOTE ]
How do you get this "free ace"?

Do you have to be playing at the table for a given length of time?

Depending on what the conditions are, that could easily be exploited, unless they put an extremely low max wager on the free ace hand.

[/ QUOTE ]

I used to get these from a riverboat casino on the Iowa/Illinois border. They mailed em to me. I'm not sure why, since I only played blackjack while waiting for poker tables to come up (and didn't give them my player card since I was usually wonging). I only gave them my player card while playing poker. There was no restriction on when you could use it or on what future action you got to choose when you had it, but the limit was something like a $25 bet (might have been $20). Other players at the table were frequently upset when I used the coupons.