3 & 4 Blackjacks in-a-row bonus -- how does it effect the house edge?

Edit: Darn it, the subject should ask, "how does it affect the house edge", not "effect." ...and I can't edit the subject. :( Anyhoo, poor English aside...


Greetings.

A local casino is running a promo right now where if a player gets three blackjacks in a row at their spot, they're paid a $500 bonus. If they get a fourth, it's a $10,000 bonus (I think they get the $500 as well). If the dealer gets a blackjack at the same time as the player, the player still gets credit for that blackjack for their "in a row" bonus, although they push their wager.

I was able to use the blackjack calculator on the Wizard of Odds site to determine the game's current edge (without the bonus), but I don't know how to factor in these bonuses. I guess I'm curious as to how much this promo decreases the house edge.

For what it's worth, the minimum bet is $5, and it's a 6-deck shoe game, dealer hits soft 17, player can double after split, can double on any two cards, re-split up to 4 hands, can resplit aces, no surrender option, and blackjack pays 3-to-2.

Thanks for any insight as to how to determine the effect on the house edge!

That's a pretty good promo considering you get the same bonus if you are betting $5 or $25 per hand. That seems like it should give you a player advantage at $5 bets. Promo benefit should be close to 2%.

Card counting doesn't help with the promo since it is a fixed cash amount. It isn't high enough that sophisticates can take advantage of the system.

Is it at Canterbury Park ?

I think I have drawn four 21s in a row, but never four blackjacks. Have probably seen other players do it.

About 1 in 10,000 for 3 in a row, I'm certain they would have a winner every day. They are probably hoping for only a single grand prize winner over the two week promotion (1 in 200K).

The odds of getting blackjack is 4.8265% for a single deck, down to 4.7451% for 8 decks. Assuming 6-8 decks and six players at the table, you can negate the effects of card removal.

The odds of getting 3 blackjacks in a row is therefore .047451 ^ 3 = 0.01068% with an expected value of $0.05089 (you must take away the 4th blackjack odds).
The odds of getting 4 blackjacks in a row is .047451 ^ 4 = 0.000507% with an expected value of $0.05079.

So the total EV of the promotion is $0.1016.

On a $5 table this is a 2.03% player edge.
On a $10 table this is a 1.02% player edge.
On a $25 table this is a 0.41% player edge.

So if this is a normal 3-2 blackjack game there is a player edge for bets up to about $15.

Must be at Canterbury. It's absolutely identical to their promo. Thank you for the number crunch, boymimbo. You have solidified my plans for the weekend:-)

Keep in mind that with almost 10,000 to 1 odds and at 80 hands per hour the likelyhood of you getting the bonus even with 24 hours of plays is still about 5 to 1, with the $10,000 at still 500 to one.

Good luck!!!

Quote: boymimbo

The odds of getting blackjack is 4.8265% for a single deck, down to 4.7451% for 8 decks. Assuming 6-8 decks and six players at the table, you can negate the effects of card removal.

Maybe This is discussed elsewhere and I've missed it, but why is that there is a greater chance for a B/J on a single-deck game than there is in a multi-deck game? There is the same ratio of Aces/10s in 1 deck as there is 100 decks right?

You are correct, but the difference accounts for the fact that the dealer will more often get blackjack as well when you do, since there are more Aces/10's in a multiple deck than in a single deck. This leads to more pushes/losses depending on whether you have a blackjack or not.

-B

Quote: toastcmu

You are correct, but the difference accounts for the fact that the dealer will more often get blackjack as well when you do, since there are more Aces/10's in a multiple deck than in a single deck. This leads to more pushes/losses depending on whether you have a blackjack or not.

-B

It is true that you will get more pushes in a multi-deck, but it's NOT why it's more likely for a player to get a blackjack.

The reason has to do with card removal and conditional probability. As an example, let's say you are first dealt a 10. In a single deck game, you now have 4/51 chance (7.84%) of hitting your Ace for blackjack. In an 8 deck game, you have 32/415 chance (7.71%). This is slightly less than in the single deck game. The reverse applies as well when you first get an Ace. Together, the effect is more blackjacks when playing single deck than multideck, regardless of what the dealer gets.

Assuming the player would get the $500 and $10,000 for four blackjacks in a row, I show every hand played is worth 10.44¢, after the first two seed hands, which can't win. So on a $5 bet, that would lower the house edge by 0.1044/5=2.09%. Close enough to the other answers. I think the difference is in whether the player gets to keep the first $500 if he hits four in a row.

Back to my original statement. It's a 1 in 10K shot at the $500 prize and EV is 2% at $5. It's a genuine promotion, and it's a player advantage, but they probably expect to only give away one $10K prize in the entire 2 weeks.

While it's a good promotion, and you were considering going anyway, it's an inducement. But I wouldn't sit there for hours trying for the prize.

Wow, great discussion.

Yes, it's Canterbury Park (as was linked to early in the thread), and yes it's 3-2 (as mentioned in my initial post). I believe that the player gets to keep the $500 if they hit the $10,000 (I haven't seen anything to the contrary).

I don't plan on camping out there to play -- I know it's a good play, but realistically I'm still playing at a loss unless I'm fortunate enough to actually hit one of the two bonuses. On the other hand, if I happen to be in the right place, right time... I've popped in for about three hours total over two days (and made $50 each time making mostly $5 bets) -- I imagine it'll be a zoo this weekend, but may try again.

For those who are nearby, you can combine this promo with an excellent promo they're running on Mondays -- play for two hours starting after 4:00pm and you're eligible to buy a steak or prime rib dinner for 10 cents. You have to have a player's card -- see the club desk for details.

The lady at my table last night had two in a row. The guy to her right who had been playing two hands dropped down to one hand. She would have hit the third one if he had kept playing two hands (ouch). (Of course, it could have gone either way -- it could have worked out that his dropping the hand could have gotten her the one she needed, too.)

If they're only hoping for one $10,000 winner, they need to hope nobody else hits it -- in the latest e-mail I got from them, they've already had one $10K winner. (Oh, also one of the dealers told me that she dealt four in a row a couple of days before the promo started -- bonus to that player, $0.)

Thanks all (and Wiz!) for the analysis of this.