Help with a bet

I was in a local pub last night when the subject of Blackjack came up. The discussion revolved around the dealer's hand averaging 18.23. I stated that I would play a game with them if they would just give me an 18 every hand. My reasoning was that I would never bust, but the dealer WOULD! The bartender was fixing to close but took me up on the bet for tonight. His reasoning was that although I would never break, I could also get NO Blackjacks. Hmmm...

Rules: Single deck. Flat betting $5 per hand.

Who is gonna win this bet tonight? Any ideas?

If you use BS your average hand is stronger than 18. You'd better use BS and sometimes stand with 17, sometimes stand on 18, sometime stand on 19-21 and sometimes bust than having a guaranteed 18. If you don't take my word for it, check beyond counting p.8. Actually, even Revere mentions it in his book.Shark

Quark,

I think you're on the right side of the bet (or at least you're not gonna lose your house on this bet) if the rule is S17. I don't have access to the references Shark mentioned, but here's my reasoning:

First, the dealer's bust probability is close to 30% (I don't remember the exact number, but it's something like 29% or something for S17 rule?). For this 29% of the time, you ALWAYS win.

Second, if the dealer has Blackjack, then you'll ALWAYS lose, which is around 5%.

Second, when the dealer does not bust and does not have Blackjack (for the rest 66% or so), the dealer's hand will be anywhere between 17 and 21. Again, I don't know the exact probabilities (which depends on whether the dealer hits S17 or not), but let's just use the following numbers (These are based on the rough assumption that half of the time the hand will be either 17 or 18, and 19, 20, or 21 for the other half. Note that the blackjack probability has been already taken care of and the H21 does not include BJ.):
1) The dealer ends up with 17: 23%. (The exact number will be somethere between 20% and 25%.)
2) The dealer ends up with 18: 23%. (Ditto.)
3) The dealer's hand is higher than 18: 54%.
Then, you will win additional 23%x66%=15% of the bets, Making your win rate to 44%. You'll push for another 14%~15% and you'll lose 42% of the time.

Now, for H17, the dealer will be more likely to bust, but his average hand will be higher if he doesn't bust, which, I guess, will probably more than compensate the increase in the bust rate. Therefore, I would say, it'll be much closer game if the rule is H17.

Just thinking out loud,
~Black Jack in the Box.

Your assumption is wrong. When the dealer doesn't bust or BJ, more times he would end with 19-21 than with 17 and 18. Bear in mind that when the dealer has 18 you only push (you don't win).Also your gain from guaranteed 18 strategy is smaller than you think. Compared with a BS player, The guaranteed 18 player gains extra only in cases of simoltanuous busts of BS player and dealer.In all other dealer busts the BS player win as well. With dealer bust probability of ~28% and BS player bust probability of approximately ~14% this is not enough to compensate for playing the rest of the hands with a meager 18.
In Revere's book the EV of 18 is -0.33%. Shark

Your reasoning sounds logical although I am no mathmetician. Shark's data doesn't sound so good, but I am inclined to bet on your analysis. Anyway... I am "hooked" into the game tonight. Not much money riding on it, just hoping to shut the big mouth up by just winning. I originally thought I would have a huge edge, then it was mentioned that I would NOT have 3:2 for Blackjacks. Still, I thought it was a player advantage.

btw, just before closing last night, we played three hands and I lost them all! They kept telling me, "I told you so". Hope that changes tonight.

Quark,

Your exact edge will depend on how many decks you use (e.g. it's advantageous for you to use as many decks as possible since the dealer's chance of getting BJ will be smaller, and he will bust slightly more, etc), on whether it's S17 or H17, and/or on many other small rules. But, no matter what, this is a very close game (essentially an *even* game for all practical purposes for tonight's fun), and it makes this particular "bet" even more interesting.

(BTW, you can always increase your edge by counting, which your friend/dealer player cannot do. ;-)

In any case, I wish you Good Cards (you'll need it :-), and keep us posted.
~Black Jack in the Box.

Disclaimer: I'm no mathematician either.

Although with eighteen you're the clear favourite against any upcard lower than Nine - the worst card for the dealer being the Seven - you will lose on the whole as you are the underdog against Nine,Ten or Ace.Your loss rate will be 0.7% on average.
If we make the reasonnable assumption that 500 hands per hour will be dealt (only the dealer needs cards!), you must expect to lose $17.5 per hour on average.

Francis Salmon

Any other day would do as well. Subjective logic doesn't prevail in BJ - math does! Shark

Quark's bet is based up him being "given" an 18 on every hand. What if he insisted that he be given a NEW 18 for each new hand, and that the played cards be discarded? Quark would receive four faces and all of the eights in the first four hands, and four 7's and all of the Aces for the next four hands, then the game would have to end because all possible two-card combinations whould have been played. Or, all of quark's cards could be removed beforehand, and the dealer could just deal hands to himself. Wouldn't this seriously reduce the chances of the dealer drawing an 18 or better?
Or whould the dealer really be hurt by the missing faces, sevens, eights, and Aces? Could he still make a lot of 18s or better by drawing lots of small cards?
Hmmmm....

He can't increase his edge by counting. He can't vary his bet size (see original message) and he gets no playing decisions... :(

If your 18 consisted of a pair of 9's you could have the advantage by splitting them against 2-6, 8 and 9.

Here are some numbers.

These numbers take into account, player 18 effects the dealer probability. That is if the player has 2,8,8, then these cards are not available to the dealer.

For S17
----------------
Bust = 26.016 %
17 = 14.911 %
18 = 13.850 %
19 = 13.864 %
20 = 18.580 %
21 = 7.896 %
BJ = 4.884 %

Earnings = -4.296 %

For H17
-------------------
Bust = 26.411 %
17 = 13.745 %
18 = 14.067 %
19 = 14.087 %
20 = 18.792 %
21 = 7.911 %
BJ = 4.987 %

Earnings = -5.622 %