Players must go first

I was part of a round recently when all 6 players busted, but of course, the dealer did not even have to draw another card to complete her hand. I know this is not a rare event but it intrigued me this time.

The dealer hand is the only one that is 'different' on a BJ table, in that all the players must 'go first.' My questions are: exactly what is this particular disadvantage faced by the player, by being forced into risk by having to 'go first?' How is it best quantified and expressed? Is this inbuilt advantage (part of the house edge)measured to be the same, no matter how many decks are used?

Exactly what component of the overall house edge is this inbuilt edge?
I'd appreciate some help with this from any learned ones who know these answers. Thank you. NB

Neutron Bomb,

According to Table 4.1, pg. 50 of Schlesinger's BJA3, for 6D standard LV Strip rules the dealer busts 28.20% of her completed hands, while a B.S. player busts 15.94% of his hands. Of course we realize that the busts are not independent. Let me quote from a post I made over on Don's ap.com website (see link below):

"I ran a CVData sim and found that the dealer in fact busted 26.20% of the rounds (counting only rounds where the players didn't all bust or have BJ's), rather than the 28.20% quoted by Don. Of the 26.20% I found, 15.83% of the rounds the dealer had a weak upcard (2-6), while only 10.37% of he rounds the dealer had a strong upcard (7-A). Since the B.S. player is unlikely to bust against a weak upcard (and if he does, it's because he drew a 10 on his hard 12 vs. the dealer's 2 or 3), let's just assume that ALL the player's 22's (or busts, for the present discussion) come when the dealer has a strong card."

Later in that thread, Don pointed out that my sample size was too small, as the 28.20% rate for dealer busting is well-known. Let's therefore INCREASE the dealer's weak and strong bust rates to be these:

Weak upcard (2-6) bust rate: 15.83%*(28.20%/26.20%) = 17.04%
Strong upcard (7-A) bust rate: 10.37%*(28.20%/26.20%) = 11.16%

Then, since the player wouldn't bust after the dealer has busted, the player would WIN rather than LOSE all of these "simultaneous bust" hands, and so would win an extra 0.1594*0.1116*2 = 0.03557808 = 3.557808% if the dealer could be persuaded to go first. Actually, the result would in fact be higher, since the player after seeing the dealer bust would split everything and then double down on hard 11 or less and any soft total.

Since in fact the dealer does NOT go first, we can conclude that this rule is worth roughly 3.56% to the house for this example.

Of course, this value will change somewhat depending on the house rules and the number of decks. For example, a game offering LS would be much, MUCH more attractive: "Hmm... I think I'll surrender this 19, since you already have a 20!" ;-)

Hope this helps!

Dog Hand

I would have to consult literature to give you a precise figure but acting last is obviously a huge advantage, and in fact it's the dealer's only advantage and all the other rules are only there to make the game playable for the player.It starts with the obligation of the dealer to hit up to 16 and stand on 17. Even with that restriction the house has a big advantage which is best illustrated if you just consider what happens if the player simply copies the dealer.Since the dealer's bust probability is roughly 28%, this would also be the bust probability of the player. The only disadvantage of the player is that he loses with busting even if the dealer would have busted as well.This makes 28%*28% or roughly 8%.If the player choses the other extreme,namely a never bust strategy the result would be about the same.Of course the player could do better by choosing a selective strategy depending on the dealers upcard (BS) but he would still have a disadvantage of roughly 5%.
It's only the Blackjack-bonus and the possibility for the player to double,split and sometimes even surrender that make the game almost even.

Francis Salmon

If the dealer had to go first, the player's advantage would be astronomical since he doesn't have to draw to fixed rules.
No, the correct question intended by Neutron Bomb is: What happens if busts by both the player and the dealer are counted as a push.
I guess your answer would be half of 3.5% or 1.77% shift in favor of the player.
If we consider that the blackjack-bonus alone is worth 2.3%,we realize that the dealer's advantage for acting last must be considerably higher than that.

Francis Salmon

Thanks Dog Hand and Francis Salmon for your well-constructed ideas on the dealer's advantage for going last.

Consider this: you are playing heads-up, 6-deck BJ (for fun, no money involved) with a pal who is the dealer. You agreed on these few rules: Dealer must stand on any 17 and must hit 16 or less. There are no splits or doubles allowed. BJ pays 3:2. Player can play only one box. There is no surrender.
What is the dealer's advantage in going last in this game?
Would this advantage be the same in a single, or double-deck game? If not, why?

In a casino when you bust and instantly lose your money, and then later in that same round the dealer also busts, in all fairness that should be a push. But of course, casinos are not widely acclaimed for their fairness. Their biased games are all definitely not 'fair.'

Both you guys have mentioned some figures and the answer seems to be somewhere between 3.5 and 5%. Perhaps we could enlist the assistance of one of these two BJ gurus now: Help! Stanford and/or Don. NB

Thanks Dog Hand.
The dealer hand will long-term bust 28.20% which is a substantial figure that must be very tempting to all those punters very nervous about hitting 12,13 or 14 V 2,3 or even 4. Of course, card counters know you should hit 12 V 4 if the TC is -2 or worse. Try telling that to mugs who badmouth you for "taking the dealer-bust card" in this case.

Or try telling them the dealer upcard 2 is the card that attracts the most dealer 21's. Fat chance they will believe it as they sit on their 12 V 2.

Your figures for weak dealer upcards resulting in a bust (17.04%) and
strong upcards (7-A) resulting in a bust (11.16%) are very interesting. I think we can conclude from the first figure that when the dealer has a weak upcard, (2-6) she is NOT going to bust 100 - 17.04 = 82.96% of the time. Correct?

And, when the dealer has a strong upcard she is NOT going to bust 100 - 11.16% = 88.84% of the time. Correct? (all long-term figures)

Thanks for you help NB

From Neutron Bomb

I think we can conclude from the first figure that when the dealer has a weak upcard, (2-6) she is NOT going to bust 100 - 17.04 = 82.96% of the time. Correct? And, when the dealer has a strong upcard she is NOT going to bust 100 - 11.16% = 88.84% of the time. Correct? (all long-term figures)

My response

No, your figures are not correct. To determine how often the dealer will bust against the weak cards (2-6), you find out the busting % for each card, add each amount together and divide by 5. For the strong cards (7-A), you do the same and divide by 8.

Hey Stephen Adams, thanks for your input. Here are my dealer-upcards-resulting-in-bust figures (from a reputable source).

2, 35.4%, 3, 37.4%, 4, 39.5%, 5, 41.6%, 6, 42.3%. (Weak)
7, 26.2%, 8, 24.5%, 9, 22.8%, 10, 21.2%, A, 11.5% (strong)

I am doing as you suggest and adding the weaks. Total 196.2 divide by 5 = 39.2
Strongs total = 169.8 divide by 8 = 21.2 (I included 4 x 21.2 for 10,J,Q,K.)

Conclusions: When the dealer has a weak upcard, she will (long-term) bust 39.2% off any of those. (She will NOT bust 61.8%)

When the dealer has a strong upcard, she will bust 21.2% off any of those. (She will NOT bust 78.8%)

Are you happy with those figures now, and the conclusions? If so, then maybe you could turn your attention to my original question concerning precisely what is the dealer advantage in acting last?
Bon chance NB

I think you created some confusion by incorporating hand frequencies into your bust numbers.So let's try to clarify a bit:
We all agree that the dealer's overall bust rate is 28.2%.Now the average bust rate for small upcards is 39.3% and the one for high up-cards is 21.2%.If we consider the card frequencies, we realize that low upcards (5/13) account for 15.1% and the high upcards (8/13) for 13.1% of this 28.2% overall bust rate.
Actually, I like your approach to consider only high upcards to establish the double-bust rate since the player will rarely bust against a small upcard.But against a high upcard the player's bust rate is far higher than the 15.94% you used.It will even be higher than the dealer bust rate since he hits all soft 17s and almost half of the soft18s. I think 30% should be a fair number.So the cases when player and dealer both bust (or would have busted) amount to 13.1%*30%=3.93%.
We shouldn't forget that the dealer acts last rule has also a hidden effect by forcing the player to choose a conservative strategy particularly against a low upcard which results very often in just losing on points. This is difficult to quantify but in view of this I maintain my 5% figure for the overall effect of this rule.

Francis Salmon

From Neutron Bomb

--- Are you happy with those figures now, and the conclusions? If so, then maybe you could turn your attention to my original question concerning precisely what is the dealer advantage in acting last?
Bon chance NB

My response

Your choice of words leaves one with the impression that you are somewhat upset at me for correcting your figures. If that is the case, that is not exactly the best way to increase ones knowledge. The correct approach is to look at ones mistakes as opportunities to increase ones knowledge.

As far as your question about dealer advantage from playing last, I believe someone else answered that question for you so I didn't bother. As I understand it, the best way to determine this figure is to pretend that the dealer and the player play exactly the same way and that there is no 3/2 payoff to the player for a blackjack. Under those conditions the player would lose by approx. 28.2% x 28.2% = 7.95%. All of the other rules in favor of the player, including 3/2 for a blackjack and his ability to hit, stand, double down or split, helps to eliminate about 7.5% of that advantage.

Thanks again Stephen Adams for your concise precision, clarity and timely advice which in my case, has swept away confusion, ambiguity and error.

I made a poor choice of words when I asked you if you were happy with those figures and the conclusions. What I meant was: "In your view, are these figures and conclusions correct?" I was never in the slightest bit upset in any way with your input and corrections. In fact I very much appreciated them.

I was a tiny bit frustrated there - which had nothing to do with you -when Dog Hand, Francis Salmon & I were a little stuck for a brief while and I'd made a request for Gurus' help which was not immediately forthcoming. (I guess they knew we would all sort it out eventually anyway.) Instead, you popped up and set the boat back on course, so all is well.

I finally have the figure I was looking for: 7.95%. Now if we subtract the figure for player-Blackjacks, we get close to Francis Salmon's 5% figure. I think. Are you happy with that idea?
Regards NB

From Neutron Bomb

Thanks again Stephen Adams for your concise precision, clarity and timely advice which in my case, has swept away confusion, ambiguity and error.

---I finally have the figure I was looking for: 7.95%. Now if we subtract the figure for player-Blackjacks, we get close to Francis Salmon's 5% figure. I think. Are you happy with that idea?
Regards NB

__________________

My response

Your overt use of compliments and the not so subtle implications of same, are duly noted. Regarding the built-in advantage of forcing the player to play first, one could say that if we subtract player Blackjacks and the doubling rule, the advantage would be about 3%. I think the definitive answer is approx. 7.95%.

You guys are wasting your obvious superior intellectual skills on a game that does not and will not exist.

Hey Dog Hand,

I really appreciated your abridged version of the BS chart so much that I printed out a few copies and gave them to pals, 2 of whom are just sometimes BS players. One was impressed enough to later insist on stuffing ten bucks in my pocket. He said that is the best one he's seen, (after he won $450.) Maybe you could capture the market with this! By the way, should I send you your $5 share to: Dog Hand, care of Stanford Wong? Regards NB

Hey Revereman,

Of course you are correct in suggesting some of us here may be better engaged, rather than speculating on non-existent aspects of BJ. We could be speculating on all kinds of stuff...

IMO, any kind of speculation concerning Blackjack - however banal or obvious - is welcome, at least by me. There is a possibility - however remote it may seem - that it could stimulate my interest which could lead ultimately to more awareness of this addictive beast of a game, (I hope!) Anything about BJ you care to speculate on, I'll read it and ponder for a while.

I busted at box 1 and instantly lost my chips. Later that same round, the dealer also busted. Stephen Adams sets this dealer-advantage at 7.95%. Obviously, we would not have a game called BJ if it were not for this built-in dealer-advantage.

Even if I go to the casino mentioned here recently where the player has the option of playing as the bank, that casino adds more rules that shrink your 7.95% advantage making that a doubtful exercise. (Just speculating here...) Regards, NB

What in the Blackjack world - (when you have blacks piled high in splits and doubles) - could there conceivably be more stunningly beautiful than a dealer bust NOW? (to her 10 she drew 2,10.)

Yeah, well, there is something. Hmmmm... Now what could that possibly be? Answer: A RASH of dealer-busts, all consecutive. I absolutely love it on that rare occasion when the dealer breaks out in a RASH of dealer busts. It doesnt seem to matter what upcard she has, A,10; doesn't matter, she busts. There is nothing she or the pit can do about it for the rest of this shoe.

It's like someone in a booth watching decided to push the 'Dumper' button. (It says near the button... "only to be pushed when Pluto, Neptune, Earth and Mercury are aligned.") Uh ha. That explains why the phenomena is fairly rare.

If this dumper has happened to you already, (outside of your dreams)then that event probably had a profound effect on any future BJ expectations from that moment. Am I right? I know it did for me at least.

I was playing $10 min, $200 max several years ago and the planets were aligned in that moment. I scored $8K from that shoe, in maybe just 10 rounds, playing 3 hands. Everyone won heaps. The table, and the masses at the back were erupting like the craps table every time she busted again. I experienced BJ heaven. I'm not going to the opposite of that; I'm leaving it stuck right there on heaven.

I want more more more of those. It seems each of us is only allocated our certain number of these events in our BJ lifetimes. I don't accept rules like that, so I've been tinkering to try to get in the booth and push the button when no-one is around.

I like to hear 'Dumper' stories. Any out there? If not, then discussion of this Q will have to do: Has anyone got a plausible explanation for a Dumper? NB