Ask the Wiz: 2 or 7 in Blackjack Question

I'm thinking this question has been answered before, but I would like to hear an authoritative answer. Is it better to face dealer '2' or dealer '7' in Blackjack?

This was brought up in this thread but I thought it would be good to start another. I went to this WoO chart pretty sure that 7 is worse, but it turns out that "it depends" [assuming I know what I am looking at]. Someone must know the authoritative answer.

My gut still says '7' is worse, but I probably have learned to hate the '2' more for it's continuous impertinence!

Mathematically I have no idea, even after consulting those charts, but it does seem that its not all that much of a difference. I've always thought that a dealer was better off if he had a 7 than if he had a 2, but if I were playing and consuming free booze, I'd not deviate from my simple strategy: Dealer 2, Hit until 13, Dealer 3-6, Hit until 12, Dealer 7 or higher, hit until 17.

The 7 is much better, for the player. This was one of the questions asked in the qualifying test at the Blackjack Ball. The following table shows the average expected value by dealer up card and whether the dealer hits of stands on soft 17. For 10 and ace, it is after the dealer peeks for blackjack.

Up Card	H17	S17
2	9.07%	9.10%
3	12.35%	12.38%
4	15.88%	15.85%
5	19.67%	19.65%
6	23.69%	23.40%
7	14.40%	14.40%
8	5.82%	5.82%
9	-4.06%	-4.06%
10	-17.36%	-17.36%
A	-36.92%	-33.78%

Table based on infinite decks.

Interesting.

But going back to the arguments I had made in the Blackjack in Ct. thread, the 'general public' may perceive H17 to be a better game, primarily because of dealer hitting when the dealer's card is a 6, with an Ace in the hole.

I added a columm showing the difference that S17 provides over H17, and this confirms what I was saying - about the 6 anyway.

The differences for all cards except Ace and 6 is negligible. For a 6, H17 is considerably better for the player. However, a dealer with an Ace up, S17 is over TEN TIMES better than the H17 advantage with a 6.

Up Card	H17	S17	S17 advantage
2	9.07%	9.10%	0.03%
3	12.35%	12.38%	0.03%
4	15.88%	15.85%	-0.03%
5	19.67%	19.65%	-0.02%
6	23.69%	23.40%	-0.29%
7	14.40%	14.40%	0.00%
8	5.82%	5.82%	0.00%
9	-4.06%	-4.06%	0.00%
10	-17.36%	-17.36%	0.00%
A	-36.92%	-33.78%	3.14%

This also supports the other obvious thing: Even if it's S17, the general public hates to see the dealer have an Ace up.

Quote: Wizard

The 7 is much better, for the player.

Up Card	H17	S17
2	9.07%	9.10%
3	12.35%	12.38%
4	15.88%	15.85%
5	19.67%	19.65%
6	23.69%	23.40%
7	14.40%	14.40%
8	5.82%	5.82%
9	-4.06%	-4.06%
10	-17.36%	-17.36%
A	-36.92%	-33.78%

Table based on infinite decks.

Okay, so I gather that Hitting Soft17 and Standing on Soft17 really doesn't make much difference at all. Oh sure, in the extreme case of a dealer's up-card being an Ace it seems to be a 3 percent difference but if its a whopping 33 percent against you already what's the difference if instead its 36 percent against you? Its not that much better to be shot with a .38 than a .45 caliber slug. For each of the other dealer up cards in the table the difference is pretty much aptly described as a smidgen and no matter what game it is or how much money is being ploughed thru it, a smidgen's difference will make a difference only to the casino, not the player. That is why the player thinks of five dollars at roulette and the casino thinks of twenty-six cents.

Now I did note that the table was based on infinite decks and if a continuous shuffler is in use that is pretty much what you are playing with, an infinite deck. We ride on airplanes with performance manuals based on a plane designed with wings of infinite length even though we know that infinitely long wings make finding a hangar a wee bit difficult. So I guess there wouldn't be much difference if there are only finite decks involved.

Quote: Wizard

The 7 is much better, for the player.

My guess was wrong. Mulling that over, it goes to show you that just because you stand with 14 vs 2, but hit with 14 vs 7, you can't come to a conclusion from that and similar decisions.

Quote: odiousgambit

My guess was wrong. Mulling that over, it goes to show you that just because you stand with 14 vs 2, but hit with 14 vs 7, you can't come to a conclusion from that and similar decisions.

The reasoning is you have to consider all of the possible dealer outcomes - 17, 18, 19, 20, non-BJ 21, BJ, and bust. It is true that a bust is more likely with a 2 up than a 7 up. The 7's advantage comes from the most likely pat hand being 17 with that upcard, giving the player a decided advantage with any hand larger than that (and thus the BS has you hit stiffs until you have at least 17). With a 2 up the pat hand outcomes are more spread out (in fact the dealer is more likely to draw a non-BJ 21 with a 2 up than any other up card, based on the Wizard's table at the URL below).
http://wizardofodds.com/blackjack/appendix2.html