Double down madness -- double 2 vs 7, but not 2 vs 5

What's the logic behind why it's right to double a 2 vs. a 7, but not in the presumably more profitable situation of a 2 vs. a 5. I've been wracking my brain, and I just can't see it.

Also, the page says to double A vs. A when a suited blackjack pays 3:2, but hit when it pays 2:1 (unsuited pays 3:2 in both cases). That seems backwards.

Thanks!

The first one, I would assume it's because if you catch a 10 on that 2 you will get to hit again because it,s 12 vs. 7, but you won't be hitting 12 vs. 5. I think these are both very marginal decisions.

The second one, it might be backwards, haven't thought about it deeply enough.

Thanks for your response.

I thought about that, but I don't think it's right. Because your EV is higher standing a 12 vs. 5 compared to hitting a 12 vs. 7. So if you know you are catching a 10, you are better off (that is, less worse off in this case) doubling vs. the 5 compared to the 7.

I think I know what's going on now though. I think if you have a 2, you are actually better off against a dealer 7 compared to being against a dealers 5. Which does seem weird to me, but I believe it's the only explanation that makes any sense.

Also, I'm looking at the blackjack EV charts here: https://wizardofodds.com/games/blackjack/appendix/9/6dh17r4/

If you hit AA vs. a dealers 5, the EV is lower than the EV if you hit against a dealer 7 (0.160827 compared to 0.164333). Of course that's not a perfect analogy, since it's a different game and a soft total, but I think it shows that it's not crazy that you could prefer a dealer's 7 to a 5 in some situations when you have a low hand.

I calculate these EVs for hitting a 2 against each upcard in an infinite-deck version of this game:

Upcard	Hit EV
2	-0.3838
3	-0.2058
4	-0.1295
5	-0.0467
6	0.0696
7	0.0182
8	-0.1931
9	-0.4096
10	-0.5389
Ace	-0.5449

EV for doubling in this game is always 2x the EV of hitting, so doubling is the correct move for any positive hit EV. It's really close with a 7 up.

My reasoning is: while a 5/6 up has a higher bust chance than a 7, the 5/6 is actually more likely to make a hand of 19-22 than the 7. A dealer 7 ends in 17 over a third of the time, which is easy to beat. When you start with a card as small as a 2, the chances you reach each score between 17-21 are similar, so avoiding that dealer 19-21 or push-22 is more valuable than just hoping the dealer busts.

Upcard	P(17)	P(18)	P(19)	P(20)	P(21)	P(22)	P(Bust)
5	0.1184	0.1229	0.1184	0.1138	0.1089	0.0931	0.3245
6	0.1148	0.1148	0.1148	0.1103	0.1057	0.0910	0.3484
7	0.3686	0.1378	0.0786	0.0786	0.0741	0.0646	0.1977

As for the A vs A situation, I'm fairly certain Wizard got this wrong by missing the rule that hitting an Ace only allows 1 card, the same as doubling the Ace. I have a writeup here: /forum/gambling/tables/39309-double-down-madness/#post974928 My conclusion is that doubling a single Ace is by far the best EV move for every upcard and every Blackjack payout, unless the game lets you keep hitting.

Yes thank you, that explains it! My assumption that seeing a dealer's 5 is always better than seeing a dealer's 7 was apparently way off.

I'm also fairly confident the A vs. A thing is an error, but this site is so good, I'm very reluctant to believe it's wrong.