double down to split aces -- doubling for less

Apologies if this question has already been posted. I did a search for posts containing all of "double", "split", and "aces", and did not find a relevant thread.

This page has a doubling strategy when doubling to split aces: https://wizardofodds.com/blackjack/appendix20.html

My question regards the strategy for doubling for less when the double must be at least table minimum. If I am currently betting the table minimum, should I still be following the double for less strategy?

Are you from Michigan? That is the only place that has that game. I don't think you should follow the double for less strategy if you can only go $5 + $5, since it's not really for less and you don't gain the advantage of the "free hit," which is all the double for less is. Ideally, you'd want to bet a penny (or more realistically, $1), but according to the site they won't let you.
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So far I've resisted driving up to check out these games but I think I might go up there in the near future to see what all the fuss is about. I'll file a report.

Quote: teddys

I don't think you should follow the double for less strategy if you can only go $5 + $5, since it's not really for less and you don't gain the advantage of the "free hit," which is all the double for less is. Ideally, you'd want to bet a penny (or more realistically, $1), but according to the site they won't let you.

This is what I expected. Is there a chart somewhere that shows the thresholds for doubling for less? Or even a chart of win/loss rates (in terms of the ratio of wins to total hands and the ratio of losses to total hands, not in money) I could use to determine the thresholds myself?

Quote: foxfan20

Apologies if this question has already been posted. I did a search for posts containing all of "double", "split", and "aces", and did not find a relevant thread.

This page has a doubling strategy when doubling to split aces: https://wizardofodds.com/blackjack/appendix20.html

My question regards the strategy for doubling for less when the double must be at least table minimum. If I am currently betting the table minimum, should I still be following the double for less strategy?

If you are betting the table minimum, and "double for less" requires at least the table minimum, that effectively means that double for less is not allowed in your case. Just use the first table on that page.

Quote: weaselman

If you are betting the table minimum, and "double for less" requires at least the table minimum, that effectively means that double for less is not allowed in your case. Just use the first table on that page.

Right -- What about twice the table minimum? Thrice? Obviously if I'm betting $1 more than the table minimum it's still not worth it if I'd only double "for less". For each betting situation where it's possibly worth it to double for less, there must exist some fraction of your bet that the double needs to be less than in order to make the double the right play. Is there chart with these fractions anywhere?

EDIT: I note that the other chart has you doubling everything <=16 anyway, so the point is probably largely moot. But there are a couple cells in the for-less table that are stands in the not-for-less table. I'd like to know the critical fractions for those cells.

It answers your question at the bottom of that page:

"When the strategy says to "double for less," bet as little on the double as you can, preferably, just a penny. If some kind of respectable double is required, and your initial wager is less than 35 times the double wager, then you should stand on soft 18 vs. 10."

Hmm... I have done some math here.

If we assume the value of our original bet is 1 unit, then:

EV(double) = 2p - 2q = 2(p - q), where p is the probability you win on a double and q is the probability you lose. (q isn't simply 1 - p since some hands will push.)

EV(double for less) = (1 + f)(p - q), where f is the fraction of a unit you're doubling for.
EV(double for less) = EV(double) * (1 + f) / 2

In order for doubling for less to be better than standing:

EV(double for less) > EV(stand)
EV(double) * (1 + f) / 2 > EV(stand)
EV(double) + EV(double) * f > 2 * EV(stand)
EV(double) * f > 2 * EV(stand) - EV(double)

According to http://www.bjmath.com/bjmath/ev/ev.htm, in all the cases where we'd want to stand if we can't double for a penny, EV(double) is negative. Thus, dividing by EV(double) flips the inequality and gives:

f < 2 * EV(stand) / EV(double) - 1

For the game represented by http://www.bjmath.com/bjmath/ev/6ds17.htm, here are the f's for the relevant plays:

A/7 v 9: f < 0.2824
A/7 v T: f < 0.0478
A/6 v T: f < 0.8459
A/6 v A: f < 0.7867

Assuming you're betting multiples of a unit, this would mean that the decision chart for those hands should be:

A/7 v 9: Double if bet is 4 units or more, else stand
A/7 v 10: Double if bet is 21 units or more, else stand
A/6 v 10 or A: Double if bet is 2 units or more, else stand

Am I missing something?

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IBYA -- I'm thinking of doing a trip in November, going Bay Mills -- Sault Ste. Marie -- Hessel -- St. Ignace -- Petoskey -- Williamsburg (Turtle Creek) -- Leelenau Sands -- Manistee. Ambitious, I know. Will probably go over two or three days. A couple hours at each. Will PM you with details. In the meantime, do you know if any of the casinos comp rooms?

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