Strange Soft-Double Strategy Question (long)

I am asking for what I suspect is a fairly complicated strategy so if more appropriate, I will re-post on green-chip (which I have not signed up for yet).

Also - I know this was brought up in a different thread but I can't find the post and I'm not sure I saw an answer. Apologies if this repeats previous information on the site. I know Stanford has a million different strategy variations for obscure rules covered in his book (tripling-down, Win on 22, etc.) but I don't have that book yet (will get it soon) and thus I am not certain if this one is covered.

I am curious about this rule and the strategy for a couple of reasons...
1. I think the correct mathematical answer will be interesting.
2. I may get the opportunity to play with this rule on a semi-frequent basis so I want to make sure I'm doing it right. So far I've been very conservative with it.

Some casinos allow you to take another hit after splitting aces but you have to double-down. BUT you can double for less for table minimum so if you have a couple black chips out on your split Aces, it only costs table-minimum $5 to get an extra card on each.
Obviously you double for the full amount on that soft-17 or 18 vs. a 5 or 6 (and any other time the count dictates it is a proper soft double against a 2-6).

But what about the other one's? Is there some sort of min/max unit limit where it is better to pay the minimum for an extra card?
In other words; When I have a big bet out, I think it makes sense to pay the $5 for an extra card on that soft 13 vs. 10. I'm trying to save my big-bet and I think the small investment is worth it.

But if I have a 1-unit bet do I really want to take a double-down on that S13 v. 10 just to save the $5 already out.

I have typically not doubled on the small bets (except when strategy would dictate a soft-double is appropriate anyway) because it doesn't seem worth it to me. Should it make a difference whether I have $5, $25 or $95 out? It feels in this instance that it should and that there is some proper cut-off...

So the answer may be something like - "On a S14 v. 10 - Double-for-one-unit if you have 3.6 units or more on that hand. However, if you have 3.5 units or fewer then stand (and hope for the best).

In fact, it may be even more complicated than that -
For example, maybe it goes something like this
Strategy for S14 vs. 10 - you double-for-one-unit if...
-- count is +5 or higher and you have 1-unit bet
-- count is +4 or higher and you have 2-units bet
-- count is +3.5 or higher and you have 3-units bet....etc.

...but it also feels like that thinking may be similar to ploppy-logic on insurance (insure a big-bet 20 or take even money a BJ...but don't insure anything else).

I hope the above examples make sense to someone out there. If not, feel free to complain or find your own best way to clarify or simplify my ideas/question.

this is on a 6-deck shoe by the way. Dealer stands S17.

One rule though that I'm not certain of - Dealer does not check under their 10...I am assuming that if dealer BJ's then the player loses only original bet....however, it's possible player loses both because I haven't seen this situation yet. I assume the double-for-less strategy would be different against a dealer 10 if the dealer got to scoop up all the chips.
I also assume dealer BJ would win the original bet only against a pair of 21's on the split A's (probably would be too much to ask for a push on those).
Dealer does check under Ace - so if he BJ's then player doesn't get to split anyway...that's why I assume you only lose the original bet if he BJ's with a 10 showing.

BTW - I keep a good Ace Side-count (as my handle would imply) so I am more likely to get those split-Aces with bigger money out.

ATTN CASINOS - Interestingly, I think this rule is a big winner for the house...Most ploppies are too tempted to leave their soft 14 v. 10 alone and will double to try to save it....but perhaps this is the mathematically correct strategy.
However, many ploppies have not bothered doubling S17 or S18 vs. 5 or 6 because they think of it as an already won hand. I suspect the house is making more money than they are losing with this rule. As stated on several occassions...give the player as many options as possibleand that gives them more ways of playing incorrectly.

Sidecount,

I'm at the office and don't have access to any tables, but I believe you would probably play out the hand rather than double for less.

There is a tradeoff between the %Win Rate and $Win Rate in that the Doubling strategy results in a lower percentage of wins, but a higher overall win from having more money down.

If a straight Double Down is inferior, you are probably better off to play out the hand.

Dtm

The answers to your question can be extrapolated from the charts in Julian Braun's book. Although that book deals with the 4-deck game, the answers would be more or less applicable to any game of 2 or more decks for this specific purpose.

In the case you mentioned, A3 vs X, here are the numbers:

stand: win 23%, lose 77%, net -54%
hit: win 43%, lose 57%, net -14%
double: win 37%, lose 63%, net -52% (-26% on 2x the money)

In this case, if you stand, you will lose $54 standing the $100 bet.
If you add the $5, you will lose 26% of $105, or ~$27.30.

Does this answer your question, two dogs....?

and I view it as most valuable because of it's flexibility.

I employ it at all times that the first card leaves me in a weak position.

The 13 vs 10 scenario is much like splitting 8's against a ten, IMHO.

Joe

This is a special situation where you double for less to cut your losses. With soft 16 or less, standing is always the worst option. In fact, doubling for the full amount is always better than standing with soft 16 or less.

Against dealer 2, double for less.
Against dealer 3, do a full double except with a5 double less
Against dealer 4,5,6 do a full double
Against dealer 7,8,9,T,A double for less (big savings here)

It doesn't cost very much to skip the full doubles against the dealer 3, so for a simplified strategy -- when you wouldn't double ordinarily, just double for less.

For 6 deck games, against a dealer 3 only double for the full amount with AA.

There is some other advice here suggesting that if you wouldn't double all the way then you wouldn't double at all but your math clearly dictates this is not true. And it suggests a very complicated strategy table could be involved for games with this feature.
Indeed my hunch seems to have been somewhat correct...if you have $100 out on a losing hand like this it is worth the $5 investment to try to save the hand. However, if you have $5 out then it is better to stand then it is to risk losing more money. Somewhere in there is the line for standing and doubling for $5 (i.e. - stand if bet is $38 or less....double if it is more than $39...or something like that). I'll look at some more of the math and make some determinations.

Thanks for your help.

Thanks for your thoughts on this. As I mentioned in response to OldCoot...there will be situations when I actually have the minimum bet and thus cannot double for less. His math seemed to dictate that just standing in this situation (ex: S13 v. X) is better than doubling here.
Right now I guess I am left to use my own best judgement on how much must be in the betting circle in order to try to save it with a $5 investment. Clearly, laying out an extra $5 to save $100 is prudent. But laying out an extra $5 on a mimimum bet just loses additional money in the long run.

>> Thanks for your thoughts on this. As I mentioned in response to OldCoot...there will be situations when I actually have the minimum bet and thus cannot double for less. His math seemed to dictate that just standing in this situation (ex: S13 v. X) is better than doubling here.

No, his math shows that standing loses 54% of the initial bet while doubline loses only 52% of the initial bet.

>> Clearly, laying out an extra $5 to save $100 is prudent. But laying out an extra $5 on a mimimum bet just loses additional money in the long run.

That isn't so. The exact numbers are:

stand: -54.009563%
double: -50.872021%

I promise that I didn't just pull these out of my hat. Surrender would be best if they allowed it, but doubling for the full amount will lose less money in the long run.