split 44 or double?

Perhaps this question should be in a different category (blackjack math for example) but basic strategy calls for splitting 44 against 5 or 6 in a DAS game. I know the index for doubling an 8 against a 6 is TC+2 and against a 5 is TC+4, which I do with hand compositions of 5/3 and 6/2. With 44 and doubling it you only get one card and have one hand, whereas splitting you're now playing two, with a chance of doubling those, or even doubling again if you get a chance to re-split. So my thinking is (without any math to back it up) is to split the original 44, irregardless of the TC positive index. (Tho of course you may end up with a bunch of 14 hands by splitting because of the higher TC. Same goes for the dealer who's 5 or 6 is showing and math-wise should have to be drawing to a bust hand.) So which is the correct play, and if it's splitting the original 44 is there a TC index where one should double instead? (I'm talking DD and shoe games here, I've never found a SD 3/2 game that allows DAS.)

If the count is right, I split, trying to get as much money on the table as possible vs. a 5 or 6

following the double index is usually better. especially if you play a system where 7s are counted as a negative, because with 44v5 and 44v6 you want the deck to be 7 rich because they bust/stiff the dealer and make you an 11.

hi-lo tends to favour doubling indexes anyway

Two reasons it is best to double when index calls for it. First, when the count is high you don't want to eat cards up splitting and taking two cards. Second, when the count is high what kind of card do you expect? You expect to get a 10 so would you prefer an 18 or two 14s?

Unless you are side counting sevens doubling passes the EV of splitting pretty quick after the index is exceeded. If the deck is rich in sevens split but if unknown or poor in sevens double. The correlation of the count tags to the EOR is much higher for doubling than splitting unless you are side counting sevens and the deck is 7 rich. The seven is the most important card for splitting 44 but has little importance for doubling 44.

Why would anyone count 7 as negative?

I think he mens the seven should be the highest weighted of the high cards and is either neutral or counted with the low cards. They are counted in the opposite direction of what they should be.

Would it not be fair to say, that at a high TC, the dealer has a very strong possibility of busting, so going for the split with the possibilty of a double ASWELL, is favourable over at best, a soft 19.

An 18 hand isnt fantastic in all fairness. Only the 20s and 21s grab the chips in the long run.

Two 14s are not very good. The 7 is the key card for splitting. Its EOR is -3.5049 for splitting 44 v 6, THe T only has an EOR of-2.1930 and the ace has EOR of 3.7826 the 6 also is messing with correlation with an EOR of -2.9183. The EORs for doubling 44 v 6 have a very high correlation, all the low cards act the same way. Except for the nine the neutral cards are very neutral. The ace is has a small EOR but is better grouped with the low cards than with the ten. EV will grow quickly on this double but is a weakly correlated guess to split without side counting sevens and without using an ace neutral count for splitting.

For 44 v 5 the split correlation is a little better. The seven's EOR is -3.2133, the T EOR is -2.3508, the ace is still better grouped with the low cards but is far less significant of a card with EOR 0.9307. The best improvement is with the low card block. The 6 is now properly grouped with the low cards with EOR 0.4607. The doubling EORs are still well correlated with this matchup. The ace now should be grouped with the high cards for doubling. This match up still favors doubling but is a much closer call.

For those who invite the large negative swings by splitting to get more money out in a weakly correlated situation without knowledge of the key card, I would recommend at least doubling on the dealer 6 or start side counting sevens so you have a strong correlation for splitting and adjust the count appropriately for 7 density for the decision. You won't be crying about your horrible downswings nearly as often if you examine the nuts and bolts of these decisions.

Although I appreciate the indepth analysis of EOR and the witty quirk about my recent horrible downswing, Side counting sevens, for hands that rarely occur is pointless. No one is a computer. Considering that landing a 4,5,6 or A on a split 4 will land you another double down decision, I doubt that a lack of sevens will affect much in the long run on this decision.

Plus, **** variance. If I get a rare 2-3% advantage im getting as much money out as I can, and yes, I will cry if i lose, but the happiness that engulfs my very being when I win wil counteract any tears lost due to my negative flux.

PLUS, dealers probably going to bust anyway at this high a count, so maths and opinions aside, im sure we can all agree that either decision would be a winner :joker:

Wrong. There is no dealer up card where the dealer is "probably going to bust."

The dealer will bust some upcards more than others, but they are all under 50%.

The dealer will probably not bust, regardless of what up card he has showing!

The chances of a dealer busting on 5/6 is 41.8% or 42.3% respectively. This is an average figure. Obviously at a low count the dealer will bust less, but at a high count will bust more with the high ratio of tens.

So really my point was with a high enough count he will bust more often than not, thus making the decision a winner either way.

My point is you have a high degree of certainty your double will succeed. Your index is a very good reflection of the true odds. For splitting, especially against the dealer 6, splitting is a guess that is often wrong as to whether it is a profitable decision. The count is a poor reflection of your correct decision for the current situation. You get a big bet out and almost always are making the right decision doubling but splitting you know 4, 5 and 6 are depleted and not very likely to be your card. Aces make a dealer 6 in a good game of S17 and gives the dealer 2 shots at making his hand if it is his downcard in either case. So you have a high likelihood of winning a double versus a guess that you will win or split at the same double amount or twice that. I like the frequent accumulation of BR with few and small downswings, both in amount and duration. We are talking about gambling you might win 2 more max bets if you get to double both hands but are more likely to be behind your double by 2 or 4 max bet or even 6 max bets if you get a doubling opportunity. If you have the BR for the swings go for it. If you don't double. The dealer 6 is a really weak split compared to the double, I still recommend doubling this even with the BR to weather the swings.

For a football analogy. You have a guy wide open at midfield or you can throw deep into a crowd of players and hope the right guy comes down with it. I didn't say to side count sevens. Only that splitting was not advisable without knowledge of the sevens given your double option. The fact the the 6 you want versus the dealer 5 is also a great downcard for the dealer actually increases your counts effectiveness for splitting. This makes it count as a low card (rather than an important high card v dealer 6) which is how you are counting it. Your intuitive I need these cards are confusing your decision. If they help the dealer more than you they are bad cards to have to be still in the deck. Your decision is based on how accurate your count reflects the EORs of the cards for your hand match up. Poor correlation results in a high index with little gain in EV after the index is exceeded. High correlation results in a low index with a quick gain in EV after the index is exceeded.

44v 6:
.. doubling ... splitting
A: +0.2836 . +3.7826
2: +2.1548 . +4.0223
3: +2.9055 . +4.0252
4: +2.2623 . +2.5864
5: +2.4518 . +2.6750
6: +0.0505 . -2.9183
7: -0.3186 .. -3.4765
8: -0.4856 .. -0.5278
9: -1.1358 .. -1.3687
T: -2.0422 .. -2.1930

Ideal count tags for 1 = 0.5 EOR
.A. .2. .3. .4. .5. .6. .7. .8 .9 .T
+1 +4 +6 +5 +5 0. -1 -1 -2 -4 doubling
+8 +8 +8 +5 +5 -6 -7 -1 -3 -4 splitting
-4. +4 +4 +4 +4 +4 0. 0. 0. -4 HILO normalized to value of the ten tag -4.

This is simply horrible splitting correlation to HILO and any ace reckoned count. The ace, six and seven are just terrible. Look at the beautiful correlation for doubling.

44 v 5:
.. doubling ... splitting
A: -0.3709 . +0.9307
2: +1.6197 . +3.9645
3: +2.4375 . +4.0262
4: +2.1879 . +2.5109
5: +2.5100 . +2.6846
6: +2.0327 . +0.8223
7: -0.3604 . -3.2133
8: -0.7370 . -0.7685
9: -1.1971 . -1.5541
T: -2.0306 . -2.3508

Ideal count tags for 1 = .5 EOR:
.A. .2. .3. .4. .5. .6. .7. .8 .9 .T.
-4. +4 +4 +4 +4 +4 0. 0. 0. -4 HILO normalized for ten tag -4
-1. +3 +5 +4 +5 +4 -1 -1 -3 -4 doubling
+2 +8 +8 +5 +5 +2 -6 -2 -3 -5 splitting
-5. +5 +5 +5 +5 +5 0. 0. 0. -5 HILO normalized to the ten tag -5

Still beautiful correlation for doubling, even better in fact. The correlation of splitting is much better but the ace and 7 are still hurting correlation but not as much. The six being a good dealer card has fixed the issue with the six from dealer 6 upcard for splitting.

For the chances of a dealer busting by upcard and count, see (Dead link: http://www.qfit.com/blackjackblog/?p=21)

For the advantage of splitting 4's vs. 5 at different counts, select Splitting Pairs - 4,4 v 5 and the rules at http://www.card-counting.com/cvcxonlineviewer3.htm. It's interesting to see the difference between DAS and nDAS.

Well that sort of makes my argument inapplicable :laugh: to be honest im surprised it doesn't reach 50% bust rate sooner, looks like a TC of 10 would just about edge it.

thanx to all for your input, especially to tthree showing the math. Looks like doubling is the way to go once the count reaches the indexes.

Split the 44 v dealer 5. The RA play is to double 44 v 6. I was disappointed you didn't have splitting 44 v 6 in your interactive index chart viewer. In this discussion that would have been the interesting one. I agree though with your index chart viewer says split the 44 v 5 over double. I use HIOPT II so the way it affects my strategy is different but I think while I might double 44 v 5 is still mathematically a split. It is 44 v 6 were I believe it is a double hence my disappointment.

This is only one single deck (S17 DAS) composition Ace-Ten (4,1,1,2,1,1,4,4,4,16) so we ought to be careful but interestingly


player's Hand 4,4
dealer's upCard 5

player's probabilities for standing
p_-1 = 0.245488758553
p_0 = 0
p_+1= 0.754511241447
p_+1.5 = 0
EV for standing= 0.509022482893 ± 0.860753223583

player's probabilities for doubling
p_-2 = 0.176239584316
p_0 = 0.0311216633483
p_+2= 0.792638752336
EV for doubling= 1.23279833604 ± 1.53483602032

player's probabilities for hitting
p_-1 = 0.168889255604
p_0 = 0.0337265552056
p_+1= 0.79738418919
EV for hitting= 0.628494933585 ± 0.755822441617

player's probabilities for splitting
p_-4 = 0.00867242268293
p_-3 = 0.0695158745888
p_-2 = 0.123774401609
p_-1 = 0.0109156800026
p_0 = 0.00576572250126
p_+1= 0.0246637081742
p_+2 = 0.343835048375
p_+3 = 0.338602216226
p_+4 = 0.0742549258402
EV for splitting= 1.52345835924 ± 2.14125949139

the desirability index for splitting is 1.52345835924/2.14125949139 = 0.71148

the desirability index for doubling is 1.23279833604 /1.53483602032= 0.80321

Doubling is the risk averse play

Sorry, I just don't accept CA calculations for counting strategies, even to one decimal, much less 12.