Index plays: why are pair splits so worthless?

[bejammin075]

Much of what I'm learning about blackjack makes sense, but this doesn't: the textbooks say that matrix plays for splitting pairs (aside from the value of splitting 10,10 in high counts) are near totally worthless. Sure, if a sim says so, I should just "trust the math" but I'd still like to get why, and I don't. To put some numbers on this, I'll refer to Griffin's 6th edition Theory of Blackjack, a table on page 30 called "Average Gains for Varying Basic Strategy". The table shows dealer up-cards listed across the top, and player hands listed vertically. If you add up the gains, in thousandths of a percent, for player hands of 12 to 16 vs. dealer 2 through Ace, I add up all those numbers to be 758/1000 of a percent. At the bottom of the table, if I add up the gains from varying pair splitting plays, excluding the 10 splits, it adds up to 15/1000 of a percent. So the gain from varying player hands of 12-16 is potenentially 50 times greater than the gain from varying non-10 pair splitting.

It seems like pair splitting is under-valued. For one thing, the decision to split leads to at least a doubling of the bet, with additional chances to double and/or split again off the new hands.

Why is it that basic strategy for pair splitting is so nearly perfect, regardless of the count, whereas non-pair hands require so much variation with the true count?

 

[Gamblor]

Well if you sat down and played BJ for a while you should know. Hands of 12-16 are very common. Splittable hands are much more infrequent, you can go shoe after shoe w/o seeing a splittable hand. Can't say this about 12-16.

 

[tthree]

Well if you sat down and played BJ for a while you should know. Hands of 12-16 are very common. Splittable hands are much more infrequent, you can go shoe after shoe w/o seeing a splittable hand. Can't say this about 12-16.

A pair of tens happen 16 times as frequently as any other pair.

 

[Gamblor]

A pair of tens happen 16 times as frequently as any other pair.

Really?? Think we're excluding this obvious I18 (v 5, 6) hand.

"if I add up the gains from varying pair splitting plays, excluding the 10 splits,"

 

[Automatic Monkey]

It's because the counts we normally use in blackjack don't have a very high correlation to the effects of the cards on split plays. You split 3's, what are you hoping to see? If you were doing a sidecount of 7's and 8's I suppose that index would be worth something.

 

[tthree]

It's because the counts we normally use in blackjack don't have a very high correlation to the effects of the cards on split plays. You split 3's, what are you hoping to see? If you were doing a sidecount of 7's and 8's I suppose that index would be worth something.

That definitely plays into it.

Gambler since you split most often v a stiff especially 5 or 6, the ratio of TT to other any other split match up is 727/43 = 16.91 so I am not sure why the "really?" from you (Blackjack Attack III page 97). I actually understated the ratio when I said 16 to 1. removing one T is much less significant to the number of Ts left than removing one of any other card to its remaining cards left of that value.

 

[blackjack avenger]

one removed, one less

A 12 can be:
8,4
4,8
9,3
3,9
2,10
10,2
7,5
5,7
Plus 3+ card combos
This is why 12 is so prominent in indicies

Now if you get a 7 & are looking for another 7 as your second card, well the 1 in your hand is one less you can receive.

The frequency of being dealt a 12 is high. The frequency of being dealt a pair is low.

 

[neversplit5s]

I agree what PPs have said...a combination of the infrequency of non-10 pairs and the weak correlation with some pairs and typical counting systems.

With 22 and 33, it would be a deck/shoe rich in "neutral" cards (with typical counting systems) rather than high or low cards that would have the most effect in determining split/no split strategy; likewise an opposite effect with 66 (with an abundance of neutral cards favoring a hit). Even with figuring in the neutrals, any correlation with 77 is weak. (The aforementioned reasons are also why the correlation with the smaller soft hands and doubling are not as great as with many other doubles.)

In most cases 55 is never split, being treated like other hands totaling 10.

Since most of the advantage of splitting 44 is from DAS potential, there does reach a point where splitting against a 4 (and at very high counts a 3) becomes worthwhile as the dealer bust rate goes up in high counts. In nDAS games you'll rarely if ever split 44 (treating the hand like others totaling 8).

With 88 being a BS split already in all cases (save for surrender and ENHC games) the main concern is 88 vs. 10; that is actually a "retrograde" index in that you'd refrain from splitting above a certain count (since you become more likely to lose the hands here). Without surrender said index is fairly high; if you can take LS this is an index probably worth knowing (also reducing your variance). Another "retrograde" index applicable to 88 is that under rule sets where you (late) surrender 88 vs. A under BS is that once the count gets high enough it turns into a play/split. (This illustrates a point I've mentioned before; after the dealer checks for BJ the EV of a 10 upcard varies inversely with the count as a dealer 20 is likely to happen, while with an Ace up it goes up with the count as a bust becomes more likely.)

A pair of 9s do have some correlation with a typical counting system, as a 10 to a split 9 gives 19 and an Ace gives 20. At some point 99 vs. 7 or A would turn into splits; for similar reasons to a pair of 8s at high counts 99 vs. 10 typically won't ever be split. (There are also negative indices for 99 against certain low cards.)

As was mentioned, the correlation is usually great against a (much more common) pair of 10s, as well as with a pair of Aces (with AA under American/OBO rules the only time you'd have any concern is if you play at very low counts).

Hope this explains the situation some (and feel free to correct me if my logic is wrong)!

 

[Gamblor]

Is it definitely true that a hi/low count is ineffective with split decisions? Sure you want a middle card after the split decision, but then you do want a deck rich in high cards for your double. Furthermore, the 10's are still detrimental for the dealer in most split decisions.

 

[neversplit5s]

Is it definitely true that a hi/low count is ineffective with split decisions? Sure you want a middle card after the split decision, but then you do want a deck rich in high cards for your double. Furthermore, the 10's are still detrimental for the dealer in most split decisions.

In the case of 22, 33, and 66, provided that it's a DAS game there isn't much room for improvement via the dealer bust rate since you're already splitting those pairs against all the bust cards. In a nDAS game some of the applicable pairs that aren't split (22 and 33 vs. a 2 or 3, 66 vs. 2) probably do have indices as the dealer bust rate goes up. Against the higher upcards (especially 9 or 10) you typically don't gain much if anything (in fact it may do the opposite) by splitting, since the chances of a dealer pat hand are greater at high counts. I'm not sure about 22 or 33 vs. 8 though; in BS those are fairly borderline no-splits (same with 66 vs. 7 and 77 vs. 8).

 

[tthree]

Is it definitely true that a hi/low count is ineffective with split decisions? Sure you want a middle card after the split decision, but then you do want a deck rich in high cards for your double. Furthermore, the 10's are still detrimental for the dealer in most split decisions.

The inclusion of the ace in the main count hurts it some for many splits. Not so for TT and 99. Counts that include the 7 typically don't weight it enough for these decisions. A side count is really what is necessary. Hilo will tell you when you have an advantage based on the cards it counts but with a poor correlation EV accumulates very slowly as the index is exceeded. Too often you are actually making the wrong decision without the help of side counting neutral cards. Except for upcard 5 and 6 the neutral cards also help make the dealers hand. That is why 5 and 6 are your best splits or doubles. If those neutral cards are severely depleted the balance tips as to the worst dealer upcard for the dealer. The non tens left make the dealer 5 or 6 while often result in another hit for smaller upcards. Those neutral cards bust the 5 or 6 while making the dealers hand for many low upcards. That what makes a block side count (maybe 7 and 8) so useful in determining the true strength of your hand or the weakness of the dealers.

 

[bejammin075]

Thanks for the info

Especially neversplit5s. I feel like I'm having no trouble remembering a lot of index plays, so I've settled on adding some pair splitting plays, just because it would bug me if I at least didn't know a few. These are Zen index numbers, which I've rounded slighly for a couple 10,10 splits. There were a lot of index plays with multiples of 4 with Zen. I fealt like these were the low hanging fruits of the pair splitting plays. The 2,2 and 3,3 hands vs. low dealer card were pretty annoying and looking like not worthwhile. These were my favorites, and easy to remember in a few sets:

A,A vs A: Split above -8

The meat block:
10,10 vs 3 or 4: Split above +12
10,10 vs 5 or 5: Split above +10

The "9,9" block, all -4 or +4 for DAS. No problem.
9,9 vs 2: Split above -4
9,9 vs 7: Split above +4 (NDAS, +12)
9,9 vs A: Split above +4 (NDAS, +8)

The "vs 8" block. The pairs 77, 33, and 22 split the same in BS DAS, with an easy pattern to remember vs dealer 8.
7,7 vs 8: Split above +4 (NDAS, Hit)
3,3 vs 8: Split above +8 (NDAS, Hit)
2,2 vs 8: Split above +12 (NDAS, Hit)

The 4,4 block. Since I have double down index plays for player 8 vs. dealer 4/5/6, I wanted to practice with consideration when the player 8 is composed of 4,4. Someone started a thread on this very thing recently. Pair splitting comes before the double down decision, so I remember it like this for DAS. With NDAS, the 4,4 isn't split, and treated like the other hands totalling 8.

4,4 vs 4: Split above +4
4,4 vs 5: Split above 0
4,4 vs 6: Split above -4
None get to the DD index.

The 4,4 situation got me thinking about other non-pair splitting index plays that could have pairs show up. Like 12 and 14 vs. dealer 2 through 6. So I've made it a point to remember the pair splitting comes first, when applicable, then double downs, then hit/stand.

 

[blackjack avenger]

10s

I would consider looking to add plays against dealer 10:
Most common dealer upcard
Most common dealer upcard when betting big

soft hands are more frequent then pairs so probably more valuable as indices.

It's known splits aren't worth much. Anyone who plays a lot realizes even BS splits are rare, much less indice pair splits.

 

[Renzey]

the textbooks say that matrix plays for splitting pairs (aside from the value of splitting 10,10 in high counts) are near totally worthless. So the gain from varying player hands of 12-16 is potenentially 50 times greater than the gain from varying non-10 pair splitting.
QUOTE]

First off, no potential pair splits come on multi-card hands. It's got to be on your first two cards. But your 16 could have started out by being a 3/2, or 10/2, or 5/3, etc, etc..
In short, 16 vs. 10 in all its forms will come about once every 28 hands.
9/9 vs. 3 will come once every 2200 hands in a shoe game.