Math Question: splitting 8's versus dealer 10

On other BJ forums there are a lot of people saying that Basic Strategy is wrong when it comes to splitting 8's versus a dealer 10, that it makes no sense to double your bet when you have bad hand (why throw good money after bad?).

What is the real math? And if Basic Strategy is correct, are there ever 'common sense' situations in which it is better not to split your 8's versus a dealers 10 (or 9 or Ace)?

Can anyone here lay out the math for both arguments?

I just found this quote which summarizes their argument:

"Any DD or split that does not win 50% or more should be dropped."

Exactly which Basic Strategy situations fall under this category? I know that the way BS works is that you will marginally make more money by your occasional DD/Split wins as the profit will outweigh losses of not splitting, but it would be nice to see the index of BS situations that are less than a 50-50 proposition.

You cannot base all decisions on whether on not the play will yield more than a slight positive return. I also assume that you want answers based on a 0 count. Soon you will here from a wizard. I am not one. I just do what they say.

Computer simulations have determined that it is better to split than to do anything else, based on a 0 count. You cannot go against the math. In the long run, you lose less by making the split and playing BS through to the end of the play.

"Any DD or split that does not win 50% or more should be dropped."

When an "expert" writes something like that -- and if you can't get them to retract within a day or two at most -- you have the perfect excuse to ignore their advice forever and a day.

This has been well understood for over 50 years. The four horsemen published the correct strategy (always split aces and eights) in 1956. Do you want to minimize your losses and maximize your winnings, or do you want to be able to brag that you "never split unless it wins 50%"?

ETF

The combinatorial analyses bear this out.

Based on Cacarulo's 6 deck charts on www.bjamth.com, standing or hitting 8,8 vs 10 has an expectation of -0.54%, whereas splitting is only -0.47%. Would you rather play one hand at -0.54% or two hands at -0.24% each?

is the same. The Computer said so! No logic, no anthropomorphisms. Just, the computer output. Debate has no place in this argument for a ploppy or Basic Strategy player

-Wylie

...pair situations where the EV is < 50%, however the alternatives are always worse.

Basic Strategy doesn't, and was never meant to, give an EV of > 50% in every situation.

It merely lays out the BEST action.

In the case of 88 vs T, it helps you win through the process of losing less.

Nothing worse than getting 2 8's against dealers 10 when you have a high count and max bet out. You know that you will be getting 2 10's or worse 2 more 8's. For me, in those high counts, with no option of surrender, I'll stand. Better to only have one bad hand than lose several big bets. But that's just me, the computers say split.

- the math grows exponentially. Guys like ET Fan get a little frustrated about these problems.

I think billb's response summarize the 'common sense' argument perfectly:

"Nothing worse than getting 2 8's against dealers 10 when you have a high count and max bet out. You know that you will be getting 2 10's or worse 2 more 8's. For me, in those high counts, with no option of surrender, I'll stand. Better to only have one bad hand than lose several big bets. But that's just me, the computers say split."

Worse: What if you have a big bet out, split 8's, then you get another 8, and then another? This has happened to me. Of course I lost all 4 bets against a dealers 20. When the big money is on the line, do you really want to take this chance (despite the math)?

... to stand if the index is +6 without DAS and +8 with DAS. That's what they said in 1980, in Braun's How To Play Winning Blackjack and that's what they say today in PBJ.

Where did you think Wong's advice came from? Wong wrote a computer program. +6 is an unusual count, though. Frequency under 2% even with excellent penetration. If you don't count, you'd be ill advised to play that way.

ETF

"But that's just me, the computers say split."

I think billb's response summarize the 'common sense' argument perfectly:

"Nothing worse than getting 2 8's against dealers 10 when you have a high count and max bet out. You know that you will be getting 2 10's or worse 2 more 8's. For me, in those high counts, with no option of surrender, I'll stand. Better to only have one bad hand than lose several big bets. But that's just me, the computers say split."

billb is talking about what's correct on high counts, not necessarily high bets.

Worse: What if you have a big bet out, split 8's, then you get another 8, and then another? This has happened to me. Of course I lost all 4 bets against a dealers 20. When the big money is on the line, do you really want to take this chance (despite the math)?

Were you counting? What was the count? If you weren't counting, you did the right thing. And, yes you want to take this chance. The bigger the bet, the bigger the difference between standing and splitting. Suppose you bet $1000. You expect to lose $535 by hitting, $537 by standing, and $500 by surrendering, but only $475 by splitting (6 deck, S17, DAS). Which of the four do you choose?

Yes, sometimes you will lose 4 bets. And sometimes, you will win 4 bets. Sometimes the split bets are doubled. All this is taken into consideration.

Finally, if you can't afford losing 4 bets, maybe you shouldn't be playing.

Blackjack, like most gambling, is a game of mathematics. Don't make it a game of hunches.

P.S.: There are times where the increase in expected value is not worth the increase in variance. This concept is known as risk aversion. This is not one of those cases.

always think you have all the answers. With only a slight modification, basic strategy can give a non-negative e.v. in every situation.

Here's the new, Lucky Best Wish Show Basic Strategy (LBWSBS):

1) For all hands with a positive or zero e.v., play according to regular basic strategy.

2) For all hands with a negative e.v. (this includes, but is not limited to, 8-8 v. 10), grab all of your chips, including those in the betting area, and vacate the casino. This requires good sprinting speed and, occasionally, good football skills, but it's an essential part of LBWSBS.

I haven't done the calculations, but a player who uses only LBWSBS will enjoy a edge far greater than that of even the best card counter. I'm sharing this long-held industry secret as a public service. Good luck, and happy sprinting.

Here's the new, Lucky Best Wish Show Basic Strategy (LBWSBS):

1) For all hands with a positive or zero e.v., play according to regular basic strategy.

2) For all hands with a negative e.v. (this includes, but is not limited to, 8-8 v. 10), grab all of your chips, including those in the betting area, and vacate the casino. This requires good sprinting speed and, occasionally, good football skills, but it's an essential part of LBWSBS.

Some playing suggestions:

- Don't buy in for more than you're going to bet. Make single chip bets. This keeps the number of chips you need to grab at a minimum.
- Don't use chips worth more than $500 because they are hard to cash in at different casino.
- Downtown Las Vegas works best for this because the distance to the doors are generally smaller. Also, since the next casino is just next door. During the light show, you easily disappear into the crowd.
- You might consider having 00J Simpson (double-O J) on your team, since, not only does he have sprinting speed and football skills, he also has a license to kill if necessary.

Get a copy of Beat the Dealer, either the '62 or '66 edition. The '66 edition is more accurate. In the back (in the appendix I suppose) is a series of tables, one table for each of the ten possible dealer upcards, duece thru ace. Be aware there is but one game to which the tables apply: the single-deck game spread at the time of publication.

For each two-card holding is there-in expressed a mathematical expectation for each alternative player action. Basic Strategy is defined as that set of player actions yielding the highest expection.