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nick777 wrote:

Look at these numbers, you too nolan, this is your quote

“The expected return on the 10 vs 6 hands is ~0.28 x Bet Size per Hand x Num Hands.

The expected return on the 20 vs 6 hands is ~0.70 x Bet Size per Hand x Num hand.

There are twice as many hands when splitting, making it 0.70 vs 0.56″

You were saying earlier in 2 handed play the figures would be

Stand – 1.4
Split – 1.12

Wow, you finally posted accurate numbers! Note the 2 handed figure is 2x the one handed figure because the are expressed in initial bet size in one of the two hands. If you express them in terms of overall initial bet size it is 0.70 vs 0.56 for both.

nick777 wrote:

Now there is a 14% chance that you will draw the same card when splitting and re-split, using 4 decks, this gives you 56 extra hands(0.14 x 400 hands, you are playing 4 handed), those 56 extra hands at 0.28 give you an extra $16, bringing your total after 100 rounds to $128($16 + $112)

This makes it

Stand – 0.70
Split – 0.64

That is using the numbers you provided

Completely wrong again. Two issues:

1. 0.70 vs 0.56 numbers are for not resplitting. We’ve been avoiding resplits to keep things less complex. If you resplit, then the expected return per hand drops dramatically. The equation is not 0.28xNum Hands any more. I remember it as ~0.17x Average Num Hands. I’d have to recheck sim results to confirm. This further reduces overall expected return, even though there are more hands.

Wizard’s site lists 0.70 vs 0.47 for repsplitting with an infiinite deck. My sim reported 0.70 vs 0.45. My sim results are shown in a screenshot around on page 2 of this thread.

2. The chance of drawing a 10 and forcing a resplit is well over 14%. Think about how many 10s are left in the decks.

nick777 wrote:

The numbers here say

http://www.geocities.com/TimesSquare/Realm/2009/BJC/Edge.html

Stand – 0.68
Split – 0.33(0.33 x 2)=0.66

Stand = +136(instead of +140)
Split = +132(instead of +112)

The link doesn’t work for me, so I can’t see what is printed. If it is another strategy table, then FOR THE 5th TIME, RETURN IS EXPRESED IN TERMS OF INITIAL BET SIZE… YOU DO NOT MULTIPLY BY 2 FOR SPLITS OR DOUBLES. That makes it is 0.68 vs 0.33, not 0.68 vs 0.66.

I’m not sure who this guy is and why he is getting different numbers than Wizard’s sim, my resplit sim, and the BJMath sim I linked to. Or the article you quoted, my no-resplit sim, and my hand calcs on page 3 for no resplits. He may be using a different set of rules than we are. I really don’t care to analyze it in detail and figure it out. In any case, every sim that has been posted says not to split. Every expert that has info on this topic says not to split. Every strategy table I have ever seen says not to split.

EDIT: The link works for me now. I see a calculator. If I enter 4 decks with resplit up to 3 hands. I get the following result:

— 4 Deck, H17, DOA, DAS, LSR, RSA=2, RSP=3 —
Player Hand: 10,10, Dealer upcard: 6 Decision: Stay
Hit:-0.85222 Stand:0.67576 Double:-1.70445 Split:-100.00000

I wouldn’t trust this calc for splits, certainly not above Wizard of Odds and other blackjack experts.

nick777 wrote:

I don’t believe yours because that +140 to +112 figure looks way off to me, i assume you will believe yours, but can you guys at least admit that you didn’t consider the 56 extra hands that come into play from re-splitting, we won’t ever agree, but if you make a mistake you shouldn’t hide it.

I’ve explicitly stated which results were for resplits and which results were for no resplits many times, going back all the way to page 3. Here is a quote from page 3: “That makes the expected gain 2*(0.61-0.33) = 0.56 (my sim gets 0.55 without resplits). If you include resplits on 20, then the expected gain drops to ~0.45”