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[Anonymous]

Sorry, my calculations above are incorrect. The difference between splitting and standing is even greater than I stated.

The actual return for splitting 10,10 against a 6, according to the Wizard’s chart I posted before, is 0.4681 (versus 0.704 for standing)

So you make $70.40 in total by standing and $46.81 in total for splitting.

It’s not even a close call. Never splitting tens is one of the clearest decisions in the blackjack strategy charts.

[Anonymous]

By the way, those figures are for a theoretical, infinite deck game.

To see the figures for different number of decks (between 1 and 8 )and different sets of rules, see here:
http://wizardofodds.com/blackjack/appendix9.html

As you can see, the Wizard has simulated hundreds of different deck/rule combinations in order to make accurate charts for a variety of different BJ games. I imagine he has run more than a trillion iterations in total.

Once you’ve created your own simulation and disproved his figures, please post your findings. In the meantime, we will continue to accept the evidence provided by the established experts.

[Anonymous]

bb1webs wrote:

I don’t have a clue who is right or wrong

That makes two of us then.

[Anonymous]

FictionNet wrote:

That makes two of us then.

Add me to that list too

I have no idea what these guys are talking about

These are the odds:

—- 4 Deck, H17, DOA, DAS, LSR, RSA=4, RSP=4 —
Player Hand: 10,10, Dealer upcard: 6 Decision: Stay
Hit:-0.85222 Stand:0.67576 Double:-1.70445 Split:0.36302

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

Stand: 0.675 x 2 = 1.35
Split: 0.363 x 4 = 1.45

But i’m sure everyone except the Wizard is wrong

[Anonymous]

Personally I think there is way to much time spent on this pissing match, I say call it a draw and everyone just walk away.:Nod:

[Anonymous]

Nick777 wrote:

even if i did prove to everyone i got something figured, i’m not sure i’d want everyone to know about it, especially the wizard’s gang

How exactly do you conclude that you figured something out, when you refuse to accept any kind of test of your theory? (either a wager on actual play, or a computer simulation?)

The way it was disproved that the world was flat was to *test* the theory that it was round. Each side can argue their position until they’re blue in the face, but providing proof ends the argument.

Incidentally, there’s been about *40 years of proof* already, as blackjack strategy has been studied exhaustively for decades by some of the best minds around. (And yes, that includes two-handed play as well as single-handed play.)

As far your jab at “the Wizard’s gang”, I remind you for the umpteenth time, the advice to stand on 10,10 vs. 6 (regardless of the number of hands) doesn’t come just from the Wizard, it’s universally agreed upon by every blackjack expert on the face of the planet. I know it’s easier for you if you can try to marginalize the Wizard, but you need to realize (and acknowledge) that you’re not arguing against just him, me, and Nolan, you’re arguing against EVERY SINGLE LAST EXPERT ON BLACKJACK WHO HAS EVER LIVED. You, alone, a non-mathematician and a non-pro blackjack player, are claiming that the rest of the world is wrong. And anyone making such a bold claim should be expected to provide some proof. But you’ve steadfastly refused to submit your theory to any kind of test.

Quote:

But i’m sure everyone except the Wizard is wrong

See, there you go again, trying to marginalize the Wizard by saying that his position is the minority view. In fact it’s the opposite: The Wizard’s position is the UNANIMOUS position among the experts, who are all in 100% agreement. You alone believe otherwise. You’re the one who’s alone in his position, not the Wizard.

bb1webs wrote:

I don’t have a clue who is right or wrong…

Really, you don’t have any clue at all? The fact that the proper strategy has been repeatedly proven by test, while Nick777 refuses to submit his idea to a test, doesn’t give you any clue at all? That’s scary.

[Anonymous]

nick777 wrote:

Add me to that list too

I have no idea what these guys are talking about

These are the odds:

—- 4 Deck, H17, DOA, DAS, LSR, RSA=4, RSP=4 —
Player Hand: 10,10, Dealer upcard: 6 Decision: Stay
Hit:-0.85222 Stand:0.67576 Double:-1.70445 Split:0.36302

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

Those are the same figures that the Wizard provides. So either the site you quote just copied them, or they independently calculated the same results.

You’ll find them in the second chart on this page:

http://wizardofodds.com/blackjack/appendix9-4dh17r4.html

Quote:

Stand: 0.675 x 2 = 1.35
Split: 0.363 x 4 = 1.45

You don’t understand what the figures mean.

The return figures are for the overall hand. There is no multiple involved.

You play one hand of $100. You are dealt 10,10 against a 6. If you stand, your return is $167.50. If you split, your return is $136.30. That’s your complete return, already taking into account the fact that when you split, you place another $100 on the table and thus, when you win, you win twice as much. That’s all already factored in.

So the figures you just quoted from that Geocities page (which were just copied from The Wizard) show exactly what we have been saying all along. In the long run, if you stand you get more ($67.50) then when you split ($36.30)

Do you see now?

Quote:

But i’m sure everyone except the Wizard is wrong

Just you I’m afraid.

Quote:

Personally I think there is way to much time spent on this pissing match, I say call it a draw and everyone just walk away.

Fair enough, but it worries me that there are so many inaccuracies and misconceptions amongst casino affiliates.

More than that though, what really surprises me is the foolish arrogance shown by assuming that one’s own theories are correct over those of the established, proven experts in the field. It’s like overruling your doctor’s advice because you have your own hunch. It’s madness.

We’re not saying these things to annoy you. It’s just fact, proven beyond doubt by the experts in the business. Why would one even think to question that, just because one’s back-of-an-envelope calculation says something different? In that scenario I would just assume that I had made a mistake, and try to learn where I went wrong.

[327007]

nick777 wrote:

I think we’re making some progress at last

Look at this example

Imagine another situation, you are playing 2 handed and have 6-6 and 7-7 against a dealer with a 10 showing, you are not the favourite under any circumstance, by splitting you lose more, you have 4 underdogs vs 1 big favourite.

The expected return is expected return per hand * bet per hand * num hand. In this case both the expected return per hand after splitting is low, and increasing num hands decreases in further. When comparing expected returns in both situation, hitting is your best option in general circumstances. Surrendering/standing is your best option using a single deck with a 7-7 vs 10 as the odds of drawing a 21 are greatly decreased with only 2 7s left in the deck.

nick777 wrote:

If you agree that this is true, what you are basically saying is that there is no advantage to playing 2 handed, so all the millions of pro blackjack players out there who play 2 handed actually have no idea what they are doing.

There are possible reasons for multi-hand play, which are listed below.

1. A reduced variance (with same overall initial bet size) — This is important, if you care about variance, as many pros do. But we aren’t talking about variance

2. A slight benefit from “depth charging” — Recall that this is counting cards in one hand and altering strategy in the second. If you are playing 4 decks with online rules (unknown shuffle, often shuffle after each hand), then the benefit will be negligible.

Why do you think just about every pro who plays multi-hand doesn’t split 10s in general circumstances (excluding a few special card-counting situations) while playing multi-hand?

nick777 wrote:

Give me an example of when it is better to play 2 handed, your odds suggest that it is never better to play 2 handed, it can only be the same as playing 1 handed, but never better, meaning, your odds of winning with any one given hand will never improve.

One situation would be playing through a large wagering requirement and wanting to minimize deviation from expected return. The reduced variance from multi-hand increases chance of falling near expected return when overall bet size is the same. However, it does not change house edge.

One possible advantage would be counting cards in a single deck. If you played 5 hands and knew the cards played in the first 4 hands, you could increase bet on the 5th and have a slight benefit. If you were playing at casino with live dealers that had known shuffle points, the benefit would be greater.

nick777 wrote:

I obviously disagree, according to your formula by playing 2 hands, the player will always lose to the house edge, only twice as much, since the bet is doubled.

How many times have I said house edge is the same when bet size and wagering are the same. If you double wagering by playing more hands simultaneously or more single-hands sequentially, then loss from house edge doubles.

nick777 wrote:

I am saying that a dealer with a 6 is one of those situations where it is better to have as many hands as possible in play, because the possibility of you winning are increased, and the possibility of you losing are decreased. Overall, not with any 1-2-3-4 hands in particular, there will be times when only 1-2-3 of your hands win and all 4 win, that is not really in question.

If you could change how many seats you were playing after seeing the dealer 6, then it would be to your advantage to sitting at all possible seats. Unfortunately you can not do this. It would not be to your advantage to split however, and reduce your expected return per hand drastically.

nick777 wrote:

By splitting your hand, the chances of the dealer drawing to 21 and beating you are 0%, technically there is no chance of it happening, even though there is, and this is going by the formula you use, so in every 100 hands you play, the dealer will still draw to 21 10 times, however, it will beat you 0 times.

The dealer has a ~10% chance of drawing a 21, regardless of whether you stand or split. He will not beat you 0 times. If he gets 21, you will almost certainly lose the several (or all) hands. REMEMBER THAT LOSSES COUNT EVEN IF YOU DON’T LOSE ALL HANDS SIMULTANEOUSLY.

nick777 wrote:

The reason is that you have an even better chance of drawing to 21 yourself, this negates the dealers 10% that beats you in the hand you are standing on, by splitting to 4 hands, you will draw to 21 around 40 times with your hands, 4 hands x 100, the dealer will still draw to 21 only 10 times out of 100, the odds actually favour my draw more to hit 21, regardless, you get the point.

Actually the dealer has a better chance of getting 21 than you do on each hand, when you split. It’s 10% for the dealer and ~1/13 for the player (only if you draw an Ace).

nick777 wrote:

I am critiquing your formula not for the sake of creating controversy, but because i find it flawed, especially in this situation, you say you will lose money by splitting to 4 hands, i say you will win 14% more money.

I also realize the fact that you have no choice but to prove yourself correct since you have a blackjack odds website that many people use, including myself on occassion, but i really think it would be in everyones best interest if you recalculated your odds for 2 handed play, it might also serve you well to have a section describing different philosophies between 1 and 2 handed play.
My odds are correct. It is ridiculous to think that odds and strategy differences change drastically for two-handed play. What happens if you are in a B&M casino and someone is sitting next to you? Do odds and strategy change drastically then to? And if he moves away, then odds and strategy return to the default?

[327007]

howardmoon wrote:

Sorry, my calculations above are incorrect. The difference between splitting and standing is even greater than I stated.

The actual return for splitting 10,10 against a 6, according to the Wizard’s chart I posted before, is 0.4681 (versus 0.704 for standing)

So you make $70.40 in total by standing and $46.81 in total for splitting.

It’s not even a close call. Never splitting tens is one of the clearest decisions in the blackjack strategy charts.
The numbers Wizard lists assume you resplit 10s. If you stand on 20 in the split hands instead of resplitting the 10s, then it is ~0.70 for standing and ~0.56 for splitting, as we have listed in the thread. If you resplit the 10s then it drops to Wizard’s numbers ~0.70 for standing and ~0.47 for splitting.

[327007]

nick777 wrote:

—- 4 Deck, H17, DOA, DAS, LSR, RSA=4, RSP=4 —
Player Hand: 10,10, Dealer upcard: 6 Decision: Stay
Hit:-0.85222 Stand:0.67576 Double:-1.70445 Split:0.36302

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

Stand: 0.675 x 2 = 1.35
Split: 0.363 x 4 = 1.45

But i’m sure everyone except the Wizard is wrong

HOW MANY TIMES DO WE HAVE TO SAY THIS. THE LISTED RETURNS ARE BASED ON THE INTITAL BET BEFORE SPLITTING. You are expected to multiply by overall initial bet, not the increased bet after doubling or splitting, or the decreased bet after surrendering.

Using the above stats it’s 0.675 x 2 (for two hands) vs 0.36 x 2 (for two hands). Obviously the better choice based on these nums is standing.

[Anonymous]

NolanA wrote:

The expected return is expected return per hand * bet per hand * num hand. In this case both the expected return per hand after splitting is low, and increasing num hands decreases in further. When comparing expected returns in both situation, hitting is your best option in general circumstances. Surrendering/standing is your best option using a single deck with a 7-7 vs 10 as the odds of drawing a 21 are greatly decreased with only 2 7s left in the deck.

There are possible reasons for multi-hand play, which are listed below.

1. A reduced variance (with same overall initial bet size) — This is important, if you care about variance, as many pros do. But we aren’t talking about variance

2. A slight benefit from “depth charging” — Recall that this is counting cards in one hand and altering strategy in the second. If you are playing 4 decks with online rules (unknown shuffle, often shuffle after each hand), then the benefit will be negligible.

Why do you think just about every pro who plays multi-hand doesn’t split 10s in general circumstances (excluding a few special card-counting situations) while playing multi-hand?

One situation would be playing through a large wagering requirement and wanting to minimize deviation from expected return. The reduced variance from multi-hand increases chance of falling near expected return when overall bet size is the same. However, it does not change house edge.

One possible advantage would be counting cards in a single deck. If you played 5 hands and knew the cards played in the first 4 hands, you could increase bet on the 5th and have a slight benefit. If you were playing at casino with live dealers that had known shuffle points, the benefit would be greater.

How many times have I said house edge is the same when bet size and wagering are the same. If you double wagering by playing more hands simultaneously or more single-hands sequentially, then loss from house edge doubles.

If you could change how many seats you were playing after seeing the dealer 6, then it would be to your advantage to sitting at all possible seats. Unfortunately you can not do this. It would not be to your advantage to split however, and reduce your expected return per hand drastically.

The dealer has a ~10% chance of drawing a 21, regardless of whether you stand or split. He will not beat you 0 times. If he gets 21, you will almost certainly lose the several (or all) hands. REMEMBER THAT LOSSES COUNT EVEN IF YOU DON’T LOSE ALL HANDS SIMULTANEOUSLY.

Actually the dealer has a better chance of getting 21 than you do on each hand, when you split. It’s 10% for the dealer and ~1/13 for the player (only if you draw an Ace).

My odds are correct. It is ridiculous to think that odds and strategy differences change drastically for two-handed play. What happens if you are in a B&M casino and someone is sitting next to you? Do odds and strategy change drastically then to? And if he moves away, then odds and strategy return to the default?

I like the fact that you take the time to explain each situation and fight for your team, it’s admirable

But i must point out some mathematical errors to you

The dealer does not have a better chance of hitting 21 with a 6 than i do with my 10’s, i don’t need just an ace, i can get a combination of other cards, 2-9, 3-8, 4-7, etc

So the dealer drawing to 21 advantage does not exist, since i have a better chance of getting a 21 total with my hands.

According to howard, the odds just changed, what are we, at the track ?

And i know michael is the marketeer for the wizard, so that explains that

This is never going to end, michael can try to discredit me all he wants, since he doesn’t seem to be good for anything else, but that doesn’t change the facts.

This is not a communist dictatorship here, agree with the wizard or else

[327007]

nick777 wrote:

$But i must point out some mathematical errors to you

The dealer does not have a better chance of hitting 21 with a 6 than i do with my 10’s, i don’t need just an ace, i can get a combination of other cards, 2-9, 3-8, 4-7, etc

So the dealer drawing to 21 advantage does not exist, since i have a better chance of getting a 21 total with my hands.

So you are saying if you draw a 4 for a total of 14, then you will hit again? You will hit a 12 vs 6, a 13 vs 6, and a 14 vs 6?! Wow, I assumed you would stand on a 12 or more vs 6 like every expert on the planet (in general circumstances). This is extremely common BJ knowledge. If you are hitting on 14 vs 6 rather than stopping at 12, then the expected return drops even more!

So what strategy do you use? Hit on hard 16 or less, regardless of dealer upcard?

[Anonymous]

Good God.

Nick, I think you’re just really, really stupid. Sorry to be rude and all, but there’s no other explanation.

Not understanding how something works is one thing, and nothing to be ashamed of. Still thinking that you must know better than the industry experts is just lunacy.

I really feel sorry for anyone who signs up to a casino through your site. It’d be like buying a car from someone who thinks it runs on magic beans.

[Anonymous]

NolanA wrote:

So you are saying if you draw a 4 for a total of 14, then you will hit again? You will hit a 12 vs 6, a 13 vs 6, and a 14 vs 6?! Wow, I assumed you would stand on a 12 or more vs 6 like every expert on the planet (in general circumstances). This is extremely common BJ knowledge. If you are hitting on 14 vs 6 rather than stopping at 12, then the expected return drops even more!

So what strategy do you use? Hit on hard 16 or less, regardless of dealer upcard?

Aha

Gotcha now

I would stand, but that has nothing to do with the odds, you can’t just throw in if’s and assumptions into your calculations, imagine everything in life was like that.

You can’t factor in human behavioural patterns into mathematical formulas, what are you going to do, add my dna to the probabilities chart.

Now howard, thats not very nice, you know i don’t like you, so i wouldn’t want to hear you say that to my face.

[Anonymous]

nick777 wrote:

Aha

Gotcha now

I would stand, but that has nothing to do with the odds, you can’t just throw in if’s and assumptions into your calculations, imagine everything in life was like that.

You can’t factor in human behavioural patterns into mathematical formulas, what are you going to do, add my dna to the probabilities chart.

Ok so that settles that one then. This conversation has left reality and we are now in bizarro world. Is it the voices in your head that tell you whether to hit or stand?

Move along people, nothing to see here. Let’s not crowd him, they can be dangerous if cornered.

[Author]

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