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I just want to make one last correction with my math, as Darko pointed out, that 6.72 figure was my bad, since i forgot i had already split once to get the 0.64 total, and already had 2 hands, causing me to over multiply one number, the 6.72 should be 3.36, then divided by 4, and the 1.4 is divided by 2.
The actual roi figure for 2 handed play is this
Standing 0.70
Splitting 0.84What i find bad business practice is that michael and most likely his pal nolan, are employees of the wizard of odds, and the whole time they were taking shots at me without even realizing i was using the very same odds formula they were using, except that i had adjusted it for 2 handed play.
What was also very bad practice was that instead of coming here and taking shots, they could’ve just listed the correct odds formula for 2 handed play, or at least make it available on their site somewhere, if they knew it.
As a result i have lost major respect for the wizard, and i am certain that they didn’t invent the calculating odds formula over there, but just put it on the web, yet they act like they did, it was most likely invented 100+ years ago by someone like me trying to beat the house.
Overall, I thought you guys gave a rather poor account of yourselves, and Michael’s attempts to get a fellow webmaster banned from an affiliate community for disagreeing with him were truly pathetic and shameful.
And now it’s time to leave you all for a while, the numbers are right, you can debate them all you want. In 2 handed play, using the example hand from page 1, splitting will return 14% more money than standing.
nick777 wrote:I just want to make one last correction with my math, as Darko pointed out, that 6.72 figure was my bad, since i forgot i had already split once to get the 0.64 total, and already had 2 hands, causing me to over multiply one number, the 6.72 should be 3.36, then divided by 4, and the 1.4 is divided by 2.The actual roi figure for 2 handed play is this
Standing 0.70
Splitting 0.84WOW, you admitted a mistake!!! I didn’t think that would ever happen. Okay, so now it sounds like you agree that if you compare standing on a single pair of 10s to splitting a single pair of 10s, you get the numbers that the blackjack experts around the world have accepted (~0.70 for stand and ~0.56 for split without resplits). But you are saying playing 2 seats at the table instead of a single hand drastically changes optimal strategy decisions?! Do you think the overall house edge drastically changes as well when playing multi-hand? What if you are in a B&M casino and several players are seated against a single dealer… Does the optimal split/stand strategy and house edge change drastically from when the other seats are empty?
You can use the cards played by the first hand to improve strategy slightly on the second hand in a card-counting sense. This is called “depth charging.” However, if you play with the same strategy in both hands, the average return per hand stays the same. If you have a million hands (and a suffiicient number of decks) the overall return would be 1 million * average return per hand. Playing 2 or more hands rather than single hand does not change the optimal split/stand strategy decisions.
Let’s extend your fomula of n!/2n * (Win rate per hand – loss rate per hand) further. If we cancel out the n, we get (n-1)!/2. For 4 hands, (n-1)!/2 = 3; and 3*(0.64-0.36) = 0.84. What if you were playing 5 hands and split all 5 to a total of 10 player hands, then it would be (10-1)!/2 = 0.18 million *(0.64-0.36) = ~50,000. Obviously, your expected return per hand is not going to be 50,000 times larger than your bet size!
It sounds to me like you are just making stuff up to get the results you want to see. You never explained why in the world you decided to multiply by factorials instead of the number of hands. If you are trying to do something with permutations and/or combinations, it is not relevant to this situation, and the formula is incorrect.
nick777 wrote:What i find bad business practice is that michael and most likely his pal nolan, are employees of the wizard of odds, and the whole time they were taking shots at me without even realizing i was using the very same odds formula they were using, except that i had adjusted it for 2 handed play.What was also very bad practice was that instead of coming here and taking shots, they could’ve just listed the correct odds formula for 2 handed play, or at least make it available on their site somewhere, if they knew it.
Now, you are just being silly. I’m an employee for Wizard of Odds?! Anyone who knows me from other forums, knows this is not correct. I’ve publically disagreed with Wizard of Odds’ info in the past… not because of incorrect math… because of outdated information. For example, I calculated different numbers on some of the Microgaming Keno returns (7-pick, 9-pick, and 13 to 15-pick), mostly likely because MG changed some of the Keno payout tables since when Wizard last checked.
nick777 wrote:As a result i have lost major respect for the wizard, and i am certain that they didn’t invent the calculating odds formula over there, but just put it on the web, yet they act like they did, it was most likely invented 100+ years ago by someone like me trying to beat the house.What “calculating odds formula” are referring to? How to compute an average (Congratulations on finally including losses in your latest formula!)? Formulas used to compute the returns from Wizard’s and my computer sims? I hope you realize the formulas I listed are common sense, and likely do not appear on the Wizard of Odds site.
I do work for the Wizard. This isn’t exactly a secret — if you click “About Us” on the Wizard’s site you see pictures of both of us.
In fact, it’s the because the Wizard is the world’s best gambling math expert that I wanted to work for him in the first place. As I keep pointing out, Nolan and I aren’t the only ones who respect his work, he’s widely regarded throughout the world as the best authority on the subject. Now, if you you want to stand alone in your opinion that a celebrated math professor can’t actually solve a simple equation, and that your analysis is superior, and that anyone who doesn’t recognize that is an idiot, that’s certainly your right. But it’s an odd position to take.
As for the idea that *my* actions were shameful — wow, if that statement isn’t an entry into the Irony Olympics, I don’t know what is. Nick, I didn’t try to get you “banned”; I simply quoted the disparaging comments that YOU made. I don’t know why you had a problem with people seeing those comments, given that you made them.
If you guys want to keep debating math, we can do that, we can start a whole new thread dedicated to it, people have disagreed over math for hundreds of years.
Just remember what you have on your site, you don’t have a winning system, you have an odds probability chart for 1 handed blackjack play.
And what you are trying to say, is that your return will be the same regardless of whether you are playing 1 hand or 2 hands, can we agree on that, that is what you’re saying ?
So i have some questions
Using a 4 card deck
1 – What are the odds of you getting 2 10’s(or 2 splitting cards with 10 value)
2 – In 2 handed play, what are the odds of getting 2 hands each with 2 10’s(or 2 splitting cards with 10 value)
What you have been saying this whole time is that your odds are the same, well i don’t agree
3 – What are the odds of a player with a 10 beating the dealer with a 6 up card.
4 – What are the odds of a player with a 20 total beating the dealer with a 6 up card.
Your whole argument from the start has been that the odds will be the same, regardless of whether you have 1 splitting hand or 2 splitting hands, each with a value of 10.
What i am saying is that the probability of you losing with 4 hands hitting on a 10 vs a dealer with a 6 make it much more profitable than 2 hands hitting on a 10 vs a dealer with a 6, 20+% more profitable, and because of that fact(4 favoured draws vs dealer 6, instead of 2 favoured draws vs dealer 6)it is more profitable than standing with the 20 over the long run. If you don’t do the correct math it will never make sense to you, in total it will come out to be around 14% more profitable of a play, depending on the number of decks.
There are other factors as well, and odds you should figure out
5 – What are the odds of you losing both splitting hands with a 10 draw vs dealer 6
6 – What are the odds of you losing all 4 splitting hands with a 10 draw vs dealer 6
There is no need for you to both to respond, unless you are practicing your Abbott & Costello routine, only one person who can actually figure out the correct odds will do, Wizards Apprentice Michael, you get the honours, Nolan is just being a fool with 50 000 totals, no need for clown biusiness, i don’t know how he came up with that number since he doesn’t have 50 000 fingers to count with.
No need for Nolan to even post to this anymore, i am not even acknowledging any of his findings, he has made himself look bad way too many times.
It’s up to you Michael, convince me, in other words prove it, start a thread in the free for all section, this one is already nearing 10 pages, get your Wizard, whatever it takes, all you have to do is tell me the exact percentages, i don’t have any problem with your 1 handed play numbers, however, you have shown nothing solid to support 2 handed play statistics, essentially you are saying that there is no difference between 1 and 2 handed play.
My whole philosophy with regards to 2 handed play is this
The house edge will always be there, but by playing 2 hands you are taking a more aggressive approach to the game, meaning you will win more and lose more on each hand, making potential gains with a monster hand much greater, like the hand used in this example.
I see the mistake you are making btw with your calculations, i’m hoping you see it too, i tried to explain, maybe i should try again, your numbers support this scenario…
Splitting 1 hand = 2 hands vs dealers 1 hand
Splitting 2 hands = 4 hands vs dealers 2 handsThis is the correct scenario
Splitting 1 hand = 2 hands vs dealers 1 hand
Splitting 2 hands = 4 hands vs dealers 1 handSince you put me through all this trouble, i hope you will be honourable and acknowledge that i am right, instead of continuing to mislead people in order to save face.
Nick777 wrote:There is no need for you to both to respond, unless you are practicing your Abbott & Costello routine…Nolan is just being a fool with 50 000 totals, no need for clown biusiness, i don’t know how he came up with that number since he doesn’t have 50 000 fingers to count with….
No need for Nolan to even post to this anymore, i am not even acknowledging any of his findings, he has made himself look bad way too many times….
Since you put me through all this trouble, i hope you will be honourable and acknowledge that i am right, instead of continuing to mislead people in order to save face….
You can’t continue to insult people like this and expect them to engage.
As I’ve said repeatedly, it’s not just the Wizard who says you stand on 10,10 vs. 6 (regardless of the number of hands you’re playing), but the entire professional blackjack/mathematical community. You want me to acknowledge that you’re right, but that would mean agreeing that 40 years of intense analysis of blackjack by the best minds in the business has come to the wrong conclusion. That would be an insane position to take.
Whom should I put my faith in?
(1) All the mathematicians and blackjack experts, who are *unanimous* about the proper blackjack strategy,
– or –
(2) Nick777
???
Easy choice.
As soon as you’re ready to accept a wager based on your supposed superior strategy let me know. Earlier you said you never shy from a challenge, but that’s exactly what you’ve done every time I’ve challenged you. If you really believe in your blackjack strategy, then put your money where your mouth is. Otherwise, I have to conclude that Nolan was right, that you don’t actually believe what you’re saying, you’re just trying to stir up trouble.
If you’re not trying to stir up trouble, then just agree to subject your strategy to a wager.
nick777 wrote:Just remember what you have on your site, you don’t have a winning system, you have an odds probability chart for 1 handed blackjack play.Multi-hand blackjack and 1-hand blackjack use the same strategy chart, assuming same rules. This should be obvious, so I doubt wizard of odds explicity states this. I certainly do not on my site. Instead I assume the reader can has some basic knowledge.
nick777 wrote:And what you are trying to say, is that your return will be the same regardless of whether you are playing 1 hand or 2 hands, can we agree on that, that is what you’re saying ?The house edge does not change. Assuming a constant bet size and wagering, the average return will be approximately the same. The variance will differ, but we aren’t discussing variance.
nick777 wrote:1 – What are the odds of you getting 2 10’s(or 2 splitting cards with 10 value)If we assume a dealer 6 has been played, then 64/207 * 63/206 = ~9.5%
A more simple approximation is (4/13)^2 = ~9.5%nick777 wrote:2 – In 2 handed play, what are the odds of getting 2 hands each with 2 10’s(or 2 splitting cards with 10 value)Roughly the above squared… 9.5% * 9.5%
nick777 wrote:What you have been saying this whole time is that your odds are the same, well i don’t agreeTHE OPTIMAL STRATEGY AND HOUSE EDGE ARE THE SAME. Obviously your odds of drawing all matching hands decrease as you increase the number of hands. If you played a million hands at once. You’d never draw the same cards in all one million hands, yet optimal strategy and house edge would remain the same.
nick777 wrote:What are the odds of a player with a 10 beating the dealer with a 6 up card.It depends on strategy. If we assume the player follows optimal strategy and does not split/resplit if he draws a 10, then… there is roughly a 61% chance of a win and 33% chance of loss. The expected return is ~0.28 x Bet Size.
nick777 wrote:What are the odds of a player with a 20 total beating the dealer with a 6 up card.There is roughly an 80% chance of a win and 10% chance of a loss. The expected return is ~0.70 x Bet Size.
nick777 wrote:Your whole argument from the start has been that the odds will be the same, regardless of whether you have 1 splitting hand or 2 splitting hands, each with a value of 10.If by “the odds” you mean optimal strategy, house edge, and overall expected return with overall bet size and wagering constant, then yes.
nick777 wrote:What i am saying is that the probability of you losing with 4 hands hitting on a 10 vs a dealer with a 6 make it much more profitable than 2 hands hitting on a 10 vs a dealer with a 6, 20+% more profitable, and because of that fact(4 favoured draws vs dealer 6, instead of 2 favoured draws vs dealer 6)it is more profitable than standing with the 20 over the long run. If you don’t do the correct math it will never make sense to you, in total it will come out to be around 14% more profitable of a play, depending on the number of decks.You mean losing all 4 hands simultaneously? Why would you worry about winning or losing all hands simulatenously unless computing variance.
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.
nick777 wrote:5 – What are the odds of you losing both splitting hands with a 10 draw vs dealer 6What are the odds of you losing all 4 splitting hands with a 10 draw vs dealer 6
The odds of simultaneously winning/losing all hands are (odds of winning or losing per hand)^ (num hands). So yes, the odds of a simulatenous win/loss in all hands decreases as the number of hands increases.
Was this your big revelation?! You do realize that losses count, even if you don’t lose all hands simulataneously don’t you? What would happen, if you played a million hands at once and had a ~zero chance of a simultaneous loss in all hands. Do you think the expected return would be 100% because you would never lose? Don’t you see how silly this is?
You are looking like a forum troll again in my mind. Each time, you seem to take a more ridiculous position than the last time. First it was splitting 10s has a higher expected return than standing in all situations. That’s an understandable mistake that some gamblers make. You’ve gone on to support this by computing averages without considering losses and posting several silly formulas. Now you are saying multihand blackjack has different optimal strategy and house edge from standard blackjack and justfying it by only looking at simulatenous losses in all hands??!! Why don’t you also only consider wins that occur simultaneously in all hands. Don’t you think the odds of simultaneously winning 4 hands are lower than simultaneously winning 2 hands?
========================================================
If you want to look at winning/losing all hands when computing overall return, then the correct way to do it is to sum the following:
-4 * Odds of losing 4 hands
-3 * Odds of losing 3 hands and pushing 1
-2 * (Odds of losing 3 hands and winning 1 + odds of losing 2 hands and pushing 2).
…Do a Google search on permutations and combinations to get valid formulas . Of course, the far easier way to compute overall return is simply looking at average return per hand * num hands.
Only one thing is obvious here
Michael has no math skills, or is keeping them cleverly hidden, but can throw reference at several people who have attempted to beat the odds and failed.
Nolan has basic math skills but cannot understand some things no matter how obvious they are, just admit that you don’t know how to figure out the correct odds for 2 handed play, if you do, put em up, don’t give me this roughly, approximately stuff, put up the exact odds, you repeat in saying that your return will be the same whether you have 2 hands drawing on a 10 vs the dealers 6, or 4 hands with a 10 drawing vs the dealers 6, how is this possible, you have 4 favourites vs 1 underdog in one situation, it’s not 4 favourites vs 1 underdog in 4 seperate 1 on 1 situations.
If it were an elimination fight where one fighter is fighting 4 other fighters, each of whom would be favoured in a 1 on 1 situation vs him, how many times would the one underdog fighter be able to beat all 4, 3, 2, or 1 of them.
Obviously the underdog fighter has a much better chance vs only 2 fighters at once, opposed to 4, yet you fail to realize that.
This is a nowhere conversation and it’s over
You guys go and kick that casino’s ass with your formula ok, if they wanna bar you for excessive winning call me, i’ll straighten them out.
nick777 wrote:just admit that you don’t know how to figure out the correct odds for 2 handed play, if you do, put em up, don’t give me this roughly, approximately stuff, put up the exact odds,
Of course I know how to compute the exact odds. For our purposes, it is a waste of time and effort to carry out to many decimal places, as there is a large difference in expected return between standing and splitting. When playing with multiple hands, there is a very slight difference in numbers from a single hand due to cards being missing from the deck that were played in the other hand. This difference is insignificant for our purposes, as we have never discussed numbers to enough decimal places for it to have an influence.nick777 wrote:you repeat in saying that your return will be the same whether you have 2 hands drawing on a 10 vs the dealers 6, or 4 hands with a 10 drawing vs the dealers 6, how is this possible, you have 4 favourites vs 1 underdog in one situation, it’s not 4 favourites vs 1 underdog in 4 seperate 1 on 1 situations.If it were an elimination fight where one fighter is fighting 4 other fighters, each of whom would be favoured in a 1 on 1 situation vs him, how many times would the one underdog fighter be able to beat all 4, 3, 2, or 1 of them.
Obviously the underdog fighter has a much better chance vs only 2 fighters at once, opposed to 4, yet you fail to realize that..
Did you even read my post? LOSSES COUNT TOWARDS YOUR EXPECTED RETURN EVEN WHEN YOU DON’T LOSE ALL HANDS SIMULTANEOUSLY. In your fighter example, what if 1 fighter wins and 3 fighters lose? And what if you win 1 hand and lose 3 hands? You do realize that you lose money in this situation, don’t you? Or is this another one of your misunderstandings of basic blackjack rules?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.
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.
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.
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.
There must be some advantages to playing 2 handed, or nobody would ever do it.
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 stand with 20, you will lose to a dealer drawing to 21 about 10% of the time, whether you are playing 1 handed or 2 handed, you will lose 10%, that doesn’t change.
Every 100 hands you play in that situation, the dealer will draw to 21 and beat you 10 times, whether it’s 1 hand or 10 hands you are playing.
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 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.
Your calculations factor in the probability that the dealer will draw to 21 and beat you, when really there is no chance of this ever happening. It will happen when you stand, not when you split.
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.
Nick, what I suggest you do is write some blackjack simulation software.
This software would need to do the following things:
Create a shuffled deck of X decks (X should be configurable at runtime)
Deal out a dealer hand and Y player hands (Y is configurable at runtime)
Play those hands out according to blackjack rules, calculating and recording the result of each possible player decision.Then you run that simulation a few billion times. Run it 1 billion times with 1 player hand, then another billion with 2 player hands, etc.
At the end, you will be provided with:
the correct decision to make in every situation (strategy charts)
the overall HAYou will then be able to test if there is any difference in HA if you have more or less player hands, and exactly which decisions give you the best return in the long run.
If you are incapable of writing this software, I suggest you stop arguing and accept the results generated by those who do understand how to simulate this. People like the Wizarde of Odds, Stanford Wong, etc, who all say that:
1. HA is unaffected by the number of hands you play
2. You should never ever split tens.(PS. Your assertation that playing more hands affects return may be based on card counters. It is true that professional blackjack card counters often move from playing 1 hand to 2 or more. That is because they wait until the current deck state is providing them with an edge, and then they increase their bet size to take advantage of that edge. This is called the ‘spread’. One way of spreading is just to increase the bet on one hand. The other is to add more hands.)
howardmoon wrote:Nick, what I suggest you do is write some blackjack simulation software.This software would need to do the following things:
Create a shuffled deck of X decks (X should be configurable at runtime)
Deal out a dealer hand and Y player hands (Y is configurable at runtime)
Play those hands out according to blackjack rules, calculating and recording the result of each possible player decision.Then you run that simulation a few billion times. Run it 1 billion times with 1 player hand, then another billion with 2 player hands, etc.
At the end, you will be provided with:
the correct decision to make in every situation (strategy charts)
the overall HAYou will then be able to test if there is any difference in HA if you have more or less player hands, and exactly which decisions give you the best return in the long run.
If you are incapable of writing this software, I suggest you stop arguing and accept the results generated by those who do understand how to simulate this. People like the Wizarde of Odds, Stanford Wong, etc, who all say that:
1. HA is unaffected by the number of hands you play
2. You should never ever split tens.(PS. Your assertation that playing more hands affects return may be based on card counters. It is true that professional blackjack card counters often move from playing 1 hand to 2 or more. That is because they wait until the current deck state is providing them with an edge, and then they increase their bet size to take advantage of that edge. This is called the ‘spread’. One way of spreading is just to increase the bet on one hand. The other is to add more hands.)
Fair enough Howard
It looks like we will never come to a resolution here, because i will not change my mind, and neither will they.
However i have no choice but to question a formula where the player will lose in the long run if he follows it to perfection.
The odds have been beaten on many occassions, even with regards to other subjects, if you take 100 scientists and mathematicians and put them in a room, you can bet they won’t agree on everything.
The point i was trying to make is that the odds are not the same as in 1 handed play, and the correct formula to figure out the true odds is much more complex than what they are using, they are breaking down every hand as if it were a 1 on 1 situation, then multiplying it by the number of hands in play, i don’t agree that this is the right way to calculate the true odds for this situation.
nick777 wrote:However i have no choice but to question a formula where the player will lose in the long run if he follows it to perfection.I don’t follow. You are questioning whether casino games have an inbuilt advantage to the house? If they did not, there would be no casinos. It’s a fairly established princinple of business that you need to take in more than you pay out, else you won’t be in business very long.
Quote:The point i was trying to make is that the odds are not the same as in 1 handed play, and the correct formula to figure out the true odds is much more complex than what they are using, they are breaking down every hand as if it were a 1 on 1 situation, then multiplying it by the number of hands in play, i don’t agree that this is the right way to calculate the true odds for this situation.The BJ professionals calculated the charts and the HA using simulations, not formulas. They write software that recreates a game, and tests the result of each possible player decision on each hand. Done a billion or more times this will provide the correct overall HA and the complete strategy charts.
Unless you have done those simulations yourself, you have no right to question their results, and you look foolish for doing so. You might as well claim that the world is flat, on the basis that you’ve never seen it curve.
I think we’re making some progress at last
I agree. while I don’t have a clue who is right or wrong, I can easily spot a post that doesn’t insult anyone on a name calling basis.
I applaud you for that Nick. :angel:
and right or wrong, it made the reading (for me) so much more pleasant that i actually was able to focus on your reasoning rather than the negative undertones.
… and what you say makes sense to a dummy like me. of course, that and the price of a cup of coffee will get you … a cup of coffee.
It wasn’t too long ago that everyone did believe the world was flat, and you would’ve been hanged for saying different.
I hardly think i’m not making sense here, not too long ago a simple math formula was used to defeat the roulette wheel, by guaging the speed of the ball accurately, i’m sure somebody would’ve said it’s not possible because of things like wind resistance.
I edited this because i really don’t want to deal with this thread anyomre, no more formulas and math, everyone go their own way here, 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.
nick777 wrote:It wasn’t too long ago that everyone did believe the world was flat, and you would’ve been hanged for saying different.Yes indeed. And those who said it was not flat had to prove it, and eventually their alternative evidence was accepted as correct.
If you wish to dispute accepted wisdom, you must be able to prove your claims, else you look foolish. Today, claiming that the world is flat without any scientific proof would make you look like a nut. This is the same as you claiming that the expert gambling mathematicians have been wrong for the last 40 years, without you providing any concrete proof for your alternative theories.
Quote:I hardly think i’m not making sense here, not too long ago a simple math formula was used to defeat the roulette wheel, by guaging the speed of the ball accurately.It wasn’t exactly simple, which is why it was conducted by a bunch of PHDs (or equivalent) and has thus far not been repeated. It required custom hardware to record the path of the ball, and then custom software to perform the calculations and predict the landing point.
But this backs up my point. Accepted wisdom was that you could not predict the landing point of the ball. They developed an alternative theory, and proved it in practice by developing the necessary tools to test it.
If you wish to dispute 40 years of accepted gambling mathematics, you must do the same. Create a simulation and prove your point, it’s not that hard. And if you don’t know how to make a simulation, and thus are unable to repeat their tests, on what basis do you think you’re qualified to question their facts?
Quote:Ignoring every advanced principle mentioned here for a moment, and looking at this simplistically…
Try to understand, you have 2 hands with an 85% chance of winning, (0.85 x 2) against 1 hand with a 15% chance of winning, (0.15 x 1)This is the correct maths for two tens against a dealer 6, assuming an infinite number of decks. The full charts, as generated by simulation, are here:
http://wizardofodds.com/blackjack/appendix1.htmlScenario 1, stand:
Return is 0.704, so for every $100 bet you get $170.40 back.So overall profit is $70.40 on your $100 bet
Scenario 2, split: (EDIT: these calcs are wrong, see next post. But the conclusion is still correct, in fact even more so.)
You now have two hands, both 10 versus dealer 6.
Your return per hand is 0.2878, so on a $100 bet you get back $128.78You have two hands, so you make $28.78 profit per hand for a total profit of $57.56.
This is clearly less than scenario 1.
Quote:You can thank me laterI’ll thank you now. Your blithe assumption that you can disprove 40 years of established mathematics with a few off-the-cuff formulas is highly amusing. I am keen to see what else you are able to disprove in the same manner.
They say the world is round, and they have all this evidence and photos and stuff to prove that, but I’m pretty sure it isn’t – I mean, I used a spirit level on some shelves I was putting up, and it said they were flat! So I must be right, those scientists don’t know what they’re talking about.
