Maringale~Regression to the Mean~Fade
December 23rd, 2011 at 9:02:19 PM
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I will use Roulette for an example, but this goes for all even money bets. "On August 18th, 1913, at the casino in Monte Carlo, black came up a record 26 consecutive times", and a Google search revealed an insane 32 consecutive red spins, at a Brazilian casino, 40 years ago. (fake??) My question for the Wizard, is that IF I HAD A CONSTANT SUPPLY OF INDIVIDUALS with the fortune or misfortune of hitting/missing 22-24 in a row, could I martingale/regression to the mean/fade, etc., them into a profit? It makes sense to me because barring an epic streak of historical proportions, my bankroll would be safe. I look forward to your reply, or any others are welcome to chime in on this approach.
December 24th, 2011 at 12:47:07 AM
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not sure what regression means here, but it sounds like your problem would be the ordinary circumstance of shorter streaks!
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell! She is, after all, stone deaf. ... Arnold Snyder
December 24th, 2011 at 3:48:53 AM
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Your real problem will be table maximums. Casino's have figured out how to stop an unlikely series from costing them too much.
Gambling is a metaphor for life. Hang around long enough and it's all gone.
December 24th, 2011 at 5:33:09 AM
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Quote: ncfatcatYour real problem will be table maximums. Casino's have figured out how to stop an unlikely series from costing them too much.
I wonder if this could be overcome by having 2 or more people make the same bet? Yes, I realize that the casino may close a table or not allow action on a color at some crazy level, but for most?
That martingale system is seductive. Problem is, the theory is sound. Wiz himself states if you had an infinate bankroll and if you had no limits and if you had infinate time that it would work. So everybody tries to see if you can work it with fewer "ifs."
NOTE: this is a theoretical question only, I know the reasons Martingals doesn't work.
All animals are equal, but some are more equal than others
December 24th, 2011 at 6:19:34 AM
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That'll just allow you to get one level past the table limit. Add two more people and you can climb one more rung up that ladder. A couple more losses, and that table will be too crowded to play.Quote: AZDuffmanI wonder if this could be overcome by having 2 or more people make the same bet?
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
December 24th, 2011 at 8:05:05 AM
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Quote: AZDuffmanProblem is, the theory is sound. Wiz himself states if you had an infinate bankroll and if you had no limits and if you had infinate time that it would work. So everybody tries to see if you can work it with fewer "ifs."
I doubt that the wizard ever said the theory was sound. Given an infinite bankroll, and infinite amount of time, and infinitely high table max wouldn't matter because you would eventually hit an infinitely long losing streak. Think about it. If everything else was infinite ( a vague concept) then so would the losing streak.
You have to be very careful of how you use the word "infinite". Mathematicians (particularly Wierstrauss) developed very specific definitions in the 19th century of how to define concepts like "infinite", so you won't be trapped into these logical fallacies.
The highest table limits I have ever seen allowed you to lose up to 10 times (doubling each time) before you hit the table limit. But 5 or 6 times is more common. But it doesn't matter how big the table limits are. Even given no house edge, you are twice as likely to hit a long enough streak to bankrupt you before you double your bankroll (assuming your bankroll is large enough to cover the maximum number of losses permitted by the table). That is a mathematical fact.
Artificially increasing your maximum bet by having dummy players doesn't mean anything.
December 24th, 2011 at 9:48:45 AM
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Quote: AZDuffmanWiz himself states if you had an infinate bankroll and if you had no limits and if you had infinate time that it would work. So everybody tries to see if you can work it with fewer "ifs."
I never said that. In fact, I have said the opposite, that even with infinite money, betting limits, and time the Martingale still doesn't win in a negative game like roulette. It has been argued here before, and it gets ridiculous because it gets into semantics about what infinity means.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
December 24th, 2011 at 12:06:13 PM
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Quote: WizardI never said that. In fact, I have said the opposite, that even with infinite money, betting limits, and time the Martingale still doesn't win in a negative game like roulette. It has been argued here before, and it gets ridiculous because it gets into semantics about what infinity means.
Sorry if I quoted it incorrect, I was going off of this:
https://wizardofodds.com/ask-the-wizard/76/
I didn't remember the semantics of infinity part.
All animals are equal, but some are more equal than others
December 24th, 2011 at 12:14:39 PM
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OK, forget roulette, never should have used it as an example.
Dear Wizard, Welcome to Ohio! I have filled "The Horseshoe" with 105,000 coin flippin' Ohio State Buckeye fans! We have sealed the exit ramps, so they will be here for a decade. 24/7, they are flippin' coins, and happy to do it. (just roll with it, establishing law of large numbers) We instruct them to come down to midfield if anyone can flip 22 heads or tails in a row. The process is mundane, but several times a month, people come to midfield as instructed. Even though they've accomplished an amazing feat, they are sat back in their seat if they can't extend their streak to 25 in a row. The few that can get to 25, we begin to fade them. No juice, no house edge, just a bankroll of $100,000 with $100 bets, and using martingale. We will also apply, "Regression to the upper mean", since mean is 50% in a coin flip, we will stop betting with these people when their percentage drops under 95%. Even though it would set world records, STILL a flawed betting system for even money games???
Dear Wizard, Welcome to Ohio! I have filled "The Horseshoe" with 105,000 coin flippin' Ohio State Buckeye fans! We have sealed the exit ramps, so they will be here for a decade. 24/7, they are flippin' coins, and happy to do it. (just roll with it, establishing law of large numbers) We instruct them to come down to midfield if anyone can flip 22 heads or tails in a row. The process is mundane, but several times a month, people come to midfield as instructed. Even though they've accomplished an amazing feat, they are sat back in their seat if they can't extend their streak to 25 in a row. The few that can get to 25, we begin to fade them. No juice, no house edge, just a bankroll of $100,000 with $100 bets, and using martingale. We will also apply, "Regression to the upper mean", since mean is 50% in a coin flip, we will stop betting with these people when their percentage drops under 95%. Even though it would set world records, STILL a flawed betting system for even money games???
December 24th, 2011 at 12:23:52 PM
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Quote: DHass22OK, forget roulette, never should have used it as an example.
Dear Wizard, Welcome to Ohio! I have filled "The Horseshoe" with 105,000 coin flippin' Ohio State Buckeye fans! We have sealed the exit ramps, so they will be here for a decade. 24/7, they are flippin' coins, and happy to do it. (just roll with it, establishing law of large numbers) We instruct them to come down to midfield if anyone can flip 22 heads or tails in a row. The process is mundane, but several times a month, people come to midfield as instructed. Even though they've accomplished an amazing feat, they are sat back in their seat if they can't extend their streak to 25 in a row. The few that can get to 25, we begin to fade them. No juice, no house edge, just a bankroll of $100,000 with $100 bets, and using martingale. We will also apply, "Regression to the upper mean", since mean is 50% in a coin flip, we will stop betting with these people when their percentage drops under 95%. Even though it would set world records, STILL a flawed betting system for even money games???
Why not do this at Notre Dame so people stay willingly and you don't need to seal the exits?
On the serious side, assuming a truly unbiased coin flip it should not matter, neither side will come out ahead in a game with no edge for either side. The 25th bet is no different than the 1st, odds are 50/50.
All animals are equal, but some are more equal than others
December 24th, 2011 at 12:27:43 PM
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Just for the records, casinos were banished from Brazil about 66 years ago.
No bounce, no play.
December 24th, 2011 at 1:00:59 PM
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Quote: AZDuffmanSorry if I quoted it incorrect, I was going off of this:
https://wizardofodds.com/ask-the-wizard/76/
I didn't remember the semantics of infinity part.
Point well taken. My position has changed on that question since that column was published. I just updated my answer to say:
Quote:I maintain that even with an infinite bankroll, betting limits, and time the Martingale still would not beat a negative expectation game like roulette. My reason is that as these elements approach infinity the expected value of the Martingale on roulette is still -5.26%.
Still, mathematicians I respect have disagreed with me. The debate tends to get very abstract and absurd, hinging on the nature of infinity, which is a man-made construct to begin with. There is nothing known in our universe that is infinite. If forced, I think it is a ridiculous question.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
December 24th, 2011 at 4:05:49 PM
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Would we still gamble if we had infinite bankrolls?
Gambling is a metaphor for life. Hang around long enough and it's all gone.
December 24th, 2011 at 6:11:37 PM
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Finding it hard to get a straight answer. I am going to continue with this "Regression to the Upper Mean" system because for 5+ years now, I'm far & above my initial investment, (sure to be pawned off as luck) so unless I run up against a Guiness Book of World Record streak (that everyone in here seems to fear) I will keep increasing my portfolio with house money.
December 24th, 2011 at 6:44:13 PM
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Quote: AZDuffmanWhy not do this at Notre Dame so people stay willingly and you don't need to seal the exits?
On the serious side, assuming a truly unbiased coin flip it should not matter, neither side will come out ahead in a game with no edge for either side. The 25th bet is no different than the 1st, odds are 50/50.
Ha ha AZ, (Notre Dame, seriously good joke.) That's precisely what we're after, "no edge for either side". Yes, the odds are 50/50, I'm just tailing people with mind numbing fortune or misfortune, NOT joining them at a streak of 10-15 in a row, those are what Vegas is built on. I'm talking about extremes on the outer realm of comprehension, that's when you start fading.
December 25th, 2011 at 6:08:15 AM
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Quote: DHass22Ha ha AZ, (Notre Dame, seriously good joke.) That's precisely what we're after, "no edge for either side". Yes, the odds are 50/50, I'm just tailing people with mind numbing fortune or misfortune, NOT joining them at a streak of 10-15 in a row, those are what Vegas is built on. I'm talking about extremes on the outer realm of comprehension, that's when you start fading.
But the thing is this and it is what most people who bet against roulette streaks miss. Say you walk up to the table and 10 reds have been rolled. YOU are a new bettor betting on one spin of the wheel. You are not betting on a streak 11 reds in a row. Yes, the odds of 11 reds in a row are long, but you have to bet for or against 11 just after a black was spun.
Same on a coin flip. I offer you a wager, "hey, want to bet I get three heads in a row?"
It doesn't matter if I have been sitting there and flipped 15 tails in a row and think I have a hot coin of if I just got it in change from a vending machine, you are betting 3 heads in a row. The odds of that are .50*.50*.50.
This is why some casino-guy put the roulette history board up. Is the casino cheating somehow? Not if it is a legit place and not some backdoor joint with rigged wheels. But the board does stimulate action, person thinks "red is due!" and makes a bigger bet then they might have.
Some people use "systems" here that are harmless. They might plan to flat bet anyways but always choose a color oppisite what just hit. As systems go this is harmless if and only if you are making a bet you otherwise would have made since there is no difference in what you pick at roulette. But if you martingale or use some other progressive system then you stand a great chance of not having to carry all those heavy cheques to the cage.
All animals are equal, but some are more equal than others
December 25th, 2011 at 7:56:09 AM
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I actually have to post a different opinion... in real terms, I believe, Martingale on roulette is not a -5.26% game.
My reasoning is as follows. While per physical spin the HA is the same, it's meaningless in context of the game as a whole, the objective being bankroll change rather than wheel spinning. When following martingale, individual spin bets are not independent, but dictated by previous events. What should be measured is EV per resolved independent bet.
For 2-deep martingale, the possibilities are as follows:
18/38: Win 1 unit on 1st spin, EV+0.4737
18/38*20/38: Win 1 unit on 2nd spin, EV+0.2493
20/38*20/38: Lose 1+2=3 units, EV-0.831
Total EV is then -0.108 of the initial bet.
For n-deep martingale, it extends to:
1-(20/38)^n: Win 1 unit
(20/38)^n: Lose 2^n-1 units
For a total EV of 1-(20/38)^n-(2^n-1)(20/38)^n = 1-(20/38)^n*2^n = 1-(40/38)^n ~= 1-1.0526^n
So a paradox only exists in common terms. Mathematically the function 1-a^n is very simple. It asymptotically approaches +1 for a<1 (game favorable to player), always equals zero for a=1, and exponentially approaches -infinity for a>1. This applies to any games, where a=1-EV of a single roll.
My reasoning is as follows. While per physical spin the HA is the same, it's meaningless in context of the game as a whole, the objective being bankroll change rather than wheel spinning. When following martingale, individual spin bets are not independent, but dictated by previous events. What should be measured is EV per resolved independent bet.
For 2-deep martingale, the possibilities are as follows:
18/38: Win 1 unit on 1st spin, EV+0.4737
18/38*20/38: Win 1 unit on 2nd spin, EV+0.2493
20/38*20/38: Lose 1+2=3 units, EV-0.831
Total EV is then -0.108 of the initial bet.
For n-deep martingale, it extends to:
1-(20/38)^n: Win 1 unit
(20/38)^n: Lose 2^n-1 units
For a total EV of 1-(20/38)^n-(2^n-1)(20/38)^n = 1-(20/38)^n*2^n = 1-(40/38)^n ~= 1-1.0526^n
So a paradox only exists in common terms. Mathematically the function 1-a^n is very simple. It asymptotically approaches +1 for a<1 (game favorable to player), always equals zero for a=1, and exponentially approaches -infinity for a>1. This applies to any games, where a=1-EV of a single roll.
Resist ANFO Boston PRISM Stormfront IRA Freedom CIA Obama
December 25th, 2011 at 2:43:37 PM
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Quote: P90I actually have to post a different opinion.
You are not calculating the probability of the game as a whole, you are calculating the probability of losing or winning n games in a row.
December 25th, 2011 at 3:57:56 PM
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Following a martingale system, that is the probability of the game as a whole for any finite number of bets.
OP's question was whether he could turn it into a profit, which would require a +EV game. However the game actually goes down in EV with martingale depth increase, so the answer is no.
For the probability of an infinitely long losing streak - such a probability is (20/38)^n, which is exponential, vs the number of hands that is linear, so the probability of an infinitely long losing streak in an infinitely long game is infinitely small. Which is I suppose where the point of contention lies.
OP's question was whether he could turn it into a profit, which would require a +EV game. However the game actually goes down in EV with martingale depth increase, so the answer is no.
For the probability of an infinitely long losing streak - such a probability is (20/38)^n, which is exponential, vs the number of hands that is linear, so the probability of an infinitely long losing streak in an infinitely long game is infinitely small. Which is I suppose where the point of contention lies.
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December 25th, 2011 at 4:58:08 PM
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Quote: P90I actually have to post a different opinion... in real terms, I believe, Martingale on roulette is not a -5.26% game.
snip...
This is a great explanation of why the Martingale is actively harmful to a bank roll more than just "a system".
If 1-a^n tends to 1 is A < 1, this implies that playing a martingale in a game where you have the odds in your favour is worse than flat betting.
I've thought a casino that had a player who played a Martingale-only strategy should have the table limits raised... the casino risks only a unit bet each time for a shot at winning the entire roll.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
December 25th, 2011 at 10:37:49 PM
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Listen all you Ivy Leaguers. Most of the replies wrestle with the ramifications of infinity, eventhough I've listed a FINITE example. (August, 1918, Monte Carlo casino, a streak of black is documented at 26 consecutive spins.) So, I ask again, If I had an ample supply of individuals involved in a streak of 22-24, could I turn a profit?, because unless a new world record is established (26+) I should be able to fade that streak with a martingale. In the highly unlikely event that a streak I was fading went beyond 26, I'd just tip my cap and call The Guinness Book of World Records.
December 25th, 2011 at 11:35:23 PM
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You got the money to fade the action for 26 straight doublings of a $5 bet?
If you have why the holy hand grenades would you be playing Roulette?
If you have why the holy hand grenades would you be playing Roulette?
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
December 25th, 2011 at 11:58:36 PM
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Quote: thecesspitYou got the money to fade the action for 26 straight doublings of a $5 bet?
Bet number 20 is over 5 million bucks. Bet 26 is over 300 million. Kinda pointless to win back 5 dollars.
"It's not called gambling if the math is on your side."
December 26th, 2011 at 7:03:14 AM
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TheCessPit & EvenBob, Please re'read my last post. I'm not following those individuals from their 1st pick; I'm starting the fading process on those individuals when they get to 22-24 picks.
December 26th, 2011 at 7:51:48 AM
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Quote: DHass22I'm not following those individuals from their 1st pick; I'm starting the fading process on those individuals when they get to 22-24 picks.
So you are trying to find extremely unlucky or extremely lucky individuals, or what?
Quote: DHass22So, I ask again, If I had an ample supply of individuals involved in a streak of 22-24, could I turn a profit?, because unless a new world record is established (26+) I should be able to fade that streak with a martingale.
So... they aren't actually playing for money, just betting on an empty wheel?
And then you want to take people who rolled a lot of black and send them to a money wheel to bet on red?
That's far more ridiculous than just believing in luck - if I take it right, you believe their roll history will follow them around?
What happens if two people with opposite roll history bet on the same wheel - will a small black hole form and swallow the ball?
Quote: DHass22In the highly unlikely event that a streak I was fading went beyond 26, I'd just tip my cap and call The Guinness Book of World Records.
If you had thousands of wheels that just had 24-long streaks, it's almost certain that you will set a new world record. What makes you think it's impossible? The Guinness Book is updated all the time.
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December 26th, 2011 at 8:30:29 AM
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P90, 1st quote; Yes, I have ways of finding them, and they don't need to know I'm following them, and don't even need to be approached. 2nd quote; No, they aren't playing roulette, it's another 50/50 proposition bet. No, I don't believe their, "roll history will follow them around". I do believe that regression the mean will take place, example; their 24 for 24 streak will eventually drop below 95% (something like 24 for 26, 27 for 29, etc.) before I move onto the next person. 3rd quote; Yes, It's very possible, at some point a record would be set, BUT, I would be well beyond my initial investment, and playing with house money before it would happen. In fact, I've been living that for the past 5+ years. THANK YOU for posting and asking pertinent questions!, great debate!
December 26th, 2011 at 10:29:25 AM
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Ah so you are finding rare occurrences of 22-long streaks and then fading the action for the next x spins with a Martingale, because "26 long streaks don't occur that often"?
Regression to the mean is meaningless over a short period (it's also Law of Large Numbers, and it's talking about over all averages), and as you said, lets not talk about infinities.
If you believe the choices are random 50/50 shots and each choice IS random and independent, the previous 22 spins have no effect on the next 22 spins. If you believe the previous spins are having an effect, then the spins are not truly random, so all bets are off.
Regression to the mean is meaningless over a short period (it's also Law of Large Numbers, and it's talking about over all averages), and as you said, lets not talk about infinities.
If you believe the choices are random 50/50 shots and each choice IS random and independent, the previous 22 spins have no effect on the next 22 spins. If you believe the previous spins are having an effect, then the spins are not truly random, so all bets are off.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
December 26th, 2011 at 10:43:37 AM
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Nevermind the fact that you will need at least $500,000,000,000,000,000,.... etc. Yep, no doubt about it. Four people should have more money than our national debt.
December 26th, 2011 at 10:43:57 AM
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Duplicate. Forum locked up on me while posting again.
December 26th, 2011 at 10:44:08 AM
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duplicate
December 28th, 2011 at 12:09:11 AM
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Sorry, looks like Keyser inadvertantly hijacked the thread.
Please clarify, "If you believe the choices are random 50/50 shots and each choice IS random and independent, the previous 22 spins have no effect on the next 22 spins. If you believe the previous spins are having an effect, then the spins are not truly random, so all bets are off".
The way I want to answer that is; I don't believe the previous 22 spins have an effect on future outcomes. But I do believe that within the next 10 or so bets, it will return to normal, even profitable at 3-7, or 2-8, etc.
Please clarify, "If you believe the choices are random 50/50 shots and each choice IS random and independent, the previous 22 spins have no effect on the next 22 spins. If you believe the previous spins are having an effect, then the spins are not truly random, so all bets are off".
The way I want to answer that is; I don't believe the previous 22 spins have an effect on future outcomes. But I do believe that within the next 10 or so bets, it will return to normal, even profitable at 3-7, or 2-8, etc.
