Old man betting, interesting way of playing (short term only) + few questions

This is not my method. I saw this and found it quite interesting.

I was in a casino playing roulette (I really love this game), but have yet to find a way of increasing my odds for the short term :)

I know you can not beat roulette, but you can increase your chances and make profit for the short term right? So if you play "smart" you can end up with a profit most of the times if I'm correct?

I have been playing roulette only for 6-7 months, so bascially a newbie :)

Anywayz to continue. I was playing roulette (a live table) along with a few others. A moment later an older man joined. He just watched for a few spins while writing down the numbers. After a few spins he put a total of 1k on the table spread like this:

100 on even, 100 on red, 200 on 2nd-12, 200 on 3rd-12, 200 on 1-34 (first column) and 200 on 2-35 (second column) a total of 1K. I was suprised, it was quite a lot of money on a minimum bet of 10 table. The next spin comes up. Number falls on 22. That is 1400 (+400 profit). he wrote down the number as well. Next spin and the number falls on 32. That is 1600. So in 2 spins he had a profit of 1000.

Next spin he decides to bet nothing. The ball falls in 2. If he would bet the same he would've lost 200. Next spin same betting system, ball falls on number 23, so that would be 1400 again...

The next 3 spins he did nothing (no bets) and the numbers were 7, 27 and 1 all losing numbers. I was really suprised. I am aware of electronic devices but as far as I could see there was nothing, he did not wear a suit or bag or anything.

So how did he knew when to bet and when not to bet? Also I tested for only a few spins his system and I did make a small profit (I did not bet big as he did).

Well after those spins he cashed out.

I calculated quickly what the "good" numbers are(when you make profit) and the bad numbers (when you lose).

Good numbers:
-35
-29
-14
-16
-22
-34
-28
-22
-32
-23
-19
-25

Bad numbers:

-6
-11
-0
-15
-8
-17
-9

There are more but that is all I remember.

So for the more "experienced" people or anyone who who like to write down their thoughs about it :)

- How did he knew when to bet and when not to bet?
- What are the chances of htting a "good" number when you play 10 times in a row?
- What are the chances of hitting a "bad" number" when you play 10 times in a row?
- Can this be used for profit on a long term (chances)?
- What more numbers are "bad"?

The 1 thing I noticed is this only works on short term plays, I guess a max of 10 spins. Or cash out when you have some nice profit. This only works as well when you play with at least 1K or at least that is the impression I have.

Sorry for the long post, but this was so funny and interesting I had to post.

Actually, 19 of the 38 numbers lose, only 16 win, and three break even:

Number	Even	Red	12s	Columns	Total
0	-1	-1	-2	-2	-6
00	-1	-1	-2	-2	-6
1	-1	+1	-4	+2	-2
2	+1	-1	-4	+2	-2
3	-1	+1	-4	-4	-8
4	+1	-1	-4	+2	-2
5	-1	+1	-4	+2	-2
6	+1	-1	-4	-4	-8
7	-1	+1	-4	+2	-2
8	+1	-1	-4	+2	-2
9	-1	+1	-4	-4	-8
10	+1	-1	-4	+2	-2
11	-1	-1	-4	+2	-4
12	+1	+1	-4	-4	-6
13	-1	-1	+2	+2	+2
14	+1	+1	+2	+2	+6
15	-1	-1	+2	-4	-4
16	+1	+1	+2	+2	+6
17	-1	-1	+2	+2	+2
18	+1	+1	+2	-4	0
19	-1	+1	+2	+2	+4
20	+1	-1	+2	+2	+4
21	-1	+1	+2	-4	-2
22	+1	-1	+2	+2	+4
23	-1	+1	+2	+2	+4
24	+1	-1	+2	-4	-2
25	-1	+1	+2	+2	+4
26	+1	-1	+2	+2	+4
27	-1	+1	+2	-4	-2
28	+1	-1	+2	+2	+4
29	-1	-1	+2	+2	+2
30	+1	+1	+2	-4	0
31	-1	-1	+2	+2	+2
32	+1	+1	+2	+2	+6
33	-1	-1	+2	-4	-4
34	+1	+1	+2	+2	+6
35	-1	-1	+2	+2	+2
36	+1	+1	+2	-4	0

The 12s column combines the two 12s bets, and the Columns column combines the two Columns bets

As for how he "knows" when to bet and when not to bet, your guess is as good as mine. I chalk it up to "just plain lucky that day."

Quote: Kingdombunnies

I know you can not beat roulette, but you can increase your chances and make profit for the short term right? So if you play "smart" you can end up with a profit most of the times if I'm correct?

No, your chances are always the same, short or long term. The only thing that *changes* is that based on how you spend your bankroll and place your bets is the distribution of results. Sure you can bet with hopes that some short term variance will be in your favor but its still balanced out on the other end with you losing your money.

@ThatDonGuy

Thnx for the chart and explanation :) That make things clearer :)

@DiscreteMaths2 thnx as well, so bascially it doesn't matter. In the end I have a good chance of winning as a good chance of losing.

Also what you are saying is that no matter what kind of system you play your win/ loss chance would be the same?

Does that mean in your opinion that all "systems" regarding roulette are of no use in the end?

Or is there a playing style regarding roulette that will give you an edge? You don't have to tell me I will find out whether it exists or not but I am curious what other people think as well :)

Quote: Kingdombunnies

This is not my method. I saw this and found it quite interesting.

I was in a casino playing roulette (I really love this game), but have yet to find a way of increasing my odds for the short term :)

That's because playing the game straight up (not ball tracking, biased wheel, etc) you can not change the odds with ANY betting system.

Quote: Kingdombunnies

I know you can not beat roulette, but you can increase your chances and make profit for the short term right? So if you play "smart" you can end up with a profit most of the times if I'm correct?

No. DiscreteMaths points this out and explains it but I just wanted to re-iterate that this logic is flawed.

Quote: Kingdombunnies

So for the more "experienced" people or anyone who who like to write down their thoughs about it :)

- How did he knew when to bet and when not to bet?
- What are the chances of htting a "good" number when you play 10 times in a row?
- What are the chances of hitting a "bad" number" when you play 10 times in a row?
- Can this be used for profit on a long term (chances)?
- What more numbers are "bad"?

1) He didn't. It was just luck. He probably does the same thing on other nights and when he doesn't bet a winning number would have come up. You happened to be part of the Law of Large Numbers where you think it's a coincidence that he didn't bet and happened to of hit a losing number.

2) His chance of hitting a "good number" is exactly the same whether you bet 1 time, or 10 times in a row. These are independent trials and do not rely on previous or future numbers. So when he writes the numbers down, he's just submitting to the gamblers fallacy that the past short term results will have any affect on the upcoming spin. 16/38 numbers are good, but on average of the winning bets he's only winning 3.875 units. When he hits a "bad" number, 19/38 times, he loses an average of 3.9 units. I hope you can see how weighted this is. The units are "close" to being the same, but he's winning 16/38 times and losing 19/38 times... You're going to do more losing than winning.

3) See answer #2

4) No. You will absolutely lose in the long term, and if you understand math means you have a negative expectation AT ALL TIMES, even the short term, but variance is the only reason 'some nights' (rarely) people walk away winners. Using our numbers from above, we can find the EV of 1 particular spin:

EV = (16/38)*(3.875) + (19/38)*(-3.9) + (3/38)*(0) = 1.63 - 1.95 + 0 = -.32 units PER SPIN

42% of the time you win 1.63 units.
50% of the time you lose 1.95 units.
8% of the time you push.

In the SHORT term, AND the long term you're expected to lose .32 units per spin, on average.

5) See ThatDonGuy's response.

Quote: Kingdombunnies

The 1 thing I noticed is this only works on short term plays, I guess a max of 10 spins...

So what about the night where you walk in and hit multiple losing numbers in a row? Anything in the short term is variance that will inevitably converge to your actual Expected Value (EV) over the long run. There is no such thing that "only works in the short term" because why wouldn't you just go do it every single night? I'll tell you why... because that adds up to the long term. So basically you're saying it only works for one or two nights, which is the same as saying "I got lucky a few times and then never did it again." That doesn't prove that it works at all, just that the player was lucky a few times. Proof that something works requires large sampling sizes, which this system would undoubtedly fail by the time it got to that many trails.

When Jesus returns, look for him first at the roulette wheel.
He'll need some pocket change.
And he will know what numbers to bet ;-!

The Wizard would say such systems are useless, I am not so harsh. They have value in that they can give a player extra enjoyment in their gambling pursuits. Roulette is a game of independent trials, so no there is no betting system that is going to change the probability of a given spin of the wheel. If you want an edge in roulette you need to find a bad wheel, a bad dealer, or rules/promotions that will be in your favor.

Quote: Kingdombunnies

@DiscreteMaths2 thnx as well, so bascially it doesn't matter. In the end I have a good chance of winning as a good chance of losing.

Also what you are saying is that no matter what kind of system you play your win/ loss chance would be the same?

Does that mean in your opinion that all "systems" regarding roulette are of no use in the end?

Or is there a playing style regarding roulette that will give you an edge? You don't have to tell me I will find out whether it exists or not but I am curious what other people think as well :)

No, you have a better chance of losing than you do of winning, which is how the math of the game is set up to work in the casinos favor and why the house always wins.

If you use different systems you might lose more but the least you'll ever lose is betting the smallest amount on the smallest house edge.

There are ways of beating roulette that aren't too secretive, but require a ton of training, data gathering, etc, that would take quite a long time and effort that most will not do. There is no "walk in to any casino and win at any roulette game" silver bullet you're looking for. One of the simplest ways to beat roulette is to find a biased wheel. Older wheels weren't made perfectly and even the slightest offset in weight, size, whatever, will bias it towards certain numbers on the wheel. You need about 8,000 spins worth of data to tell if any numbers are biased or not which would take a long ass time of reading those boards to see if it's true. Then you have the problem that casinos sometimes rotate wheels at tables, or switch them out altogether, which means you'll have to have a way of identifying "your" wheel.

But if you can find a place that uses older wheels, confirm it has a bias, and confirm a distinctive mark on the wheel so you know it's the right one... Then yeah, you can beat roulette by simply betting the biased numbers for as long as they'll let you and eventually you'll win.

Thnx Romes and DiscreteMaths2 for the reply.

And Romes thanks for answering all my questions.

Yes I do realise you can not just walk in and find the winning system.

Of course somewhere in my mind I had hoped for some kind of system exepect the bias wheels. Because of the many so claimed Holy Grails, sometimes you don't know what to believe :)

Thats why I appreciate the honest answers (thet are in no way harsh). Just try to collect as much information as possible.

Thnx!

Anyone who says they're beating roulette with a betting "system" or "method" (they're both the same), is a liar.

Quote: Ibeatyouraces

Anyone who says they're beating roulette with a betting "system" or "method" (they're both the same), is a liar.

You may have insulted one or more members here.You, of all people, should know better ;-)

no, there is a diffence in being correct over calling someone a liar.

Quote: ontariodealer

no, there is a diffence in being correct over calling someone a liar.

According to the rules, as written and implemented that is not correct. You cannot call an a$$hole an a$$hole even if everyone knows that the member in question is, in fact, a serious a$$hole. 'liar' would be similar I assume ;-)

Quote: TwoFeathersATL

According to the rules, as written and implemented that is not correct. You cannot call an a$$hole an a$$hole even if everyone knows that the member in question is, in fact, a serious a$$hole. 'liar' would be similar I assume ;-)

One senior member here (and likely more) says he has a way of winning at roulette, which he will not share with anyone. It pains me to agree with 2F, but calling a member a liar is not permitted.

Of course, the rules have proven to be somewhat flexible...

Quote: RonC

One senior member here (and likely more) says he has a way of winning at roulette, which he will not share with anyone. It pains me to agree with 2F, but calling a member a liar is not permitted.

Of course, the rules have proven to be somewhat flexible...

Now you have me all curious ;)

Anywayz, I have been reading a lot of different "systems" on different forums. Have been reading books/ theories like Law of the Third, 80-20 system, magic square, KTF and GUT.

Now some of them are at the moment beyond me (I don't understand them) yet :D

Some people use them and claim they win more then they lose on any given day. Perhaps this is true.

Quote: Ibeatyouraces

Anyone who says they're beating roulette with a betting "system" or "method" (they're both the same), is a liar.

For years I was beaten up by Roulette. However, now, with shrewd observation of the wheel and waiting for certain sequences to show up, coupled with strict management of my bankroll, I have totally defeated the house edge on the single zero game. I'm not saying my system is a consistent winner, but I just cannot lose over even a short session, and my sessions are usually very short anyway.
Am I a liar, in which case pour on the insults or self ban.

Roulette is one of the most entertaining games at the casino, IMHO. Especially when you know you can't lose.

Quote: Kingdombunnies

Now you have me all curious ;)

Anywayz, I have been reading a lot of different "systems" on different forums. Have been reading books/ theories like Law of the Third, 80-20 system, magic square, KTF and GUT.

Now some of them are at the moment beyond me (I don't understand them) yet :D

Some people use them and claim they win more then they lose on any given day. Perhaps this is true.

Don't bother. Save your effort. ALL of those systems are bunk. They nearly all rely on getting the punter to win MORE OFTEN than lose, but when he loses, he loses badly.

Many will give you variations on systems where you can win on more days than you lose. That's easy*. But for those systems, WHEN you lose, you lose a lot. And of course, there's nothing to say that you won't do the losing before you do the winning, though ON average, some of those systems are unlikely to lose on the first session, thus getting you drawn in by a sucker system.

*
E.g. System where on average you win £100 per day on most days of the month, only losing roughly two days of the month ( single zero roulette ) You are very likely to win the first few times you try it and very unlikely to lose on your first try. ::-

Each day, walk into the casino and bet $100 on each of the numbers 1 through to 35 all at the same spin of the wheel. You'll need to get your chips down quick.. You'll probably win. Collect up your chips and go home. Repeat tomorrow. On the occasional day that you lose, you'll only lose $3,500 so take that out of your winnings from last month.

Quote: OnceDear

Don't bother. Save your effort. ALL of those systems are bunk. They nearly all rely on getting the punter to win MORE OFTEN than lose, but when he loses, he loses badly.

Many will give you variations on systems where you can win on more days than you lose. That's easy*. But for those systems, WHEN you lose, you lose a lot. And of course, there's nothing to say that you won't do the losing before you do the winning, though ON average, some of those systems are unlikely to lose on the first session, thus getting you drawn in by a sucker system.

*
E.g. System where on average you win £100 per day on most days of the month, only losing roughly two days of the month ( single zero roulette ) You are very likely to win the first few times you try it and very unlikely to lose on your first try. ::-

Each day, walk into the casino and bet $100 on each of the numbers 1 through to 35 all at the same spin of the wheel. You'll need to get your chips down quick.. You'll probably win. Collect up your chips and go home. Repeat tomorrow. On the occasional day that you lose, you'll only lose $3,500 so take that out of your winnings from last month.

Okay thnx for the tip. Then I won't read those. But what is a good book to read that makes sense?

Also I don't have just 3500 which I could bet like that. Also when oyu bet 1-35 with 100 if you lose you will lose 3500 like you said. If you win you end in a draw. Or do I misunderstood/ miss something you've said?

Quote: Kingdombunnies

Okay thnx for the tip. Then I won't read those. But what is a good book to read that makes sense?

Also I don't have just 3500 which I could bet like that. Also when oyu bet 1-35 with 100 if you lose you will lose 3500 like you said. If you win you end in a draw. Or do I misunderstood/ miss something you've said?

Yolu missed something: Your winning stake getting returned.
If you win they give you 3500 of winnings Plus the 100 stake you'd laid on the winning number so you turned your 3500 into 3600 for an easy 100 profit.

There are no books on roulette, that I'm aware of that say 'You won't win with roulette systems' but if you find one, buy that.

Google " Oscars Grind". It's a system that will allow you to win in roulette most of the time. In the end, though, your losses will exceed your winnings. You'll have many more winning sessions than losing ones, but your losing sessions will eat up all your winnings.

@Oncedear of course. *facepalms* myself...:p

I have heard good things about John Patrick and his books.

@billy, thnx I will be checking that 1 out :)

Quote: TwoFeathersATL

According to the rules, as written and implemented that is not correct. You cannot call an a$$hole an a$$hole even if everyone knows that the member in question is, in fact, a serious a$$hole. 'liar' would be similar I assume ;-)

I should have added that 'sometimes ya gotta do what ya gotta do'
The frequency of those actions dramatically increases in the presence of a$$holes...and liars.... 2F

Oh, and apparently I caused RonC some minor pain. For this I apologize. Also I have placed his name in the 'doubtful' column on my Christmas card list ;-)

I have a positive EV roulette betting system.

You just need an infinite bankroll and time, and find a table with no betting limits.

Quote: PeeMcGee

I have a positive EV roulette betting system.

You just need an infinite bankroll and time, and find a table with no betting limits.

Care to elaborate?

Anywayz, are people familiar with Jack Wise Kennedy?

And what do you think of it? Right now I am halfway in his book.

Quote: Kingdombunnies

Care to elaborate?

Are you so inexperienced that you have not yet read of Martingale? Are you not familiar with the concept of sarcasm?

Quote:

Anywayz, are people familiar with Jack Wise Kennedy?

And what do you think of it? Right now I am halfway in his book.

You are not paying attention are you?
THERE IS NO WINNING SYSTEM!!!!!

OhDear! What have you done to your avatar?
Looks like a pregnant sloth?

Quote: OnceDear

Are you so inexperienced that you have not yet read of Martingale? Are you not familiar with the concept of sarcasm?

You are not paying attention are you?
THERE IS NO WINNING SYSTEM!!!!!

I have a word puzzled for you....

D MM

Let me know Via PM. Figure it out in 30 min and I have a casino swag TS 4 you

Quote: OnceDear

Are you so inexperienced that you have not yet read of Martingale? Are you not familiar with the concept of sarcasm?

You are not paying attention are you?
THERE IS NO WINNING SYSTEM!!!!!

Why would martingale have positive EV as its inputs approach infinity ? An infinite sum of roulette outcomes is still going to be equal to the normal negative EV.

Quote: DiscreteMaths2

Why would martingale have positive EV as its inputs approach infinity ? An infinite sum of roulette outcomes is still going to be equal to the normal negative EV.

I never said that PMG was correct with his system. But he was describing Marty. ( badly, because he was not correct)

Quote: TwoFeathersATL

OhDear! What have you done to your avatar?
Looks like a pregnant sloth?

Me relaxing after a big meal
https://www.google.co.uk/search?q=neil+sofa+sloth&rlz=1C1CHBF_enGB696GB696&espv=2&biw=1920&bih=979&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwiIjqeyhKvNAhXFKMAKHS_wBOgQsAQILA#tbm=isch&q=neal+sofa+sloth

The creator of Oscars Grind supposedly had over 500 winning trips in a row.

Quote: OnceDear

I never said that PMG was correct with his system. But he was describing Marty. ( badly, because he was not correct)

Indeed, I was describing Martingale. And it may seem a tad counter intuitive, but the system does have a positive EV as it approaches infinity.

The Math
(Assuming a double zero wheel, and betting on red/black or odd/even)
The probability that you win on the first bet: 18/38
The probability that you win on the second bet (so you lose first then win): (20/38)*(18/38)
The probability that you win on the third bet: (20/38)*(20/38)*(18/38)
….and so on….

Each of these will net you 1 unit. Therefore, the expected value is just the sum of all of these probabilities:



That summation above is a sum of a geometric series. Therefore, all that above is equal to:



Therefore your expected value is 1 unit for each round of a martingale system given that the number of bets is infinite (which, of course only exists in theory).

While that series does equal one that equation is not expected value since you are not actually including the discrete random variable, just probabilities.

Quote: DiscreteMaths2

While that series does equal one that equation is not expected value since you are not actually including the discrete random variable, just probabilities.

The random variable is your winnings.

Edit: But even if I just gave the probabilities…the sum is still one. Meaning, the probability that you will have a winning bet is one.

Quote: PeeMcGee

Quote: DiscreteMaths2

While that series does equal one that equation is not expected value since you are not actually including the discrete random variable, just probabilities.

The random variable is your winnings.

Edit: But even if I just gave the probabilities…the sum is still one. Meaning, the probability that you will have a winning bet is one.

Yes the random variable is your winnings. The probability approaches 1 but is never actually 1. For the gambler, the only thing that matters is the win, if you are super duper close to a win the casino isn't going to give it you, you either win or you don't. Thats the whole appeal of martingale that the probability of winning is pretty much a *sure thing*. But that still doesn't change EV to positive.

Quote: DiscreteMaths2

Quote: PeeMcGee

Quote: DiscreteMaths2

While that series does equal one that equation is not expected value since you are not actually including the discrete random variable, just probabilities.

The random variable is your winnings.

Edit: But even if I just gave the probabilities…the sum is still one. Meaning, the probability that you will have a winning bet is one.

Yes the random variable is your winnings. The probability approaches 1 but is never actually 1. For the gambler, the only thing that matters is the win, if you are super duper close to a win the casino isn't going to give it you, you either win or you don't. Thats the whole appeal of martingale that the probability of winning is pretty much a *sure thing*. But that still doesn't change EV to positive.

This is equal to one. It does not approaches 1. It does not approximate to 1. It is one. It is one as much as 1 is one.

The probability of winning with Martingale is one given infinite bets. Which, again, exists only in theory. Of course, in reality, a person cannot have infinite money nor time. But if a person could, Martingale’s expected value does indeed equal that expression up top. Which is one.

The probability of winning a hand approaches 1, but is not equal to 1.

Quote: TwoFeathersATL

OhDear! What have you done to your avatar?
Looks like a pregnant sloth?

I thought it was a photo of Ernest Shackleton.

Quote: PeeMcGee

I think saying that that expression equals 1 does not prove that expected value is positive. One can easily write out an expected value summation which approaches negative infinity as n goes to infinity.

I would think that if a sum of terms is positive, at least one term within the sum must be positive. If so, then the EV can't be positive.

Quote: RS

The probability of winning a hand approaches 1, but is not equal to 1.

It is equal to 1.

0.999 repeating is 1 (the internet loves to debate that, but it is a mathematical truth).

Quote: MrGoldenSun

Quote: PeeMcGee

I think saying that that expression equals 1 does not prove that expected value is positive. One can easily write out an expected value summation which approaches negative infinity as n goes to infinity.

I would think that if a sum of terms is positive, at least one term within the sum must be positive. If so, then the EV can't be positive.

1 is the expected value. 1 is positive. If you can provide proof of a negative infinity expected value, please do so.

I think my original thought was wrong because my sum was wrong, in that it was simply going to be a sum of individual trials from n=0 to infinity.

If you look at the EV based on (P(series concludes in exactly n rolls))*(Value of random variable when series concludes in n rolls) then this is exactly what you computed since the second term is 1. So I think I agree the EV is 1.

I guess the random variable probability density function can be defined as (18/38)*(20/38)^n for all nonnegative integers n and this is not problematic. But it has been a very long time since I was in probability courses. So maybe I am missing something.

And of course this is of no practical value since the EV is in fact negative for ANY finite time, bankroll, or betting limit, which is usually the important point to make to people in this discussion. :)

Wizard actually says this: "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." This is from https://wizardofodds.com/ask-the-wizard/betting-systems/martingale/

Quote: PeeMcGee

This is equal to one. It does not approaches 1. It does not approximate to 1. It is one. It is one as much as 1 is one.

The probability of winning with Martingale is one given infinite bets. Which, again, exists only in theory. Of course, in reality, a person cannot have infinite money nor time. But if a person could, Martingale’s expected value does indeed equal that expression up top. Which is one.

I don't have a calculus book laying around but from Wikipedia:
"In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence has defined first and last terms, whereas a series continues indefinitely. A value may not always be given to such an infinite sum, and, in this case, the series is said to be divergent. On the other hand, if the partial sum of the first terms tends to a limit when the number of terms increases indefinitely, then the series is said to be convergent, and the limit is called the sum of the series.

Formally, suppose a1, a2, ... is a sequence of real numbers. It can be stated that the real number L is the limit of this sequence, namely:

lim n → ∞ a sub n = L

which is read as

"The limit of an as n approaches infinity equals L"

to mean

For every real number ε > 0, there exists a natural number N such that for all n > N, we have | a sub n − L | < ε.

Intuitively, this means that eventually all elements of the sequence get arbitrarily close to the limit, since the absolute value | an − L | is the distance between an and L. Not every sequence has a limit; if it does, it is called convergent, and if it does not, it is divergent. One can show that a convergent sequence has only one limit."

I am pretty sure I am saying this correctly: the probability of succeeding using martingale can get arbitrarily close to 1 given infinite time and bank roll but since its never actually 1 there will always be negative expected value.

Quote: MrGoldenSun

I think my original thought was wrong because my sum was wrong, in that it was simply going to be a sum of individual trials from n=0 to infinity.

If you look at the EV based on (P(series concludes in exactly n rolls))*(Value of random variable when series concludes in n rolls) then this is exactly what you computed since the second term is 1. So I think I agree the EV is 1.

I guess the random variable probability density function can be defined as (18/38)*(20/38)^n for all nonnegative integers n and this is not problematic. But it has been a very long time since I was in probability courses. So maybe I am missing something.

And of course this is of no practical value since the EV is in fact negative for ANY finite time, bankroll, or betting limit, which is usually the important point to make to people in this discussion. :)

Wizard actually says this: "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." This is from https://wizardofodds.com/ask-the-wizard/betting-systems/martingale/

Well, that’s cool that the Wizard had already addressed the problem. I have mad respect for the Wizard, but I strongly disagree with him on this. He is correct that it does become a little abstract and nothing in our universe is infinite. But the question is not “is it possible?”. The question is “what if it were possible?”. More precisely, what if it were possible to have infinite time and money—does Martingale become positive EV? And it indeed does. Again (as you stated), only when time and money is infinite. A person have to think outside of the finite realm here.

And the Wizard’s opinion towards the concept of infinity is kind of surprising. This is such an important concept in so many different fields. It shouldn’t be shrugged off as simply ‘a man-made construct’. So that hurts a little :(.

Quote: DiscreteMaths2

Quote: PeeMcGee

This is equal to one. It does not approaches 1. It does not approximate to 1. It is one. It is one as much as 1 is one.

The probability of winning with Martingale is one given infinite bets. Which, again, exists only in theory. Of course, in reality, a person cannot have infinite money nor time. But if a person could, Martingale’s expected value does indeed equal that expression up top. Which is one.

I don't have a calculus book laying around but from Wikipedia:
"In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence has defined first and last terms, whereas a series continues indefinitely. A value may not always be given to such an infinite sum, and, in this case, the series is said to be divergent. On the other hand, if the partial sum of the first terms tends to a limit when the number of terms increases indefinitely, then the series is said to be convergent, and the limit is called the sum of the series.

Formally, suppose a1, a2, ... is a sequence of real numbers. It can be stated that the real number L is the limit of this sequence, namely:

lim n → ∞ a sub n = L

which is read as

"The limit of an as n approaches infinity equals L"

to mean

For every real number ε > 0, there exists a natural number N such that for all n > N, we have | a sub n − L | < ε.

Intuitively, this means that eventually all elements of the sequence get arbitrarily close to the limit, since the absolute value | an − L | is the distance between an and L. Not every sequence has a limit; if it does, it is called convergent, and if it does not, it is divergent. One can show that a convergent sequence has only one limit."

I am pretty sure I am saying this correctly: the probability of succeeding using martingale can get arbitrarily close to 1 given infinite time and bank roll but since its never actually 1 there will always be negative expected value.

So…you start off (your first paragraph) talking about series and sum. But then you go on talking about sequences and the definition of limit. Two very different topics. The expression I gave for the expected value is a series (not a sequence). I provided the sum of this series. The sum of the series is 1. Exactly 1.

This is way above my paygrade but if the expected value is one, wouldn't one also be the initial bet, so given an infinite br and infinite hands, you'd be right where you started? You can't bet zero, so you have to start with one, no?

Quote: billryan

This is way above my paygrade but if the expected value is one, wouldn't one also be the initial bet, so given an infinite br and infinite hands, you'd be right where you started? You can't bet zero, so you have to start with one, no?

The initial bet does not matter—as all bets are already factored in. Under Martingale, when you have a winning spin you are paid back the total amount of all your bets plus 1. That is, profits will always be 1. So technically, I calculated the expected value of your profits. Which is one.

That's just how the notation is defined for series, by definition the sum of an infinite series is the limit of partial sums. Yes its = 1 but not in the sense that 0 + 1 = 1. It's = in how the = is used for the definition of a limit. 1 is the limiting value of the series. Mathematicians chose to use the = sign because in most applications you can treat the sum as that exact number without consequence, in calculating EV we can not. 0.9 followed by any finite number of 9's is not usefully equivalent to 1.

I mean I suppose you could make the argument that if you never stopped playing you don't have negative EV but at the same time you cannot say you have positive EV because you never completed the bet.

Quote: DiscreteMaths2

That's just how the notation is defined for series, by definition the sum of an infinite series is the limit of partial sums. Yes its = 1 but not in the sense that 0 + 1 = 1. It's = in how the = is used for the definition of a limit. 1 is the limiting value of the series. Mathematicians chose to use the = sign because in most applications you can treat the sum as that exact number without consequence, in calculating EV we can not. 0.9 followed by any finite number of 9's is not usefully equivalent to 1.

I mean I suppose you could make the argument that if you never stopped playing you don't have negative EV but at the same time you cannot say you have positive EV because you never completed the bet.

But 0.9 followed by an infinite number of 9s IS equivalent to 1. I’m not sure why you are trying to link this back to a finite example.


I’m not sure if I can provide a way that can make you see that and 1 are equivalent. As in the same exact number.


Maybe try this….can you give me a number in-between and 1?

Quote: PeeMcGee

I’m not sure why you are trying to link this back to a finite example.

Because you cannot play roulette an infinite amount of times. You can however, play roulette any increasingly large amount of finite times and approach infinity. I thought your were talking about the latter. If you are talking about the former and trying to define it, then ok. I would disagree but at least that makes sense.

Quote: DiscreteMaths2

Because you cannot play roulette an infinite amount of times. You can however, play roulette any increasingly large amount of finite times and approach infinity. I thought your were talking about the latter. If you are talking about the former and trying to define it, then ok. I would disagree but at least that makes sense.

Any finite number of trials has a negative expectation. We are purely in the realm of the theoretical here.

I agree that I was a bit surprised by the Wizard's view. I suspect part of it is that he gets a lot of questions about the martingale and is really tired of it. Also, it seems like one of his primary goals is to provide practical advice, so maybe he's less interested in the theoretical question?

Quote: PeeMcGee

Maybe try this….can you give me a number in-between and 1?

I had this exact thought earlier this morning. (For anyone curious, the answer is no.)

They are the same number because thats what we defined the sum of a series to be. Just because there is a limit doesn't mean you can work backwards and make something impossible, possible. For example the lim of 1 / n as n -> infinity is 0. However, that does not mean there is a number you can give n that would make 1 / n = 0. The solution to that is not infinity.