What am I missing?

What Am I Missing?

It's a modified Martingale system - European Roulette $5 min $2,000 max - $2,475 bankroll

Player waits for a streak of 2 (same colors or even even / odd odd). Then starts off playing $5 opposite of the streak. If the player loses, the player bets $10 on the same color. After losing with $10 the
player jumps to $30. And every following lose double the bet plus $10. (70, 150, 310, 630, 1,270)

This allows for 10 of the same color to be played in a row without losing. And the odds of 10 in a row are 1,024:1 (minus the “0” coming up once in every 37 times. That’s about 27 times per 1,000. 1,024 - 27 = 997). So I understand that this system is most advantageous in the short-run, but if I am only going to lose (on average) once every 997 rounds and I win 996 x $5+ every round, then I should be a winner in the long-run as well.
Aside from Gambler's Fallacy, what's wrong with this system? What am I missing?

You start using math but then for some reason stop and say "This system looks like it wins."

Finish your work and you'll see what's wrong. All of your wins don't cover the huge loss. Your expected loss will equal your average betsize * # spins * house edge.

Quote: Checkinitout

Aside from Gambler's Fallacy.........

probably enough

Quote:

what's wrong with this system? What am I missing?

With Martingale you are giving the idea of betting more when you are losing too much status. There is a certain mystique to the idea of 'double or nothing' that can affect any of us, and it sounds like this is adding $10 too [hard to follow for me]. But the thing about the Martingale [pure double or nothing] to realize is that it has been around for centuries and has never worked for anybody enough so we can cite a single person that prospered doing it.

Try betting more when you are winning, much more fun

If you're going to streak bet, bet with the streak. You only lose once per streak. JMHO.

Thanks for the input Sabre.
Are the odds of seeing 10 reds in a row in European roulette not really 997 to 1?
I thought it was pretty simple math, and I included the house odds by reducing the total number by 27.
Here's the rest of the math:
1 (11 in a row streak) lose = -$2,475
996 ($5 minimum) wins = $4,980
Total winnings of $2,505

First of all, the probability of red not coming up at all in 10 consecutive spins on a European wheel is (19/37)¹⁰ = about 1 / 784.3, not 1 / 997.

However, what you are "missing" is this:
In your calculation of the odds of not getting 10 losses in a row, you are including all of the cases where one of the first two bets wins, in which case you win zero as you did not bet anything.

You win when red comes up twice in a row and then does not come up eight more times in a row.
The probability of this = (18/37)² x (1 - (19/37)⁸) = about 23.5%

Remember: the probability of a fair coin tossed 10 times coming up heads all 10 times is 1 / 1024 - but so is the probability of the first 9 tosses being heads and then the 10th time being tails. Do not include past events when calculating future probabilities.

Hi Check,
Welcome to the forum

Quote: Checkinitout

What Am I Missing?

About 200 years of Martingale being discredited. Some of it on this forum.

Quote:

It's a modified Martingale system - European Roulette $5 min $2,000 max - $2,475 bankroll

Player waits for a streak of 2 (same colors or even even / odd odd). Then starts off playing $5 opposite of the streak. If the player loses, the player bets $10 on the same color. After losing with $10 the
player jumps to $30. And every following lose double the bet plus $10. (70, 150, 310, 630, 1,270)

This allows for 10 of the same color to be played in a row without losing. And the odds of 10 in a row are 1,024:1 (minus the “0” coming up once in every 37 times. That’s about 27 times per 1,000. 1,024 - 27 = 997). So I understand that this system is most advantageous in the short-run, but if I am only going to lose (on average) once every 997 rounds and I win 996 x $5+ every round, then I should be a winner in the long-run as well.
Aside from Gambler's Fallacy, what's wrong with this system? What am I missing?

Your calculation of probability of the losing streak is wrong and you consider yourself to get a win in every one of your 1000 or so plays, But you don't

Quote: Checkinitout

Thanks for the input Sabre.
Are the odds of seeing 10 reds in a row in European roulette not really 997 to 1?

No.
The odds of seeing red 1 time in a row is 18/37 = 0.486486 = 1 in 2.05555555556
The odds of seeing red 2 times in a row is 18/37*18/37 = 0.23666910153 = 1 in 4.22530864198
The odds of seeing red 3 times in a row is 18/37*18/37*18/37 = 0.11513631966 = 1 in 8.68535665295

The odds of seeing red 10 times in a row is 18/37*18/37*18/37*18/37*18/37*18/37*18/37*18/37*18/37*18/37
= 0.0007425194 = 1 in 1346.76614213
By which point you have lost . . .
5+10+30+70+150+310+630+1270+2550+5110 = $10,135

Oh but hang on, you didn't bet the first two times*
so you actually only lost
5+10+30+70+150+310+630+1270 =$2475

That's all right then.

And that's just streaks of reds. Your system can also find itself being wiped out by the equally probable streak of blacks..

BUT In your estimation where you assume that you made 997 wagers, taking >$5 per wager you overlooked the fact that you observed far far more than 997 spins as you waited for your streak of 2. You are accounting for wins on spins where you didn't even place a bet.

Let's take an example.
Arrive at table.
watch
Red
Black
Red
Red
Place a $5 bet on Black and win. You saw 5 spins and are up $5
You cannot now bet on the next spin, because you don't have your streak of two
Red
Black
Red
Red
Place a $5 bet on Black and lose. You saw 10 spins and are up $0
Place a $10 bet on Black and lose. You saw 11 spins and are down $15
Place a $30 bet on Black and lose. You saw 12 spins and are down $45
Place a $70 bet on Black and win. You saw 13 spins and are up $25
So you are lucky so far and are up an average of 25/13 = $1.92 per spin.
Well done.
NOT an average of >$5 per spin as you anticipated.

See how over the course of 1346 spins you could be up by less than 1346x5 You probably will be!!

All those spins have to be taken into account for the probability calculations, but they don't all yield profit.

This might help you.
https://wizardofvegas.com/forum/gambling/betting-systems/21359-debunking-roulette-marty-with-pictures/

* Oh. and the only benefit that you will get from waiting till a streak of two is established is that you will spend less time gambling. It's as effective as only placing a bet when a black cat has crossed your path from left to right.

What are you missing?

It's a bit confusing and misleading to make long chains of calculations and percentages here. That tends to obscure the basic, elementary point of why NO Martingale system can EVER work in a negative expectation game:

Every bet you make at roulette has a negative expectation. Your theoretical result--think of it as "average," though that's somewhat inaccurate--is the sum of the expected value of all the bets you make. Therefore, any system involving a progressive series of bets is simply creating a sum of negative numbers, which CAN NEVER ADD UP TO A POSITIVE NUMBER. In fact, when you make that big bet that is inevitably called for, that's the worst bet in the whole system, because its -EV is greatest.

You have to think of every bet in gambling in terms of expected value. If you bet $100 on Red or Black (etc.), that bet has a negative expectation of $5.24. This is REGARDLESS OF THE ACTUAL RESULT OF THE BET. This is what confuses so many people. They say, "How can I have an expected loss of $5 when I'm going to either win or lose $100?" The EV figure reflects the greater probability of losing.

The fact that you may find yourself ahead at some point while playing your system doesn't alter the fact that you should lose in the long run, and the likelihood of that approaches certainty the more you play--just as the likelihood of winning does for the casino. There is no way to beat roulette, or even to improve on the house edge. It's not like literally millions of people haven't been trying for hundreds of years, and what I find amazing is that people keep popping up with new systems, none of which work.

It's not the fact that these games are -EV. These players erroneously believe they are "due to win."

Quote: Joeshlabotnik

What are you missing?

It's a bit confusing and misleading to make long chains of calculations and percentages here. That tends to obscure the basic, elementary point of why NO Martingale system can EVER work in a negative expectation game:
.

To be fair to the OP, he had a stab at calculating his probability of losing his 2K bankroll, albeit in error, and then he estimated what he would win if he had that 'cycle of games' where he lost the expected average number of times. That's where the wheels fell off. He massively overestimated how many winning wagers he would place.
It all became muddled by his waiting for a streak of 2, which could either be red or black.

Quote: OnceDear

To be fair to the OP, he had a stab at calculating his probability of losing his 2K bankroll, albeit in error, and then he estimated what he would win if he had that 'cycle of games' where he lost the expected average number of times. That's where the wheels fell off. He massively overestimated how many winning wagers he would place.
It all became muddled by his waiting for a streak of 2, which could either be red or black.

My point was that entering the calculation phase was pointless. If you can learn to accept the simple premise that a series of negative numbers, no matter how arranged, can never add up to a positive number (i.e., a winning expectation), then you don't need to delve into those laborious calculations at all. It's like spending time, money, and effort to build a perpetual motion machine.

Another factor in the illusion is that there actually is no such thing as a streak in a series of independent trials. One result does not influence the next. This is perhaps the hardest perception to shake loose, because our brains are hardwired to perceive patterns. Just goes to show that casinos are the most masterful applied psychologists in the world.

Quote: Joeshlabotnik

My point was that entering the calculation phase was pointless. If you can learn to accept the simple premise that a series of negative numbers, no matter how arranged, can never add up to a positive number (i.e., a winning expectation), then you don't need to delve into those laborious calculations at all. It's like spending time, money, and effort to build a perpetual motion machine.

Another factor in the illusion is that there actually is no such thing as a streak in a series of independent trials. One result does not influence the next. This is perhaps the hardest perception to shake loose, because our brains are hardwired to perceive patterns. Just goes to show that casinos are the most masterful applied psychologists in the world.

Not arguing with you for one moment. We gave him the full range of 'what he's missing' from different angles. He has plenty to work with and can make it as hard or as easy as he sees fit......

Oh, I never did say to him...
His system would be brilliant if he had his $2475 bankroll and was about to be shot if he couldn't raise $2500 for a plane ticket out of a war zone. :o) Almost guaranteed to work out for him. (~99% probability of success )

The guy asked wat was wrong with his math because he was coming to a conclusion that was suspect. I dont think he shouldb talked down to. Not everyone is at the same place mathematically and he did the best thing by asking for help from those more knowledgeable

Quote: darkoz

The guy asked wat was wrong with his math because he was coming to a conclusion that was suspect. I dont think he shouldb talked down to. Not everyone is at the same place mathematically and he did the best thing by asking for help from those more knowledgeable

Agreed. I don't see that we talked down to him, though it's often something I/we slip into doing.
Kudos to the OP for having a stab at the maths and at least suspecting that he had it a bit wrong. Hope we clarified it for him without talking down to him.
So, CheckItOut, No offense meant by me sir.

It wasnt everybody and hadnt progressed that far but i could see it easily becoming a thread of insults. It looked like it might b heading tjat direction

My experiences:

I have seen 11 reds in a row come up when playing roulette online for fun. For the math novice, that may seem nearly impossible, but if one plays long enough, it is only a matter of time before something like this happens. Imagine that you wager $5 on black and decide to double it after each loss. After 11 reds, you will need to put out $10,240 for the next spin.

In other separate sessions, I have seen 9 reds as well as 9 blacks in a row. Only one word can describe the ultimate outcome of every person who tries a martingale-type system:

Disaster

Not only hav i seen ten of a color in a row - i hav been able to take advantage of it on 2 separate occasions (wen i hadnt missed the streak coming at the end of it or chickened out and not wagered - and yes i hav lost money wen i didnt chicken out)

But on those two occasions i played for 23 straight reds (made about $900 because i was too chicken and lowered m subsequent bets) and the other went for 14 straight but i made $3500 because i didnt chicken out

Thank you.