Odds Question

I'm trying to wrap my head around this. I understand that Roulette spins are disconnected events and one spin does not affect the others. If you discount the Zero/Double-Zero so that we are only talking about the 36 possible single numbers and I cover 10 streets on every spin (30) leaving the house 2 (6 numbers - regardless what they are) My odds of hitting one of my numbers is 30/36 (no zeros) or 5:1 in my favor. My question is, of those six numbers, what is the probability that the house will hit one of those six numbers four times in succession before one of my numbers hits?

Hi folditnow,

Welcome to the forums.

To answer your question, the probability is probably very low.

However, the payoff for a winning number on a roulette wheel is, no matter what the bet, always LESS than what the true odds say the payoff should be. This is true whether you are betting on particular color, or on a range of numbers, or on odd/even, or on a specific number, or whatever. And that payoff that is less than what it should be is what gives the house its edge.

There is no Martingale System or method of betting that can overcome this edge.

Your "odds of hitting a number" (notice the quotes) might be "in your favor," (again, in quotes) depending upon how you bet. (30/38 in your example. I don't know why you discount zero and double zero), but each time you win you are winning LESS than what you should be winning, if there were no house edge at all.

Eventually this house edge will make itself felt. You can't get around it or ignore it.

Usually this kind of question gets asked for one of two reasons,

* the OP has taken a beating from a losing streak

or

* the OP is plotting a martingale attempt

8/38 times the house wins the bet, or 0.2105263157894737, which is one in 4.7499999999999996438. 4 times in a row is one in about 509 ...

I am not the math-go-to-guy but I think that is correct as 5 to the 4th power is 625, for a check

So if it is case #1, you were modestly unlucky
If it is case #2, you are probably tempted to press your luck and martingale. That brilliant idea is centuries old and has been resoundingly discredited as a way to gamble but has been perfect for driving gamblers crazy.

Quote: folditnow

... If you discount the Zero/Double-Zero so that we are only talking about the 36 possible single numbers ...

People always want to ignore those green spots. But it's those green spots that put holes into whatever plans you're cooking up.

Bottom line: you'll give yourself a headache working on the math for a system that just won't work.

Quote: folditnow

what is the probability that the house will hit one of those six numbers four times in succession before one of my numbers hits?

If you are discounting the green numbers completely then I think it is 1 in 1296.

Thanks for the responses guys!

I realize the payoffs are skewed in favor of the house. Casinos were not built off of winners and I'm not trying to suggest it's possible to beat the long term odds because I know better. I discounted the zeros for clarity, removing the decimal so it's easier to calculate, because lets face it, how often am I going to sit and play long enough for the decimal to get me? Nobody sits at a table of any kind long enough for the Casino's edge to reach equilibrium, so there are streaks, highs and lows that can be plotted on a graph. If you look at these over a long period of time it will approach a waveform that alternately dips and rises over a baseline, eventually approaching the center. We call this entropy. Everything in nature operates in this manner. In order to have highs, you must have lows. Everything is cyclicle in nature, approaching a mean over time.

So this is not a fools errand. I realize that I cannot beat the game long term. If I sat there continuously playing I will eventually lose. But good gambling is taking the best bet with the best odds. Yes you lose sometimes. But if there is any possible advantage you can acheive, you had better grab it.

Now, the Martingale. Yes it has it's weakness, in the fact that eventually you will hit the table maximum or run out of money. Martingales are normally run on outside bets, which are all 1:1 even money bets. What I am suggesting is (like bookmakers do) spreading that action over several or more seperate bets so that your exposure to risk is divided by your bet. Simply put, I can make a 10 dollar bet on black and cover 18 numbers, but the house also has 18 numbers, plus the zeros, for either 19 or 20 chances to win against my 18. Obviously in the long run I am screwed.

If instead I placed 10 one unit street bets, i'm dividing my risk over 30 numbers (as opposed to one of two colors), increasing my chance to hit. Black/Red is 18 to 19/20, My way is 30/37 (Euro) . I will eventually get beat, but, If I Martingale just these 10 units individually one time, my relative chance to hit with the martingale is much higher than the 1:1 chance of an outside bet (which is not actually a true 1:1), but i will only be able to do this a certain amount of times due to the street bet maximums (which should also tell you that this idea is sound. They only put maximums on things that could hurt them.

I've been testing this very successfully, I just cant figure the multiple odds of hitting on successive spins. Can't figure the formula, not a mathemetician.

Quote: folditnow

Now, the Martingale. Yes it has it's weakness, in the fact that eventually you will hit the table maximum or run out of money.

It is a myth that table maximums were instituted to stop Martingale players. In fact, casinos love Martingale players, just as they love any gambler with a system. Gamblers with any kind of system will always play for longer periods of time.

Table maximums are there for one reason only. A casino, like any business must worry about cash flow. If individual bets are too big, the gambler might take home too much money on any given day.

Quote: folditnow

I'm trying to wrap my head around this. I understand that Roulette spins are disconnected events and one spin does not affect the others. If you discount the Zero/Double-Zero so that we are only talking about the 36 possible single numbers and I cover 10 streets on every spin (30) leaving the house 2 (6 numbers - regardless what they are) My odds of hitting one of my numbers is 30/36 (no zeros) or 5:1 in my favor. My question is, of those six numbers, what is the probability that the house will hit one of those six numbers four times in succession before one of my numbers hits?

Probably of hitting a number is 30/36 = 5/6.
Probability of not hitting a number is 6/36 = 1/6.

Probability of not hitting a number 4 times in a row is 1/6^4 = 1/1296 (what Dr. Itch wrote).

table maximums DO stop the martingale, how is that a myth? if there were no maximums martingale players would always win, bankroll notwithstanding

thank you that is what i needed

thanks

Quote: folditnow

table maximums DO stop the martingale, how is that a myth? if there were no maximums martingale players would always win, bankroll notwithstanding

Not true. Your not guaranteed to win from now through eternity.

Quote: folditnow

Thanks for the responses guys!
...I discounted the zeros for clarity, removing the decimal so it's easier to calculate....

Don't Calculators can cope

Quote:

...so there are streaks, highs and lows that can be plotted on a graph. If you look at these over a long period of time it will approach a waveform that alternately dips and rises over a baseline,

NO. IT WON'T

Quote:

... eventually approaching the center. We call this entropy.

No it won't: No we don'tt

Quote:

Everything in nature operates in this manner. In order to have highs, you must have lows. Everything is cyclicle in nature, approaching a mean over time.

That is just so not true

Quote:

So this is not a fools errand.

Yes it is. It REALLY is.

Quote:

...But if there is any possible advantage you can acheive, you had better grab it.

There is none. get over it.

Quote:

I've been testing this very successfully, I just cant figure the multiple odds of hitting on successive spins. Can't figure the formula, not a mathemetician.

You will have great success... until you don't!

With your system, you need to consider the probability of increasing your available wealth (bankroll) by x%. Maybe you have $50k and you want to put it to work to make another $50k. It should be enough to know that you have probability of less than 50% of doing so.
Try reading this to discover why you are having success and why that is a bad thing.
https://wizardofvegas.com/member/oncedear/blog/2/#post1370

Incidentally, I use marty for fun very often. It can be great fun and profitable more often than not. It's the 'not' that you have to consider.

Oh, and as a courtesy to you.

Chance of not hitting 4 times in a row with your system on Euro roulette
1 in 780.57

Chance of not hitting 4 times in a row with your system on US roulette
1 in 509.06

Chance of not hitting with your system on no zero roulette
1 in 1296

Those pesky zeros do have a MASSIVE impact.

Thanks for straightening me out. Is that me not hitting? or the house?

Quote: folditnow

Thanks for straightening me out. Is that me not hitting? or the house?

Rather a lot of difference, don't you think?

Using single zero game

If you place 4 'bet events'*, it doesn't matter if they are one after another, or whether you go for a pee or a vacation between them, then if each 'bet event' covers 30 of the 37 numbers, then

30 times in 37 the first bet will see you a winner
7 times in 37 the first bet will see you a loser.

30 times in 37 the second bet will see you a winner
7 times in 37 the second bet will see you a loser.

30 times in 37 the third bet will see you a winner
7 times in 37 the third bet will see you a loser.

30 times in 37 the forth bet will see you a winner
7 times in 37 the fourth bet will see you a loser.

If you consider those 4 bets as one 'cycle' then 1 cycle in 1/( ((7/37)^4) = 780.57 you will lose all four betting events.

If you bet one dollar on 30 different numbers, each time leaving eight numbers alone (I'm including zero and double zero, of course), here's what you can expect:

Yes, your chances of winning on any individual spin are are 30/38, or .789.

However...

on the average, you will win 30 times out of 38 spins. Each time you win, you win $6.00.
on the average, you will lose 8 times out of 38 spins. Each time you lose, you lose all $30.00.

To compute the house edge, the formula, in this case, can be computed this way:

(((8/38) * -30) + ((30/38) * 6)) / 30

(There are other methods that achieve the same result.)

This equals -.05263... which, not coincidentally, is exactly the house edge for the game of roulette.

Your system is an attempt to give yourself less of a chance of losing any individual spin, by betting on a whole bunch of different numbers. Yes, you have more winners than losers. But it all comes down to, as I said before, when you do win you are being paid at less than true odds. You can't overcome that with any system or manner of betting.

how do you compute the "average win" as $6? Based on what odds and which bet? Street bets pay 11:1

Quote: folditnow

how do you compute the "average win" as $6? Based on what odds and which bet? Street bets pay 11:1

Did I say welcome to the forum?
Well, welcome to the forum.

However, please make an effort FoldItNow. The maths is not fantastically hard.

Ed has considered placing 30 x $1 bets to cover those 30 numbers: You on the other hand are choosing to place 10 x $1 bets on the streets. So he's staked more than you plan to, but you are covering the same numbers and the same odds apply.
When one of his numbers wins, he gets paid $35 + his $1 stake giving him $36 in total. He put down $30: He picks up $36. Therefore he won $6 profit.
In your case, covering the same numbers with your 10 street bets of $1, if one of your numbers wins, you get paid $11 + the return of your $1 stake.
So you put down $10 and you stand to pick up $12

He wagered 3 times what you did and won 3 times what you did.

Anyhow, enough of the maths.
For every $1 you place on the European table, you will, on average lose $(1/37) or about 2.7c The more you put on the table and the more bets you place, the more ( on average ) you will lose. You will sometimes win, you will sometimes lose. But it is no cycle. Wins don't follow losses in a cyclical way. The universe does not guarantee that you will win as often as you lose. Indeed it pretty much guarantees that the difference between number of wins and number of losses will grow.

You Cannot and will not beat roulette in any meaningful way by structuring your bets or by Martingaling. You just won't!
The best you can hope for will be to have more fun losing.

If you are fabulously rich and have $35,000,000 to play with, then put $1,000,000 on the numbers 1 to 35 on a European game.
You will probably win $1,000,000 with probability of 35/37 = 94.6%
Easiest million bucks you will ever make.
Unless you lose!
Repeat that until you do lose. How many spins do you expect to survive? How many millions will you expect to walk out with? [ Clue. Less than 35 ]

Trust me, max bet or no max bet, there will be casinos delighted to take your bets, because on average they win, and they average over millions of players over a lifetime of play.

Here is another way to look at the martingale:

It is a very specifically structured way of betting in order to get you back to where you started when you lose. That gives it a special appeal for some reason, but when you think about it, it's just a way to bet more when you are losing.

It can and sometimes is done a different way, for example instead of doubling the bet after a loss you could bet double plus a certain amount so that you get ahead after losing your bets when you finally win one. Or, really, if you think about it, you might just wing it , approximately double, or just some larger amount, the idea is the same. If you get away from that specific structure, though, the idea loses its charm some - doesn't it? After all, anybody could think of betting more after losing, and that is really all it is.

Why not bet more when you are winning? It really is much more fun.

Original Question: Odds of those 6 hitting are 6/36, or 1/6. Odds of it hitting 4 times in a row... (1/6)^4 = .0008, or about 1 in 1250... which for most gambling is really not all that infrequent.

Real question (including the zeros), your odds of losing go up to 8/36. Odds of hitting 4 times in a row.... (8/36)^4 = .0024, or about 1 in 400. See how those two little zeros just jumped your odds of losing by a lot? 1 in 400 is something you'd probably see if you only went to the casino a couple times.

Quote: Romes

Original Question: Odds of those 6 hitting are 6/36, or 1/6. Odds of it hitting 4 times in a row... (1/6)^4 = .0008, or about 1 in 1250... which for most gambling is really not all that infrequent.

Real question (including the zeros), your odds of losing go up to 8/36. Odds of hitting 4 times in a row.... (8/36)^4 = .0024, or about 1 in 400. See how those two little zeros just jumped your odds of losing by a lot? 1 in 400 is something you'd probably see if you only went to the casino a couple times.

Romes, you forgot to pop the zeros into the denominator, so it's (8/38)^4 or 1 in 509.

But your point is spot on.
Those zeros more than double the likelihood of failure

Quote: OnceDear

Romes, you forgot to pop the zeros into the denominator, so it's (8/38)^4 or 1 in 509.

But your point is spot on.
Those zeros more than double the likelihood of failure

Doh, you're correct =(. Eh, close enough... lol.

Quote: folditnow

table maximums DO stop the martingale, how is that a myth? if there were no maximums martingale players would always win, bankroll notwithstanding

You are absolutely correct, of course. Even a cursory look at the issue reveals that Martingale (or any other progressive betting system) will end up winning if there is no limit on bet size.
Of course, another purpose bet maximum serves is that it reduces volatility on the table, in other words it limits the overall win/loss a table can have on a given day.

The infinite bankroll, infinite table maximum argument is always funny. If you had an infinite bankroll, why are you gambling? Fine, you want it more realistic. If your bankroll is 1 million dollars, why are you trying to win $6 in a spin of roulette?

That's an easy questions: to beat the "system".
On a serious note, these are not rational or realistic situations, but it is fun to imagine the possibilities.