Help with simulating results on a roulette system

I know roulette systems do not work in the long-run but I was just wondering if anyone could help me prove failure on a thought I had. European roulette wheel has 37 numbers and pays 35:1. Suppose we were to construct a progressive betting system of betting on a single number each and every spin. The betting ranges on a single number wager can be between $1 and $200. We are to start with $1 and slowly increase our bets. Specifically, we want to progress our bets in such a way that when we win, we are able to move back a minimum 38 spaces on our progression chart. What I mean is, for example, our first 36 bets will be for $1, since if we win on any bet within the first 36 attempts we will be at least back to even so we would start back at number 1 on the progression chart. If we lose the first 36 bets then we bet $2 and keep betting $2 until we reach a point where our next bet would not allow us to move 38 spaces or more back on our progression chart. So your chart would also show a cumulative loss column as we bet $1, $2, $3, etc. all the way up to $200. So when you win a bet at any dollar amount you would want to move back on the progression chart to that number where your cumulative loss amount would be after you win. If your win brings you to a cumulative loss of $0 or is negative then you start over at the first $1 bet. Make sense?

My thought was that although you would need an astronomical amount of cash to reach the $200 bet level, the fact that you are moving back slightly more spaces on the progression chart (38 spaces) than the odds of hitting your number (1 in 37), the law of averages would kick in even after a long bout of negative variance and eventually bring you toward the beginning of the progression chart.

This would take a little bit of time to construct the chart if anyone has time. If not I then I can do one when I have a little bit of time. I'm just curious how this would prevail in a large simulation. I'm sure it would fail at some point but I'm just curious to see the results if someone here has the knowledge of how to create a test run with these constraints.

If this has been tested before then I apologize for repeating but I have been searching for one and was not able to find a similar test. All the other systems I come across progress so quickly and reach table limits before the law of averages kick in.

Thanks for any input

What do you mean by "until we reach a point where our next bet would not allow us to move 38 spaces or more back" ? Not allowed by what or whom ?

You see a betting system from the wrong perspective. If you want to design a betting system, you need to specify a goal. Once you have a goal, you can find the betting pattern that will fit best to your goal. Not the other way around.

Quote: MangoJ

What do you mean by "until we reach a point where our next bet would not allow us to move 38 spaces or more back" ? Not allowed by what or whom ?

You see a betting system from the wrong perspective. If you want to design a betting system, you need to specify a goal. Once you have a goal, you can find the betting pattern that will fit best to your goal. Not the other way around.

I wrote that incorrectly. I meant 38 or more spaces. It's kind of difficult to explain without attaching a spreadsheet. I was trying to think of a betting pattern that has an incredibly slow progression that can sustain very long periods of bad luck and see how it would fare in a long simulation. I would start with placing $1 on number 12 (or any number for that matter). I would bet $1 for 36 times in a row. If I win in these first 36 spins I go back to bet number 1. So, on my 20th spin if I hit my number then I go back to bet number 1 and I have gained a $16 profit (Cumulative loss amount to that point after 19 spins was -$19 and I won $35 with my win).

Example 2:
Then I start all over with bet #1 for $1. Now let's say I miss my next 36 spins, so my cumulative loss to that point is -$36. Now I start betting $2 per spin. We will keep betting $2 per spin until we reach a point where a win will move us backward on our betting table of at least 38 spots. So, we know that a $2 bet will win us $70. Lets say we are on our 50th spin. This means that we have previously lost $36 on our first 36 spins and lost $2 on our next 13 spins. So our cumulative loss at the point just before our win would be $62. Our win of $70 has covered all previous losses and leaves us with an $8 profit so we would be able to start over with bet #1 for $1. In this example we moved back 50 since this was our 50th spin and we can start all over.

Example 3:
Now lets say we lose our first 36 spins for $1. Then at $2 per spin we hit our number on the 70th spin. Let's see if this will allow us to move at least 38 spaces backward to a previous cumulative loss point. We lost $36 on our first 36 spins and $2 each spin up to the 69th spin. This would be a cumulative loss amount of $102. With our win on the 70th spin we win $70. So this brings us to a net cumulative loss of $32 after our win. So now we go back to the point in our progression chart where we were previously losing $32 which would be on our 33rd spin. So I ask myself, did this win allow me to move back at least 38 spots on our progression chart? The answer is no because moving from spin #70 to spin #33 is only moving back 37 spaces after my win. So this means I have to alter my betting chart by 1 spin. So actually my $2 bets should end at bet #69 on our progression chart and bet #70 should be $3. If you do the math with betting $2 on the 69th spin then you will see that you will be able to move back exactly 38 spaces.

The significance of moving back no less than 38 spaces is that after a win we will always move backward on our progression chart more spaces than our odds of hitting our number on average (1 in 37). So over a long sustained course of betting we will always move closer to the beginning of our progression chart, because moving back to the beginning is where we ultimately make money.

So in creating our betting progression chart we will always increase our bets by $1 and bet this amount until we reach a point where we are able to drop backward on our progression chart no less than 38 spaces. I have already figured out where our $2 bets end and our $3 bets start. Goal is to build the chart up to a $200 bet and run a simulation to see how many instances it takes to bust our bank roll. Not sure if this is possible but I think it would be very interesting to see the result.

If there are any statistic gurus out there then have at it!

Quote: rob74

I was trying to think of a betting pattern that has an incredibly slow progression that can sustain very long periods of bad luck

What do you mean by "and".

If you want a slow progression, flat bet. If you want to sustain very long periods of bad luck, bet $0 (obviously). Hence, your best betting strategy for slow progression *and* sustainability is not to bet at all.

But that's not what you want to hear, right ? Because you want to play no matter what. Then at least make it the second best betting strategy, flat bet table minimum.

Quote: rob74

I know roulette systems do not work in the long-run but I was just wondering if anyone could help me prove failure on a thought I had. European roulette wheel has 37 numbers and pays 35:1. Suppose we were to construct a progressive betting system of betting on a single number each and every spin. The betting ranges on a single number wager can be between $1 and $200.

If you understand and accept that flat betting is ultimately in the house's favor then it's easy to "prove failure" for any system of variable betting. (If you don't believe the house has the edge when you're flat betting, then that implies you think you have the edge just by putting your money on the table and you don't need a system in the first place.)

So let's assume that you understand and agree that if you never vary your bet, the house has the edge. And that's true if you take bathroom breaks too, or leave the casino to get a meal, or go home altogether, as long as you come back later to play more. As long as you bet the same consistent amount when you're playing, you never have the best of it.

So consider your specific system: there are 200 different bet amounts. Imagine you had 199 brothers and you all went to the roulette table at once. Whenever the system calls for a $1 bet, you make the wager and everyone else bets nothing. Whenever the system calls for a $2 bet, your first brother makes the wager and everyone else (including you) bets nothing. Whenever the system calls for a $3 bet, your second brother makes the wager and everyone else (including you) bets nothing. And so forth. It's easy to see that regardless of the rules of the system, each brother is either betting their chosen amount or they're not playing at all. In other words, they're all flat betting. Therefore, none of them individually have the edge over the house. As a result, the combination of all of their individual flat bets can't have the edge either.

I trust that "proves failure" as you intended that phrase to mean, yes?

MathExtremest, very good example with the 199 brothers. The only difference between my system and the typical Martingale system is that with Martingale you will reach your table max much faster and much cheaper. I was just curious how many spins on average it would take to go busto with my system. I would guess in the tens of thousands at least.

Quote: rob74

MathExtremest, very good example with the 199 brothers. The only difference between my system and the typical Martingale system is that with Martingale you will reach your table max much faster and much cheaper. I was just curious how many spins on average it would take to go busto with my system. I would guess in the tens of thousands at least.

Okay, this is all I am doing. I'll do up until $25 bets, if you want to go further, the method is clearly very easy to follow, so have a blast!

For what's it worth, the rest will either be two spins or one spin, with it being two spins with decreasing frequency.

Bets $1-$25

36 Spins = -$36

$2 to return $72

(72-36)/2 = 18 Spins

$3 to return $108

(108-72)/3 = 12 Spins

$4 to return $144

(144-108)/4 = 9 Spins

$5 to return $180

(180-144)/5 = 7 Spins (Overall Loss $179)

$6 to return $216

(216-179)/6 = 6 Spins (Overall Loss $215)

$7 to return $252

(252-215)/7 = 5 Spins (Overall Loss $250)

$8 to return $288

(288-250)/8 = 4 Spins (Overall Loss $282)

$9 to return $324

(324-282)/9 = 4 Spins (Overall Loss $318)

$10 to Return $360

(360-318)/10 = 4 Spins (Overall Loss $358)

$11 to Return $396

(396-358)/11 = 3 Spins (Overall Loss $391)

$12 to Return $432

(432-391)/12 = 3 Spins (Overall Loss $427)

$13 to Return $468

(468-427)/13 = 3 Spins (Overall Loss $466)

$14 to Return $504

(504-466)/14 = 2 Spins (Overall Loss $494)

$15 to Return $540

(540-494)/15 = 3 Spins (Overall Loss $539)

$16 to Return $576

(576-539)/16 = 2 Spins (Overall Loss $571)

$17 to Return $612

(612-571)/17 = 2 Spins (Overall Loss $605)

$18 to Return $648

(648-605)/18 = 2 Spins (Overall Loss $641)

$19 to Return $684

(684-641)/19 = 2 Spins (Overall Loss $679)

$20 to Return $720

(720-679)/20 = 2 Spins (Overall Loss $719)

$21 to Return $756

(756-719)/21 = 1 Spin (Overall Loss $740)

$22 to Return $792

(792-740)/22 = 2 Spins (Overall Loss $784)

$23 to Return $828

(828-784)/23 = 1 Spins (Overall Loss $807)

$24 to Return $864

(864-807)/24 = 2 Spins (Overall Loss $855)

$25 to Return $900

(900-855)/25 = 1 Spin (Overall Loss $880)

Probability

I totaled up 136 Spins, if you want to re-count, feel free, I skimmed through it and just kept a mental count. Okay, so if we assume it is 136 spins, then the probability of winning any one on a 0 is 1/37 and 1/38 on a 0/00, so the probability of not winning is simply one minus that:

(1 - 1/38)^136 = 0.026599001455289355 or 1/0.026599001455289355 or 1 in 37.595396266319035 to fail.

(1 - 1/37)^136 = 0.02408272526271234 or 1/0.02408272526271234 or 1 in 41.523539761021794 to fail.

Sorry I'm not going further, too boring, will go further for money....j/k

EDIT

For what it's worth, the average bet, if there have been 136 spins and $880 has been lost is $6.470588235294118.

The expected loss is simply a function of House Edge, so this system is expected to lose:

880 * .0526 = $46.288000000000004 per run on 0/00, and:

880 * .0270 = $23.759999999999998 per run on 0 Roulette.

You'll lose 6.470588235294118 * .0526 = 0.3403529411764706 * 136 = 46.288, so:

$0.3403529411764706 per spin, on average, with 0/00, and:

6.470588235294118 * .0270 = 0.17470588235294118 * 136 = 23.76, so:

$0.17470588235294118 per spin, on average, with Single-Zero.