Roulette HolyGrail. 37 people go into a casino - and the house edge appeared.

So here are the "rules" or lack of...
There are 37 players, each player has his/her own number to play and they play
that number only, every spin.
No progression - flat betting only. No skipping spins, no qualifications, etc.
Just every spin they bet their number for a total of 3,000 spins.
They flat bet $25.00 per spin.
Here are the results when the 3,000 spins are completed :

Player Outcome Low High
0) -2100 -4625 3900
1) -3000 -4375 4750
2) -3900 -3900 4750
3) -3900 -3900 5850
4) 7800 -3475 8850 Winner
5) -7500 -10700 3575
6) -6600 -6600 2475
7) 3300 -2350 7700 Winner
8) -6600 -6950 2950
9) -2100 -4825 7525
10) 4200 -3100 6525 Winner
11) 600 -6575 3075 Winner
12) 3300 -5575 3875 Winner
13) -4800 -8450 3100
14) -6600 -7650 0
15) -5700 -8050 2350
16) -300 -3525 4050
17) 2400 -3900 3350 Winner
18) -16500 -17400 1325
19) -18300 -19550 575
20) 6000 -1900 10125 Winner
21) 3300 -625 9400 Winner
22) 11400 -3875 11450 Winner
23) 9600 -6300 9950 Winner
24) -13800 -14725 4400
25) 7800 -950 8325 Winner
26) 12300 -2325 14775 BEST
27) -8400 -11075 375
28) -3900 -5600 3500
29) -1200 -3750 2875
30) -6600 -10500 1725
31) -15600 -17325 625
32) -19200 -19200 325 WORST
33) 5100 -1600 6350 Winner
34) 2400 -4825 2875 Winner
35) -2100 -3700 4025
36) 4200 -9250 7025 Winner

House Outcome
75000 75000

Winners(14) 71400 Total: 37.83%
Losers (23) -146400 Total: 62.16%

Winners (lowest): -9250

Top Winners: Outcome Lowest
22) 11400 -3875
23) 9600 -6300
4) 7800 -3475
25) 7800 -950
20) 6000 -1900
33) 5100 -1600
10) 4200 -3100
36) 4200 -9250
7) 3300 -2350
12) 3300 -5575
21) 3300 -625
17) 2400 -3900
34) 2400 -4825
11) 600 -6575


14 players would have won - flat betting their specific number over 3,000 spins played.
So you can assume that you have a 37.83% chance of winning by simply flat betting one number
for this long. The total that the winners made was $71,400.00 (or 2,856 units).
This is 204 units profit average per person.
You can also assume that you have a 62.16% chance of losing flat betting one number
for this long. The total that the losers lost was $146,400.00 (or 5,856 units).
This is 254.61 units lost average per person.
The "house" made $75,000.00 (as expected) or 3,000 units in total.
=====================================================

Worth noting of course is that EVERYONE (aside from #14) made a profit and
had they stopped at that point, they would have left in profit.
That means 36 players flat betting would ALL have walked out a winner.
This means if you flat bet a single number, you have a 97.3% chance of winning
your playing session, instead of 37.83% if you never stopped.
Also, when you factor in #14's outcome of all 3,000 spins - and combined it
with the profits that all other 36 players achieved (had they stopped on any profit)..
the entire group won as a whole making it a 100% success rate overall.
In the big picture - over 3,000 spins of possible played spins in the session - the
entire group of 37 people won - if the profits are split (of course).
All player in total made a profit of $9,375.00 (or 375 units) for a split of
$253.38 per person.

But here's the house edge... which I found interesting.
If you flat bet and stop on any profit - you had a 97.3% chance of walking out
a winner. You have a 2.7% chance of walking out a loser. I won't post the house edge
for a single zero table - but it's 2.7% :)

Player Stop on Any Profit Spins Balance All
0) 75 465 Winner 75
1) 575 13 Winner 650
2) 175 29 Winner 825
3) 200 28 Winner 1025
4) 750 6 Winner 1775
5) 875 1 Winner 2650
6) 350 22 Winner 3000
7) 100 32 Winner 3100
8) 475 17 Winner 3575
9) 350 58 Winner 3925
10) 50 142 Winner 3975
11) 425 19 Winner 4400
12) 200 100 Winner 4600
13) 725 7 Winner 5375
14) -6600 3000 Loser -1275
15) 775 5 Winner -500
16) 325 275 Winner -175
17) 500 16 Winner 325
18) 100 428 Winner 425
19) 175 65 Winner 600
20) 800 4 Winner 1400
21) 600 12 Winner 2000
22) 525 15 Winner 2525
23) 350 1066 Winner 2875
24) 850 2 Winner 3725
25) 575 49 Winner 4300
26) 625 119 Winner 4925
27) 375 21 Winner 5300
28) 625 623 Winner 5925
29) 50 70 Winner 5975
30) 250 26 Winner 6225
31) 625 11 Winner 6850
32) 325 59 Winner 7175
33) 550 14 Winner 7725
34) 825 3 Winner 8550
35) 150 30 Winner 8700
36) 675 9 Winner 9375


6,861 spins total (all players combined) and $9,375.00 profit total (or 375 units)

Hopefully in this format and explanation (no errors this time) the info
will be useful.
I see a good argument in here for "random has limits".. but that's for another
thread in the works.

If you want a suggestion on how to use this info to win, I would simply
suggest to play a number, increase the bet 1 unit on any win better than
37 spins and drop it back to 1 unit on any win more than 37 spins and stop when
in profit. Even the doomed #14 would have ended this test in profit that way
because it was (at one point) climbing right back to the expected hit rate
as it's going to do (or "drifting" if you prefer). (on spin 2,239 it was only down
7 units down and 1 win would have made it end in profit...)
=======================================================

Cheers

You ran extremely lucky, which can happen in a small(3000) sample size. I'll let a better math guy than me address it, but to only have one out of 37 never be positive is quite lucky. Probably average is 3 or so. Your max win on any number is 875. Your max loss is 75,000. Probably half the time you get at least one 5000 loss.
Let the math guys have at it!

I'm not a math guy and I did not read more than a couple lines. But I think i am not going out on a limb here by saying its roulette, it can't be beat, and leave it at that.

This is awful. Carry on, nothing to see here.

The lesson I’ve taken away from this is, don’t bet on #14.

I’ll report back with my results

Using the 2nd chart, might want to start betting a straight-up number in sequence and change the number you're betting on by +1 and raise the bet 1 unit each time you advance to a new number after no winners after 37/38 spins. Seems some numbers are just so dead you can't stay long. 23 times out of 37 times a winner came along within 37/38 spins. You could stay on the same number and keep winning on it until it loses after 37/38 spins in a row, then move on to the next number. If you're at 2 or more units on a win, reduce 1 unit.

By definition of your trial someone will win the first spin and everyone else will have lost. So if everyone stopped when they were ahead then one person wouldbail out with +35 units and the other 36 people would be -1 into the second round.

For a while, unless a number repeats, several people will give up until on the 37th spin anyone still left in the game is 36 down and some have had their number come up and set a profit of 36 or less.

From about there it's going to take two numbers coming up before people still in the game can show a profit, after 70 spins it's three times etc.

So your trial will probably show a profit if numbers didn't tend to repeat earlier. Thus you need to rerun many trials of 3000 to get a fair idea. I'm guessing in cases where the same numbers kept coming up you'd be in bad shape as lots of people would be building up their losses and in the long run this offsets the good runs.

Quote: TurboGenius

Hi Turbo, welcome to the forum(I guess).

Just so you know, the Boss man Mr. Michael Shackleford AKA The Wizard is not as tolerant as places like the corrupt GamblingForums when it comes to roulette and other -EV games betting systems. You won't find any love from the Moderators, Advantage Players, Math guys or Regulars here either.
=======================================================
cheers

Moderators doing exorcisms out there. Really don't need that for this.

Quote: TurboGenius

Worth noting of course is that EVERYONE (aside from #14) made a profit and
had they stopped at that point, they would have left in profit.
That means 36 players flat betting would ALL have walked out a winner.
This means if you flat bet a single number, you have a 97.3% chance of winning
your playing session, instead of 37.83% if you never stopped.

Of course - in part because 61.7% of the time, one of your first 35 bets (assuming a single-zero wheel) will win, which means you are ahead. It's where the amounts you win when you stop versus the amounts where you lose when you stop (either voluntarily or by force - presumably, because your bankroll is zero, or you have to leave the table for some reason) differ that show you what effect the House Edge really has.

I ran a simulation of 50,000 sessions where there were 37 players, each of which flat-bet on a different number, and stopped either when they were ahead for the first time or there were 1 million spins.
Here's what I got:
1/56 of the time, everybody was ahead within the first 1000 spins
1/19 of the time, everybody was ahead within the first 2000 spins
1/12 of the time, everybody was ahead within the first 3000 spins
1/9 of the time, everybody was ahead within the first 4000 spins
13.1% of the time, everybody was ahead within the first 5000 spins
19.6% of the time, everybody was ahead within the first 10,000 spins - that means that 4 out of every 5 times, at least one person is never ahead at any point in 10,000 bets of a particular number.

Of course, the larger your initial bankroll is, the more likely you are to be ahead at some point by flat betting.
I ran another simulation of how many spins it will take for someone to either be ahead at some point, or always be behind in 1,000,000 spins.
In 3.5 million "runs," I get:
75% of the plays are ahead before getting to 100 spins
84.7% are ahead before 300 spins
87.9% are ahead before 500 spins
91% (about 10 out of every 11) are ahead before 1000 spins
93.1% (about 13 out of every 14) are ahead before 2000 spins
94.1% (about 16 out of every 17) are ahead before 3000 spins
95% (about 19 out of every 20) are ahead before 5000 spins
On the other hand, about 1 out of every 36 players will be behind after every spin even after 1,000,000 spins.

Seems like the more spins you had, the more the winner's column filled in. If 55 out of 56 times at least one person wasn't ahead within 1000 spins, why is 4 out of 5 worse at 10,000 spins?

Quote: ChumpChange

Seems like the more spins you had, the more the winner's column filled in. If 55 out of 56 times at least one person wasn't ahead within 1000 spins, why is 4 out of 5 worse at 10,000 spins?

Because you are comparing 37 different people playing against just one.

Your first statement is correct. The higher your bankroll, the more likely you are of reaching a particular "stop point" before busting.
This is also the "principle" behind Martingale - in a 50/50 game, with 7 plays before you go bust, you go bust before ever being ahead 1/128 of the time, but with 10 plays, it's 1/1024 of the time, and if it's 20, it becomes 1/1,048,576 of the time.

The "problem" is, when you do lose, almost always the size of the loss is more than the combined sizes of all of your wins.

I'd likely use a strategy to put $40 in the video roulette machine and bet $1 on a single number, note my balance when I win and choose a stop point 40 spins below that. The roulette machine displays the hottest & coldest few numbers so I could avoid the really cold ones and not expect them "due." I could keep betting on the same hot number until it didn't show up 40 times in a row, then pick another hot number to try and double my bet to $2. I may have to have $80 handy to insert into the machine to cover that. When I win in less than 40 spins, I can lower my bet $1 per spin.
I'm just trying to waste time and get some points on my card and hopefully come out a little bit ahead. I could win $10-$30 per 5 to 25 spins with $1 bet multiples.
$1 = $40
$2 = $80
$3 = $120
$4 = $160
$5 = $200
I could limit my progression to 5 units with a $600 bankroll.

I should make my bet equal to a balance value rather than a rule about lowering strictly on a win.

Bet	Balance	Win
$1	≥ -$40	$36
$2	≥ -$120	$72
$3	≥ -$240	$108
$4	≥ -$400	$144
$5	≥ -$600	$180

I did a little math of my own;

Being generous, lets assume that you have the fastest croupier in the world and despite such a huge amount of players he can (since he is the best) handle 25 spins per hour. That's 5 days of roulette, non-stop. I wish I had that much time on my hands (along with so many friends and the necessary funds).