Mathematics of a Roulette Progression

Firstly, I know that no progression or system can beat roulette. You risk a huge amount to win a very small amount. The losses will always will wipe out any winnings plus expected loss due to the house edge.

I'm just curious about some of the mathematics involved in a particular situation.

Situation:

Game is Rapid Roulette - Single Zero
House edge = 0.027027027 or 2.7%
Min chip = $0.50
Min bet = $2.50
Average Spins per hour = 54
Session Bankroll =$504

So here's the progression:
1) Place 9 ($0.50) street bets on 1 - 27
2) Place 9 ($2.50) street bets on 1 - 27
3) Place 9 ($10.50) street bets on 1 - 27
4) Place 9 ($42.50) street bets on 1 - 27

Odds of winning one progression = 1 - (10/37)^4 = 0.9946642791 or 99.46%
Odds of getting to approximately a 50% chance of going bust = (1 - (10/37)^4)^129 = 0.5015004056 or 50.15%

Bet Sequence	Amount Bet per Street	Total Amount Bet (9 street bets)	Gross Win	Net Profit	Weighted Odds	Weighted Profit
1	$0.50	$4.50	$5.50	$1.50	0.7297297297	$1.09
2	$2.50	$22.50	$27.50	$3.00	0.1972242513	$0.59
3	$10.50	$94.50	$115.50	$4.50	0.0533038517	$0.24
4	$42.50	$382.50	$467.50	$6.00	0.0144064464	$0.09

So according to my table if I add up all my Weighted Profits I get $2.01
If I'm doing this right haha. This tells me that I should average a profit of $2.01 every time one of my numbers hits anytime during the progression.
That makes sense to me because on average I will profit $1.50 most of the time, $3.00 some of the time, $4.50 a few times and $6.00 rarely.

Okay assuming all the math above is correct, I'm trying to calculate my winnings per hour. Assuming I get really lucky and don't go bust. haha ya right! In my scenario the average spins per hour was 54 spin. My guess is I would take the $2.01 and multiply that by the 54 spins and then multiply that by the odds of winning (27/37)????

2.01 * 54 * (27/37) = $79.20 per hour on average

OR

Would I take the idea that no matter where I win in the progression I will be up a multiple of $1.50

For Example look at these series of outcomes:

W W L W L L W W W W = $15 / 10 spins = an average of $1.50 per spin in 10 spins.

L L W L W W L W W W W L L W L W W L W W = $30 / 20 spins = an average of $1.50 per spin in 20 spins.

and after 54 spins

W L W............W L W = $81 / 54 spins = an average of $1.50 per spin.

It would appear that the average win per hour should be $1.5 * 54 = $81.00 because, assuming I don't go bust, no matter which point in the progression I win, I will be up exactly $1.50 * number of spins.

$81.00 per hour is pretty darn close to $79.20 per hour so its probably not that big a deal but I'm curious as to what I'm doing wrong mathematically. I am not that good with math so be gentle. haha!

Thanks!


p.s. I was thinking maybe the discrepancy between the $81.00 and $79.20 could be based on the fact that in a hour session of 54 spins I wont necessarily end with a Win on the 54th spin. That would skew my $81.00 per hour down a little bit.

example:

W L W W L .......... W W W L = $79.50 / 54 spins = $1.47 dollars per 54 spins.

I don't know I'm confused. haha!
Please explain.
Thanks!

Quote: danepeterson

I'm just curious about some of the mathematics involved in a particular situation.

Okay assuming all the math above is correct,

I'm trying to calculate my winnings per hour.

Assuming I get really lucky and don't go bust. haha ya right!
In my scenario the average spins per hour was 54 spin.
My guess is I would take the $2.01 and multiply that by the 54 spins and then multiply that by the odds of winning (27/37)????

2.01 * 54 * (27/37) = $79.20 per hour on average

OR

You need the average length of each game
With a prob of 1 you play the 1st spin
With a prob of (10/37 - a loss) you play the second spin
(10/37)^2 you play the third spin and so on.
the sum product should be 1.838647267 spins per game (nice of you never lose)
So about 30 wins per hour

A bit more...
Your average bet is done the same way
avg bet
$4.50
$6.08
$6.90
$7.55
total $25.04

You also have a 0.005335721 chance of losing $504.00 for a weighted average of -$2.69
add that to your 2.01 for a net of -0.68 each time you play this system.
-0.68/$25.04 = -0.027027027 (-1/37)
[ev/avg bet = house edge]
no matter what you do you still can not change the house edge.

At least you know what you are up against.
A 50/50 chance of an average win of $260 before the first disaster
about 251 wins in a row (26% chance) to double your $504 before the first disaster

Sure adds some excitment to playing
Good Luck

Thanks!!!