How to calculate Average Profit per win in a progression when there is multiple ways to win?

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 how to calculate the Average Profit per win when there is multiple ways to win?

Game is Rapid Roulette - Single Zero
House edge = 0.027027027 or 2.7%
Min chip = $0.25
Min bet = $2.50

I know how to calculate it with only one winning outcome.
You take the odds of winning and multiply that by the odds of losing in a sequence at each point in the sequence. Then multiply those by the profits and then add them together to get your Average Profit per win.


So as an example in this particular progression:
1) Place 10 ($0.25) street bets on 1 - 30
2) Place 10 ($1.75) street bets on 1 - 30
3) Place 10 ($10.75) street bets on 1 - 30
4) Place 10 ($64.75) street bets on 1 - 30

Bet Sequence	Amount Bet per Street	Total Amount Bet (10 street bets)	Gross Win	Net Profit	Weighted Odds	Weighted Profit
1	$0.25	$2.50	$2.75	$0.50	0.8108108108	$0.4054054054
2	$1.75	$17.50	$19.25	$1.00	0.1533966399	$0.1533966399
3	$10.75	$107.50	$118.75	$1.50	0.0290209859	$0.0435314789
4	$64.75	$647.50	$712.25	$2.00	0.0054904568	$0.0109809136

If add up all my Weighted Profits I get $0.6133144378 or approximately $0.61 for my Average Profit per win.

But how would I calculate it for a similar progression but with multiple types of wins?

So as an example in this particular progression:
1) Place 9 ($0.25) street bets on 1 - 27 AND 1 ($0.25) split bet on 28 and 29
2) Place 10 ($1.75) street bets on 1 - 27 AND 1 ($1.75) split bet on 28 and 29
3) Place 10 ($10.75) street bets on 1 - 27 AND 1 ($10.75) split bet on 28 and 29
4) Place 10 ($64.75) street bets on 1 - 27 AND 1 ($64.75) split bet on 28 and 29

Bet Sequence	Amount Bet per Street	Amount Bet on Split	Total Amount Bet (9 street bets and 1 split bet)	Gross Win if Street Hits	Gross Win if Split Hits	Net Profit if Street Hits	Net Profit if Split Hits
1	$0.25	$0.25	$2.50	$2.75	$4.25	$0.50	$2.00
2	$1.75	$1.75	$17.50	$19.25	$29.75	$1.00	$11.50
3	$10.75	$10.75	$107.50	$118.25	$182.75	$1.50	$66.00
4	$64.75	$64.75	$647.50	$712.25	$1100.75	$2.00	$390.50

How would I calculate it with this progression?????

These are some guesses of mine:

(27/37)*($0.50) + (27/37)*(8/37)*($1.00) + (27/37)*((8/37)²)*($1.50) + (27/37)*((8/37)³)*($2.00)
+
(2/37)*($2.00) + (2/37)*(8/37)*($11.50) + (2/37)*((8/37)²)*($66.00) + (2/37)*((8/37)³)*($390.50)

OR

(27/37)*($0.50) + (27/37)*(10/37)*($1.00) + (27/37)*((10/37)²)*($1.50) + (27/37)*((10/37)³)*($2.00)
+
(2/37)*($2.00) + (2/37)*(35/37)*($11.50) + (2/37)*((35/37)²)*($66.00) + (2/37)*((35/37)³)*($390.50)

OR????

hahah! I have no clue!
Can someone please show me how to calculate it and what it would be in this particular case??? Also how would you calculate it if say there were 3 or 4 or 5 or n different outcomes.
My math skills are somewhat limited so be gentle.

Thanks!!!

?????

Anyone??????

You shouldn't bump the thread without telling a joke, pursuant to the Rules. I may have a look at this thread at some point tomorrow, I'd look it over tonight and try to figure out something for you, but I've had a few drinks at this point...so it's certain to be wrong.

I would have liked to help, but I confess I don't understand the problem at hand.
Could you be more specific?

I might have even been able to do this last night in a somewhat inebriated state, it actually seems fairly routine. Basically, all you have to do is determine the probability of each individual win based on the time that it is won, and then take each individual win and multiply it by the profit at that point.

I'm going to go with your numbers from above, and this is what I get:


27/37 * .5 = 0.36486486486486485

2/37 * 2 = 0.10810810810810811

(8/37 * 27/37) * 1 = 0.15777940102264426

(8/37 * 2/37) * 11.50 = 0.13440467494521552

(8/37 * 8/37 * 27/37) * 1.5 = 0.051171697628965715

(8/37 * 8/37 * 2/37) * 66 = 0.1667818293092216

(8/37 * 8/37 * 8/37 * 27/37) * 2 = 0.014752201118260387

(8/37 * 8/37 * 8/37 * 2/37) * 390.50 = 0.2133605383955808

I don't know what the purpose of your Weighted Odds or Weighted Profits is because it doesn't seem like it would be relevant to your average profit per win. It seems to me as though I can just sum what is above to derive your average profit per win and that I don't have to assume winning is the only possibility in order to do so:

0.36486486486486485 + 0.10810810810810811 + 0.15777940102264426 + 0.13440467494521552 + 0.051171697628965715 + 0.1667818293092216 + 0.014752201118260387 + 0.2133605383955808 = $1.2112233153928613

Okay, so what I get is that when you do win your average profit will be: $1.2112233153928613

Just to make sure this is sensible, I will now calculate the value of expected loss:

-775 * (8/37 * 8/37 * 8/37 * 8/37) = -1.6937712395039703

This would make the expected value of the overall system play -1.6937712395039703 + 1.211223315928613 = -0.48254792357535736

Given the House Edge of 1/37, this would represent an average bet of:

0.48254792357535736/(1/37) = 17.85427317228822

The probability of betting $2.50 is 29/37 * 2.50 = 1.9594594594594594

The probability of betting 20 is (8/37 * 29/37) * 20 = 3.389335281227173

The probability of betting 127.50 is 127.5 * (8/37 * 8/37 * 29/37) = 4.671786468718537

After three losses, you'd bet $775 regardless of the result, so 775 * (8/37 * 8/37 * 8/37) = 7.833691982705863

The sum of these bets is:

7.833691982705863 + 4.671786468718537 + 3.389335281227173 + 1.9594594594594594 = 17.854273192111034

We've got a slight error due to rounding, but both round exactly to 17.8542732

Okay, so all of the proofs check out, and the average profit, when you do profit will be: $1.2112233153928613

However, the expected result of this system is -0.48254792357535736 per run.

Have a great day!

THANKS!!!!!!!!!!

No problem, next time you have another one of these, feel free to ask. I tend to enjoy doing system math, though I make no promises of timeliness.