Math on betting system for single zero roulette.
| Betting Sequence |
Amount Per Straight Up Position |
Total Wagered |
Investment | Win | Net Gain | Profit | ROI |
|---|---|---|---|---|---|---|---|
| 1 | $1 | $5 | -$5 | +$35 | $31 | $31 | 620.00% |
| 2 | $1 | $5 | -$10 | +$35 | $31 | $27 | 270.00% |
| 3 | $1 | $5 | -$15 | +$35 | $31 | $22 | 146.67% |
| 4 | $1 | $5 | -$20 | +$35 | $31 | $17 | 85.00% |
| 5 | $1 | $5 | -$25 | +$35 | $31 | $12 | 48.00% |
| 6 | $1 | $5 | -$30 | +$35 | $31 | $7 | 23.33% |
| 7 | $2 | $10 | -$40 | +$70 | $62 | $33 | 82.50% |
| 8 | $2 | $10 | -$50 | +$70 | $62 | $24 | 48.00% |
| 9 | $2 | $10 | -$60 | +$70 | $62 | $14 | 23.33% |
| 10 | $3 | $15 | -$75 | +$105 | $93 | $35 | 46.67% |
| 11 | $3 | $15 | -$90 | +$105 | $93 | $21 | 23.33% |
| 12 | $4 | $20 | -$110 | +$140 | $124 | $37 | 33.64% |
| 13 | $5 | $25 | -$135 | +$175 | $155 | $49 | 36.30% |
| 14 | $6 | $30 | -$165 | +$210 | $186 | $56 | 33.94% |
| 15 | $7 | $35 | -$200 | +$245 | $217 | $58 | 29.00% |
| 16 | $9 | $45 | -$245 | +$315 | $279 | $86 | 35.10% |
| 17 | $10 | $50 | -$295 | +$350 | $310 | $74 | 25.08% |
| 18 | $12 | $60 | -$355 | +$420 | $372 | $87 | 24.51% |
| 19 | $15 | $75 | -$430 | +$525 | $465 | $122 | 28.37% |
| 20 | $18 | $90 | -$520 | +$630 | $558 | $143 | 27.50% |
| 21 | $21 | $105 | -$625 | +$735 | $651 | $149 | 23.84% |
| 22 | $25 | $125 | -$750 | +$875 | $775 | $171 | 22.80% |
| 23 | $30 | $150 | -$900 | +$1,050 | $930 | $205 | 22.78% |
| 24 | $35 | $175 | -$1,075 | +$1,225 | $1,085 | $215 | 20.00% |
| 25 | $45 | $225 | -$1,300 | +$1,575 | $1,395 | $355 | 27.31% |
| 26 | $55 | $275 | -$1,575 | +$1,925 | $1,705 | $450 | 28.57% |
| 27 | $65 | $325 | -$1,900 | +$2,275 | $2,015 | $495 | 26.05% |
| 28 | $75 | $375 | -$2,275 | +$2,625 | $2,325 | $490 | 21.54% |
| 29 | $90 | $450 | -$2,725 | +$3,150 | $2,790 | $590 | 21.65% |
| 30 | $100 | $500 | -$3,225 | +$3,500 | $3,100 | $465 | 14.42% |
So the odds of me not having one of my 5 numbers come up in the 30 spins is (32/37)^30 = 0.0128 = 1.28% = (1/77.9). Can I assume this means that in 77 rounds of 30 (2,310 spins total), I should expect to lose my entire bankroll of $3,225 once in 77 rounds of 30 spins? If this is true can I say that I'm expected to hit one of my 5 numbers in 30 spins, 76 times out of 77?
If I add up all the profits $4,540 and divide that by 30 to get my average profit per round of 30.
$4,540/30= $151.33
Couldn't I say that if I take my average profit per round of 30 spins $151.33 and multiply that by the 76 rounds of expected wins. Then subtract the 1 time that I am expected to lose my entire bankroll of $3,225
$151.33 * 76 = $11,501.08
$11,501.08 - $3,225 = $8,276.08
I understand that expected results aren't going to be the same as actual results but I'm just curious. I think I'm doing something wrong with my math because this seems way too easy to make money. The casino wouldn't have made it this easy to beat. Can someone tweak my math and show me what I'm doing wrong.
Thanks!!!
You bet $5 straight up and only win $35 for a net of $31???
Is this the new metric system?
I get $175 for a $5 wager on a win.
Time to party on a Saturday night!
Quote: danepeterson
If I add up all the profits $4,540 and divide that by 30 to get my average profit per round of 30.
$4,540/30= $151.33
Couldn't I say that if I take my average profit per round of 30 spins $151.33 Can someone tweak my math and show me what I'm doing wrong.
Your average profit per completed round will be far less than $151.33. You hardly ever will make it to the final rounds where you start getting triple digit profits. The majority of your profits will fall into the less than $40 per round figure.
The previous poster said it succinctly. You will lose the 2.6% or so times the amount you bet, on average. No system will change that.
Quote: mustangsallyyour table makes no sense.
You bet $5 straight up and only win $35 for a net of $31???
Is this the new metric system?
I get $175 for a $5 wager on a win.
Time to party on a Saturday night!
Sally? He is putting $1 on 5 separate numbers. Only one of those numbers can hit. He will win $35 on that number, and lose $4 on the 4 losers. It is time for you to party on a Saturday night.
Quote: SOOPOOYour average profit per completed round will be far less than $151.33. You hardly ever will make it to the final rounds where you start getting triple digit profits. The majority of your profits will fall into the less than $40 per round figure.
The previous poster said it succinctly. You will lose the 2.6% or so times the amount you bet, on average. No system will change that.
I think this is the exact issue with the table. 151.33 is - I think, i haven't verified - the unweighted average of the wins. But the wins aren't equally likely to occur. The higher $$ wins are less likely to happen because the system restarts on a lower $$ win. So what is missing is a weighting of the probability of each win in this system.
Quote: danepeterson
If I add up all the profits $4,540 and divide that by 30 to get my average profit per round of 30.
Average is not the same as expectation though. Because the probabilities of each outcome are different, you have to weigh each value with its respective probability to compute the expected profit instead of straight, unweighted averaging.
Doing it correctly, expected profit from one round is $40.66
Edit: I gotta learn to check earlier replies before jumping in :) Sorry guys, but, at least, I have also given the actual expected value, not totally worthless :)
Quote: mustangsallyyour table makes no sense.
You bet $5 straight up and only win $35 for a net of $31???
Is this the new metric system?
I get $175 for a $5 wager on a win.
Time to party on a Saturday night!
sorry if i wasnt clear. Im making 5 straight up bets each spin. so with $5 wagered im placing $1 dollar on five different numbers. So if i win $35 on one of the numbers that hit minus the $4 dollars i lost equals $31.
Quote: weaselmanAverage is not the same as expectation though. Because the probabilities of each outcome are different, you have to weigh each value with its respective probability to compute the expected profit instead of straight, unweighted averaging.
Doing it correctly, expected profit from one round is $40.66
Hey how did you come up with 40.66??? can you show me the math.
Thanks!!!
Quote: rdw4potusI think this is the exact issue with the table. 151.33 is - I think, i haven't verified - the unweighted average of the wins. But the wins aren't equally likely to occur. The higher $$ wins are less likely to happen because the system restarts on a lower $$ win. So what is missing is a weighting of the probability of each win in this system.
Perfect how do I calculate the weighting of the probability of each win????
Quote: danepetersonPerfect how do I calculate the weighting of the probability of each win????
spin 1: 5/37; spin2: 5/37*odds of not winning spin 1; spin 3: 5/37*odds of not winning spin1 or spin2; ...spin n. (I think...)
So the weighting of the higher payouts are extremely low.
expand your table to show these values in another column, as shown in the above post.Quote: danepetersonHey how did you come up with 40.66??? can you show me the math.
Thanks!!!
spin1 to spin30
0.135135135 multiply this by the profit from spin1
0.11687363 multiply this by the profit from spin2
0.101079897 and so on
0.087420451
0.075606877
0.065389731
0.056553281
0.048910946
0.042301358
0.036584959
0.031641045
0.027365228
0.023667225
0.020468951
0.017702877
0.015310596
0.013241596
0.011452192
0.009904598
0.008566139
0.007408553
0.006407397
0.005541532
0.004792677
0.004145018
0.00358488
0.003100437
0.002681459
0.0023191
0.002005708
then add them all up.
Avg win $40.66
Excel can use the sumproduct function.
98.716347% probability of winning one session.
53 in a row would be 0.504221119 (the median)(98.716347%^53)
or about a 50/50 chance of winning $41*53 before losing the starting bankroll.
Quote: danepetersonHey how did you come up with 40.66??? can you show me the math.
First probability is 5/37
Second is 32/37*5/37
Third: (32/37)^2*5/37
Nth: (32/37)^(N-1)*5/37
I used a spreadsheet to weigh your profit numbers at each step with these probabilities.
BTW, your table seems to be wrong. For example, looking at the last row:
30 $100 $500 -$3,225 +$3,500 $3,100 $465 14.42%
Your "net gain" $3100, the amount you have bet so far is $3225. The "profit" should be -$125, not +$465.
Quote: weaselmanBTW, your table seems to be wrong. For example, looking at the last row:
30 $100 $500 -$3,225 +$3,500 $3,100 $465 14.42%
Your "net gain" $3100, the amount you have bet so far is $3225. The "profit" should be -$125, not +$465.
Thanks for the reply. Sorry my spreadsheet skills are pretty awful.
| Betting Sequence |
Amount Per Straight Up Position |
Total Wagered |
Investment | Win | Net Gain | Profit | ROI |
|---|---|---|---|---|---|---|---|
| 1 | $1 | $5 | -$5 | +$35 | $31 | $31 | 620.00% |
| 2 | $1 | $5 | -$10 | +$35 | $31 | $27 | 270.00% |
| 3 | $1 | $5 | -$15 | +$35 | $31 | $22 | 146.67% |
| 4 | $1 | $5 | -$20 | +$35 | $31 | $17 | 85.00% |
| 5 | $1 | $5 | -$25 | +$35 | $31 | $12 | 48.00% |
| 6 | $1 | $5 | -$30 | +$35 | $31 | $7 | 23.33% |
| 7 | $2 | $10 | -$40 | +$70 | $62 | $34 | 85.00% |
| 8 | $2 | $10 | -$50 | +$70 | $62 | $24 | 48.00% |
| 9 | $2 | $10 | -$60 | +$70 | $62 | $14 | 23.33% |
| 10 | $3 | $15 | -$75 | +$105 | $93 | $36 | 48.00% |
| 11 | $3 | $15 | -$90 | +$105 | $93 | $21 | 23.33% |
| 12 | $4 | $20 | -$110 | +$140 | $124 | $38 | 34.55% |
| 13 | $5 | $25 | -$135 | +$175 | $155 | $50 | 37.04% |
| 14 | $6 | $30 | -$165 | +$210 | $186 | $57 | 34.55% |
| 15 | $7 | $35 | -$200 | +$245 | $217 | $59 | 29.50% |
| 16 | $9 | $45 | -$245 | +$315 | $279 | $88 | 35.92% |
| 17 | $10 | $50 | -$295 | +$350 | $310 | $75 | 25.42% |
| 18 | $12 | $60 | -$355 | +$420 | $372 | $89 | 25.07% |
| 19 | $15 | $75 | -$430 | +$525 | $465 | $125 | 29.07% |
| 20 | $18 | $90 | -$520 | +$630 | $558 | $146 | 28.08% |
| 21 | $21 | $105 | -$625 | +$735 | $651 | $152 | 24.32% |
| 22 | $25 | $125 | -$750 | +$875 | $775 | $175 | 23.33% |
| 23 | $30 | $150 | -$900 | +$1,050 | $930 | $210 | 23.33% |
| 24 | $35 | $175 | -$1,075 | +$1,225 | $1,085 | $220 | 20.47% |
| 25 | $45 | $225 | -$1,300 | +$1,575 | $1,395 | $365 | 28.08% |
| 26 | $55 | $275 | -$1,575 | +$1,925 | $1,705 | $460 | 29.21% |
| 27 | $65 | $325 | -$1,900 | +$2,275 | $2,015 | $505 | 26.58% |
| 28 | $75 | $375 | -$2,275 | +$2,625 | $2,325 | $500 | 21.98% |
| 29 | $90 | $450 | -$2,725 | +$3,150 | $2,790 | $605 | 22.20% |
| 30 | $100 | $500 | -$3,225 | +$3,500 | $3,100 | $475 | 14.73% |
What its supposed to say is after the 29th spin and no win i will be down -$2,725. On my 30th spin I invest $500 more dollars for a total investment of -$3,225. If one of my numbers hits on the 30th spin I will win $3,500 and lose $400. Which leave me with a total of $3,100. I had started the 30th round at -$2,725 and I now have $3,100 dollars. A profit of $475.
Quote: guido11198.716347% probability of winning one session.
53 in a row would be 0.504221119 (the median)(98.716347%^53)
or about a 50/50 chance of winning $41*53 before losing the starting bankroll.
Thanks awesome explanation!
Quote: vendman1This system, is of course bunk...you're working against a HE of 2.63% all the time on a single zero wheel, nothing can change that. Period. End of Discussion. P.T. Barnum was right....one born every minute.
I agree. Unless he is betting Red. Then I am willing to provide his bankroll for 10% of the profits.
(32/37)^30 = 1/77
$40.66 * 76 = $3,090.16
$3,090.16 - $3,225 = -$134.84
The house edge is 1/37 = 2.7%
-$134.84 / 0.027 = -$4,989.08
So does this mean in 77 rounds of 30 spins I should expect to invest somewhere around $4,989.08 and have a total profit of -$134.84 because the of the house edge??? Obviously the actual results will differ but if i were able to approach infinite bets I should see this average come out???
Quote: vendman1This system, is of course bunk...you're working against a HE of 2.63% all the time on a single zero wheel, nothing can change that. Period. End of Discussion. P.T. Barnum was right....one born every minute.
Hey where did you get the 2.63% HE???
I thought the house edge is 1/37 = 0.027027027027 or 2.7%
Can you please show your math.
Thanks!
