The expected profit from having a positive odds on the casino is simply that positive odds times the total amount of money bet. Regardless if you bet $10 000 at once or $100 on 100 different occasions
Given a wheel w/o a double zero which pays 36 times the money when winning on a single number, the return is simply calculated as 36 divided by the odds you have. If you have the 1/35 chance to guess the right number given you technique, then your return is 36/35 = 2.8%. Some other examples for different odds and cash profit if you bet 10 000 (say, 100 times $100):
1/34 -> 5.9% -> $590
1/33 -> 9.1% -> $910
1/32 -> 12.5% -> $1 250
1/31 -> 16.3% -> $1 630
1/25 -> 44% -> $4 400
So, it is obvious that any improvement on the odds is worth A LOT! Small odds gove profit which one has to work hard for. Better odds substantially improves the return ratio.
It is possible, that even if you have good odds, you might get unluck and loose your whole budget on a long string of losses. This risk is radically greater than most people might think. The formula would be (1-(1/odds)^number of losses in a row), where “odds” is for example 33 if you have 1/33 to guess the right number.
Here is a small table for some odds and probabilities for loosing strings:
1/35 -> 23 losses in a row -> 50% probability
1/35 -> 77 losses in a row -> 10% probability
1/35 -> 100 losses in a row -> 5.5% probability
1/33 -> 22 losses in a row -> 50% probability
1/33 -> 75 losses in a row -> 10% probability
1/33 -> 100 losses in a row -> 4.6% probability
1/30 -> 20 losses in a row -> 50% probability
1/30 -> 68 losses in a row -> 10% probability
1/30 -> 100 losses in a row -> 3.4% probability
There IS a substantial risk to loose even 100 times in a row, even with an odds of 1/30 in roulette! With that odds, on average you would profit 20% on everything you bet. But there is a 1 in 29 chance that you still loose one hundered times in a row! Betting $100 each time, would take you down with $10 000, even though your predicition worked by the book, giving you 1/30 odds compared to the natural 1/37 odds.
A single digit percetage risk might maybe is acceptable. But the 10% probability for any odds worse than 1/30 to generate a string of 70 or so losses in a row, should be a WARNING! Conservative money management is necessary. Half of the gambling evenings, you will start out with more than 20 losses in a row. Every ten times with about 70 losses in a row. And if you make it a habit, you will sometimes see 100 losses in a row, even when everything is as it is supposed to be!
So, to be a bit safe, do not bet more than 1% of your betting budget at once. Do it daily, and you will leave the table bancrupt only once per month if you have 1/30 or worse odds on the casino…