Standard deviation of bankroll

Has anyone developed a standard deviation and confidence interval of bankroll based on information such as edge and numbers of betting? Looking to develope a method to know that whether i am playing a “winning game” or losing game based on fluctuations of bankroll.

The reason i bring up this topic is that i am not sure if i am playing a winning game or just happen to be “lucky”

That is the main in play and nobody will give you a solution because it does not exist.

I understand what you are trying to say. Taking blackjack as an example, we know that card counting has an edge of 1%, and the variance of the game could be calculated usinf monte carlo simulation. Hence, the optimal betting using the kelly formula could be calculated. The optimum maximum bet would be around 1% of the bankroll

For roulette, i have read some books which has brought up betting using kelly formula but incomplete. The main reason is becasue the advantage in roulette varies greatly on conditions as a change in air pressure or the way delaer spin the ball might change the advantage significantly.

Taking betting 1,3,5 numbers in 1 spin as an example, there is clearly a correlation that betting 5 numbers require a smaller bankroll than 3 or 1 number with the same risk of ruin.

I think you overestimate such things as air pressure, the dealer’s way in which he spins is visible - so again maybe are too much overestimated…
The same as in Blackjack in roulette, the most important is the actual situation, the same as in BJ - players need to know the rest cards in the deck to know what they can expect, in roulette also players need to know what they can expect. and do know about that from air pressure… hmm very dubious, if possible do profitable…

The edge of blackjack is changing according to the true count. I suspect it is the same for roulette as a ball might bounce further when the air pressure decreases. If the air pressure decreases too much, it might completely miss the original diamond and reach the next one. However, no one or not that i know of has succesfully quantify these things and develope a method to calculate the optimal bet based on a given risk of ruin, edge and bankroll.

The most we can do is to use data of given pressure, the way dealer spin the ball, direction of ball, wheel speed to give an edge and to use kelly formula to bet according to the calculated edge.

My educated guess might be that becasue there are too much variables in roulette, we might give a confidence index to bet and never bet fully kelly but quarter kelly instead? However, i dont see roulette has as much information as blackjack on the internet that i can find datawise.

Although we can quantify data such as air pressure, i always doubt if the air pressure gauge is accurate and whehter the previous data is usable when casino level the wheel