I am a math guy and understand that edge is important. However, often many ignores the variance in the payout 35:1. Even though we have a 30% edge, we can easily not win in 100 spins by betting a single number or even more and that might wipe out some people’s bankroll. Betting more numbers might have a slightly less edge per number. However, overall, the sharpe ratio (expected value /variance )(a term used in finance) might be higher, meaning the risk to reward ratio is better. In statistical term, it is the first moment divided by the second moment. However, if we bet all 37 numbers, we are playing a losing game and my goal is to find out the optimal betting number.

With more numbers to bet, the payout decreases and the chance of winnings increase and this decreases risk significantly while the advantage decrease only a small fraction to a certain point.

Bet numbers often comes in 1, 3, 5, 7, 9 or even 12. I have been testing out which one is the best to maximise the growth in bankroll. Lets assume the hit rate is 1/30 or the edge is 20%. I have found out that betting 5 numbers or 7 numbers might be the best but lacks the math to support this except actual gameplay results.

I would be grateful if anyone can provide a mathematically explantion for this. It could be a mathematical formula or a monte carlo simulation using programmes like R.

In 99% you are not right… 5-7 numbers have too big dispersion that will be best.

Math guy, who can’t solve such a simple task? Strange…

Simplest variant - write some simple macros and run the simulation. But the problem is that you as a math guy, do not understand that need to have full data for solving such a task.
When you will have in front of your eyes the full data that you need - then maybe the solution will come itself if you are a math guy…

And one more - “optimal” and “best” are slightly different categories and not always they will coincide…

Thanks for the comment. I have done some caluctions using ball jump data of a wheel and its given advantage and using kelly formula. It shows that betting more numbers are better.

Assume bet 19 units on 1 number, total 19 units on 3 ,5,7,9,11,13,15,17 sectors respectively, using fully kelly, betting 19 numbers are the best. Required bankroll for full kelly for 1,3,5,7,9,11,13,15,17,19 sectors are 3325, 1045, 589, 394, 285, 215, 168, 133,106, 85 units repectively for 19 units bet each round. However, in terms of practicality, i think 5 or 7 is good becasue required bank roll required are not much more than betting 19 numbers and time use for 5 or 7 numbers bet is reasonable.

However, the above calculation has a flaw and it is i must predict the ball drop number perfectly. In reality and i aint sure how to take that into account for the human error, whole sector shift error.

The main moment to decide what is better xx or 5 is to know the real situation on the wheel is knowing how many positive numbers are on the wheel and then trying to find reasons why bet only 5 of them and not bet others …
Of course can be a reason - too small bankroll, but then the solution - before play do some job for which you will get a wage and create bancrol which you need…
Other reasons I cant to create…

The reason i bring up this topic is that vb is quite simple, there is usally a normal distribution of a center number of ball jump yardage or you name it or close to normal distribution. However, if i am playing bias, especially for a single pocket bias, even then hit rate is so good to be low 20s, lets say 1/23, we still need thousands of unit to play to gurantee win before the standard deviation wipe us out. This is also why bias (pocket bias) espically, if not whole sector bias need thousands of spins of data to confirm the bias is actually there.

You say you are a “math guy”, then give a full example of how your theory that 19 numbers is best to bet but in the same comment, say that for this to be true you need to predict perfect ball drop every time!

Listen to what @bebediktus is saying and investigate it further for yourself. Stop demanding people’s input without doing the work yourself. It’s outright insulting to all those on this forum.

Furthermore, there is much information on threads for this and all else you asked in recent times in this forum. Use your search toolbar and do some work for a change.

How i got 19 is by calculating the realized edge using the yardage data of a wheel i have been taking data of and it appears to be 31 percent by betting 19 numbers.I then use kelly formula f=(bp-q)/b where b is the payout odds and p is the probability winning and q being (1-p). I set p to be 19/27.5 and q being 1-p. I then divide 1 by f and it is the required bankroll to bet fully kelly which is around 85. I dont have the excel with me now but for a 140 percent edge of betting 1 number only, the required bankroll is like higher than 3000 units for fully kelly.

You see that the 140% edge betting 1 number and 30percent edge betting 19 numbers although the edge is decreased by 5 folds but the risk decrease by 30 folds.

My assumption is that i bet 19 units on 1 number, 19 units on each of the 19 number sectors, so the money on the table each spin is the same.

Given not everytime the right drop number is predicted, we need to bet a lower fraction of kelly so we need an even higher bankroll. Please let me know if i am wrong. The reason i bring up this question is

When betting big, i must choose a lower risk approach, edge is one thing but risk is also very important. Imagine the lottery is free of charge but you can only buy 100 tickets only, this is unlimited edge but you just will not get the prize.

It is physcologically better if the swings are smaller and makes myself more emotionally stable and dont shake that much when betting a lot of money.

When betting at the table maximum, using the above exmaple, clearly betting 19 numbers has a higher overall edge than betting 1 number. 30%x10000x19>10000×140%

I have also take into account the diamond prection accuracy and i personally can achieve around 70% for a lightly tilted wheel using ffz. I understand that betting too many numbers maybe be playing into negative edge if diamond accurracy is not high enough. Using the formila [B.DxS.F+(1-BD)xR.F]xB.F.×36/SL-1. Therefore, i guess betting too many numbers are bad and so does betting too few numbers.

Dont get me wrong, i have the answer to most question. However, i need proof! I have not seen anyone post something with a logical mathematic explanation or scientific approach to this topic. If you read other professional gambling books such as professional blackjack, you will see clear mathemactical explanation.

And want that somebody will make that proof to you ?

Yes, but those are different cases firstly blackjack is not roulette - hare calculations are slightly different because part of randomness here is far bigger, secondly with writing all calculations these guys fired blackjack as a game…and that was a good lesson…

Plus your question how you it posted not need any mathematical explanation here is simply logic - the player must do all that he can to cover as possible more % of positive numbers and less as possible negative numbers… and as I noticed you did even not give data which is need to do such calculations…

I get the idea. My previous model is flawed and i need to take into account of

Accuracy in ball jump data collection (if the whole data systematically shift by 2 pockets, it might be disatrous as when you see the ball hit the dimaond and look at the number directly under it, there might be a delay.

Even though the right dimaond is predicted, the drop number might have a error again as each ball revolution time is different, the slow down rate is the same but a longer spin would casue the rotor to slow down more and we definitely need to predict at the right ball speed every spin

Air pressure is a bit tricky, 5mbar of difference but can the dominant dimaond to shift. Howeber, 20mbar of difference can cause the ball to have 1 revolution difference. We can adjust the acc of the ball to compensate for this and it is a tricky thing. Lets say you have a vb system, air pressure change, you think this might be becasue of the moon or something like that but it is really the air pressure.

Some delaers spins the ball a bit weird, also need to classify when taking data becasue again, the ball might travel 1 rev further when the hidden 3d spinning force convert into circular motion.