bet size

Hi
Is there any formula between these parameters:

house edge a%
total invested money b
winning money c
minimum bet d
number of bets e
possibility of (c/b) %

and any other parameter that can be important (like the game type, I am mostly interested in Blackjack and Craps)assuming that I am following betting system.

Basically what I want to know is that how much money should I bring to the table (with a certain minimum bet), that the fluctuation of my bank is (for example (c-b)/b=20% of my bank) and I can be comfortable (more than 80% possibility) that before I tank my bank I will reach to 120% of my bank and would have the chance to cash out.

http://en.wikipedia.org/wiki/Kelly_criterion

Try Easy.Vegas . It has a page on sizing of bets to avoid Gamblers Ruin with a 90 percent confidence level. I don't fully understand the math on that page but start there and see if you need any additional information or not.

There is not going to be a simple formula -- you need to take variance into account as well.

What I would probably do is figure out the average amount of money that is bet (it will be the sum of an infinite sequence), and multiply that by the house edge. That will give the average loss per session. From that you can easily compute your success ratio given firm stopping points (both win and loss).

For example, in your case, you said that you will stop if you lose everything, or get up to 120% of what you started with. If you want to be successful 80% of the time, that means that you will be down 4% on average (4 wins and 1 loss = down 20% every 5 sessions = down 4% per session).

So, if you are playing craps at a 1.4% edge on the pass line, you can't bet an average of more than 4 / 1.4 = 2.86x your starting amount on average, or you will be down more than 4% on average, meaning that you will not hit your goal of an 80% success rate. The odds bets throw a wrench into these calculations; you would need to replace 1.4% with the weighted average of the house edge after odds (and calculate your average total bet amount including odds)

In general, the more aggressively you bet, the better off you are in terms of success rate, but it also means that you get less time at the table, which may be a bad thing depending on your goals.

Quote: FONCOLA

Hi

Hi
is that COLA as in the drink?

Quote: FONCOLA

Is there any formula between these parameters:...

kind of
expected value and variance are important in calculating any risk of ruin problems.
Bankroll and weighted average bets are important too.

one method:
SHORT TERM RISK OF RUIN FORMULA (From D. Schlesinger's BLACKJACK ATTACK, p 162)
in Excel
Risk =NORMSDIST((-B-ev)/sd) + EXP((-2*ev*B)/(sd^2)) * NORMSDIST((-B+ev)/sd)
this works well once you see how it works. or you can get the book and read it too.

The Wizard has a Blackjack RoR page from simulations that might help.
https://wizardofodds.com/games/blackjack/appendix/12/


How about some numbers for your Craps play, bankroll, average bets, how many bets for how long, stuff like that and we can work our way thru it
There are a few threads here (WoV) already on Bankroll requirements and Risk of Ruin that you can search for.
another method:
I will use expected value and standard deviation and the Bell Curve in my calcs. Maybe a sim or actual calculation just to make sure.

But you might want to work out an example for your type of play.
That seems to carry more weight in the learning curve.


The bottom line about how much money to bring is
how much Risk are you willing to take?
Sometimes you only have so much Bankroll so you be limited from there.

like, bust out every other session?
1 out of 3
1 out of 4
yes, like that
maybe 1 out of 20 or even 1 out of 100

the less risk the greater the bankroll requirements for the same size bets
always a catch
like me
Sally

I think qfit.com has some free analyzers that consider most of the OP's inputs.

Quote: 98Clubs

I think qfit.com has some free analyzers that consider most of the OP's inputs.

like this one
http://www.qfit.com/CVRoRC.htm

It uses the Blackjack Attack formula too.

What will throw most people is the per 100 values.
so when we play a session of only 40, now what do we do and how accurate are the results?
I tried this a few years back and it was just easier and for smaller sessions more accurate to use the ev and sd for the bets you make in a session of play.
simple to understand IMO.

here is a small example of Risk of Ruin using ev and sd and what it means.
https://wizardofvegas.com/forum/questions-and-answers/math/10123-risk-of-ruin/
I think there are a few other threads that really are better

let's see if the OP wants to give some parameters to work on an example with.

Sally