Suggestions on starting bankroll for each game.

Hi- Long time reader of the wizard's sites- first time poster.

I was wondering if it was possible on each game to list a couple estimations of suggested bankrolls to start with in order to consider playing a game for a length of time or with certain probable expected returns.

Example: To play 3-card poker for 1 hour with an expected house edge of 2.5% and a table minimum of $10 per bet- if also playing pair plus- you could expect to need $x to play for 1 hour.

Im my mind I would sit and think if I was playing 3-card poker and wanted to play a while Id consider the table minimum and the number of bets I have to make .. for example with three card its min. $10 but ante+play+bonus all together would come up to $25/$30. and Ive always taken 20 times that minimum bet to be my starting point (in this case $500). Dont ask me why, Ive just always taken 20x minimum bet.

Another example would be bonsm hold'em- 5 units needed to cover all spaces x table min of $10 bets= $50x20= $1,000 as a good guage of where to start if I was to sit there for a long time.

I know my numbers sound way over the expected need and thats why Im asking- maybe this could be added onto each games page? ... Its just a quick guage I use when I sit at the tables. I could not find anything on suggested starting bank rolls .. and to make it easy for the readers to calculate maybe you coudl mention it in terms of units of minimum bet so they can convert it to any table of that type of of game as needed.

You need to decide what risk of ruin % you can tolerate to determine the starting bankroll requirements. If you want a 0% risk of ruin in one hour, just figure out how much you could possibly lose if you lost every hand (given your speed of play), and that's your max bankroll requirement.

So its as easy as figuring $30x50 hands = $1,500 for 0% chance of ruin in those 50 hands.

id imagine you could devolope an idea for a chance of ruin to be in proportion to the expected probability of return. So it would/could change based on the house edge for each game you wanted to play... or I coudl be sounding nuts to want to think of it to that extent.

If I think of a minimum $10 table I usually see people sit down with between $100 and $500 to start themselves- which seems like a low bankroll when you think of it in terms of hands per hour and risk of ruin- so it brings up the question as to what is a typicaly used or natural RoR that is used... 10% 25% 50%?

Quote: dwheatley

You need to decide what risk of ruin % you can tolerate to determine the starting bankroll requirements. If you want a 0% risk of ruin in one hour, just figure out how much you could possibly lose if you lost every hand (given your speed of play), and that's your max bankroll requirement.

The essential factors you need to consider are:

the rate of play, i.e. how many bets per hour
the minimum bet you can make
the house edge and standard deviation of the bet or bets you are going to make (most important)
the "risk of ruin" you will accept

For example, take craps, making $5 passline bets and taking double odds. The average bet will be $11.67, since odds are taken only 2/3 of the time, the ev per bet is -.0707 and the standard deviation per bet is $14.29.

How many rolls per hour? Of course, this will vary considerably, depending on how many players at the table, what kind of bets are being made, etc. Let's assume 100 rolls/hour. Passline bets are resolved, on average, in 3.375 rolls, so we would expect to resolve about 30 of these bets. That means the ev is 30 * -.0707 = -$2.21 and the standard deviation is $14.29 * sqrt 30 = $78.27.

Now, if your luck is such that you end up one standard deviation worse than the ev, that would be losing about $80. How about two SD worse? That's about $160 down. The probability of being two standard deviations WORSE (one-tail test) than expectation is 2.28%, or odds of about 43 to 1 against. So, if you started with $160, you'd have an excellent chance of lasting an hour. BTW, the same probability applies to ending up two SD BETTER than expectation, which would be -2.21 + (2 * 78.27) = + about $150.

This is pretty detailed, but the point is that the most important factor is the volatility of the bets you are going to be making, a factor poorly covered in most gambling books.
Cheers,
Alan Shank

First of all, don't play 3-card poker! (If that was just a hypothetical, I apologize. But at most places it is a HUGE money-suck). Occasionally it's fun, but I wouldn't make it a bread-and-butter game.
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Alan has the right idea. His example was for craps, but this is the best method to come at any game. Determine the factors that he numerates, that you can get an exact calculation of how big your bankroll needs to be for the amount of risk you are willing to take on.