RoR/BR question

I've been thinking about how much bankroll plays a part in risk of ruin. I see that the risk of winning and risk of losing are also included in the equation so I could ask this in several different ways, but:

How can one properly calculate the RoR of a session if their bankroll is fluctuating the entire time? What happens when they become up or down 20-30 units? Wouldn't this mean that the RoR is significantly different from when it was first calculated at the beginning of the session?

sorry if this is a novice question, but this has been puzzling me recently.

I think you should look at this way Harvey..

If your bankroll X is changing by huge percentages (i.e 80% or more) because of a 20-30 unit loss.. you are way under-rolled for the game. Risk of Ruin is the chance of going broke determined by a bankroll to play a particular game using a given amount as the smallest UNIT...

For EXAMPLE:
you have a $10,000 bankroll and you plan to play a $5 blackjack min game red chip game. The number of UNITs you have is 2000 ($10000 bankroll/$5 min bet)

Given this blackjack game you make an educated guess (via Simulations or known examples) that you expect to win about 4.5 bets / hour varying your bet between $5-$60. But you have to take into consideration the luck factor (we call it variance). This is determined by STANDARD DEVIATION (STDev). STDev can indicate what are the reasonable "swings" are (positive or negative). This number can be found via simulations and we find that for this game we have a STDev of about +-45 units/hour (+-$225/hour). As I've been told two times STDev (+-$550/hour in this case) isn't normal but can happen.

We take the formula for RoR and if we have a $10k bankroll we get a less than 0.01% chance of going broke playing this game.

Now let's say your bank roll is only $200 (40 units) and you try to play this game. The RoR for this situation would be 83.66%

You really shouldn't be playing your FULL bankroll at the time.. you should commit a portion of your bankroll at one time for each session then recalculate your RoR after the session for your whole bankroll and adjust accordingly.

Don't take shots unless you have a plan

Thanks hardNock
You gave me a better perspective on RoR than what I had before.
0.01% must be really good

a good rule of thumb to calculate standard deviation for any session is

Average Bet x (SQRT of Hands played) x 1.1

Assume a bet spread of 10-100 over a time span of 2 hours (and play 50 hands an hour)
lets just assume that most of your play will be between TC 1 and TC 2 which is something like a 25 dollar bet and house edge (due to Advantage play) of about 0%

your standard deviation for the session will be

25x10x1.1 = 275 (or 27.5 units)

so if you think about bankroll and long-run ROR, all you have to do is approximate the "infinite session". lets assume that you will play 500 hours of blackjack in your lifetime, at 50 hands per hour.

you will need an approximate bankroll of
25x 158. x 1.1 = $4350 (or 435 units) IN ORDER TO WITHSTAND ONE STANDARD DEVIATION over that entire "session"

the normal distribution graph shows that 68% of the time (in a completely even game), your profits or losses will fall within one standard deviation from the mean (the mean is zero, because we are playing a fully 0% ev game).
This means that 16% of the time, you will bust out if you only have a bankroll of 435 units. This would equate to a 16% Risk of ruin.

A safer BR size would be 1000 units of your minimum bet in order to withstand 2+ standard deviations of play across this lifetime of 500 hands. why? because 2+/- standard deviations in the normal distribution graph account for 95% of all scenarios. This equates to a a 2.5% risk of ruin.Why 2.5% and not 5%? because standard deviation can be really bad or really good! in calculating risk of ruin, we only worry about the really bad variance that can hurt us. Therefore if 100 people play exactly the same way as described above, about 2.5 of them on average will go bust with a 1000 unit bankroll.

Lastly please note that this is assuming an even 1-1 game with no house edge.
This math really puts into perspective the value of wonging out during negative expectation shoes and only playing favorable counts which give the player long-term advantage.

If we adjust the EV of this game to say, +1% (the normal edge than a poor advantage player can squeak out)
then the MEAN of that normal distribution graph is nonzero. Specifically it will be (%Edge x dollars wagered)

in our 500-hour lifetime scenario, average bet=25 and hands played = 25,000 so lifetime dollars wagered would be 625,000. A 1% player edge would mean that we can expect a profit of $6,250 over this lifetime, however due to normal variance across the 500 hours, (i.e. $4350 that we calculated earlier), 68% of the time we could end up anywhere between a profit of $1900 or a profit of $10,600.

Wow Midwestern, it makes me take stock of why I'm doing this with a small BR and solidifies in my mind that its for fun. and the chalange.

yeah. card counting is definitely a grind. the math (given my assumptions) works out to profit of 1.25 units per hour, which is not bad for a hobby, but certainly not enough to make someone really rich unless your base unit is large and you can afford an effective spread.
the math really makes you appreciate wonging in and out though. if you did a "play all" scenario, can you imagine how much time & money you'd waste in negative expecation counts waiting for a high count?
it also makes you appreciate different forms of cover that contribute to longevity as an AP. without longevity you cannot make any money. Mad props to the pros on this site that have made $$$ over a long span of time. It's not an easy business.
my friend from MIT basically said that after 2003 anyone who used to focus on blackjack then focused on online texas holdem.
If skilled player played correctly at the right money level, his advantage in poker far outreached the advantage that he could have counting a single deck in blackjack.
Take this with the ability to play 6, 8, or 12 tables at once and you've got a money factory. If only i had figured this out earlier!