Inverse of ROR

[Cardguy]

Not sure I'm asking this correctly, but... Is there a way to calculate the inverse of ROR? I want to know the amount of money that corresponds to a ROR of 25% (or 50% or whatever I choose) given a particular game I'm playing. For example, let's say I'm playing 8D, S17, DAS, LS 75% pen spreading from $10-150 with HiLo and full indices (for simplicity let's assume all play). If I play forever, I know I'll win money. I'd like to know that there's a 25% chance that I'll go X amount in the hole and a 50% chance I'll go Y in the hole before things turn around. The way I'm currently trying to get this info is by plugging different BR amounts into CVCX until I see a ROR that equals the percentage I'm interested in. Using this method, it looks like a 50% ROR corresponds to a BR of $2,937 with the above rules. A 25% ROR corresponds to a BR of $5,874.
I take this to mean that I have almost a 50% chance of losing 3K and a 25% of losing 6k before my "luck" turns. Am I looking at this correctly? Is there a calculator that does this?
Thanks!

[Bodarc]

Set your bankroll to the amount it actually is. Set your risk of ruin to the desired amount. Input your expected hours of play in the box down from your bankroll. Then look at the top right hand corner under "Expected Results" and use the spinners to set your probability. This will show that probability of your results, loss and gain.

[DSchles]

Use this: https://card-counting.com/blackjack-calculator-c2.htm

And all the calculators, based on BJA3, can be found at this site at: https://www.blackjacktheforum.com/re...hp?do=calcpage

Don

[ZenMaster_Flash]

Cardguy:

You said --- "I take this to mean that I have almost a 50% chance of losing 3K and a 25% of losing 6k before my "luck" turns."

You 'take that' incorrectly. It means that if you play (perfectly) until you either double your bankroll OR go broke, those amounts give you a ONE Standard Deviation chance of you hitting the former before the latter occurs. One or the other must happen given sufficient time. You mentioned a 50% Risk of Ruin. You can get very close to that with one hand bet on the Banker at Baccarat. We are not gamblers. If we were that would sound pretty good. Expert / Professional BJ players tend to look for a R.O.R. as low as 1% or 5%. "Pure Kelly Betting" (hardly plausible in BJ) holds a 13.5% R O R.

From how you worded your question -
you may think that if you have a sufficient bankroll "your luck will (always) turn."
That is false. You can play perfectly and still go broke.

[DSchles]

You wrote: "It means that if you play (perfectly) until you either double your bankroll OR go broke, those amounts give you a ONE Standard Deviation chance of you hitting the former before the latter occurs."

I'm sorry, but neither notion is correct. The risk of ruin formulas have nothing to do with doubling your bankroll. They aren't a part of any of the formulas. Nor is one standard deviation.

Don

[RS]

You wrote: "It means that if you play (perfectly) until you either double your bankroll OR go broke, those amounts give you a ONE Standard Deviation chance of you hitting the former before the latter occurs."

I'm sorry, but neither notion is correct. The risk of ruin formulas have nothing to do with doubling your bankroll. They aren't a part of any of the formulas. Nor is one standard deviation.

Don

The "one standard deviation chance" threw me off...still confused as to what that means.

But I'd always been told or under the impression ROR is "% to lose entire BR before doubling it". If that's not the case -- what does that % number even mean? Or am I mis-reading something, here?

[Three]

But I'd always been told or under the impression ROR is "% to lose entire BR before doubling it". If that's not the case -- what does that % number even mean? Or am I mis-reading something, here?

RoR: The chance that you will go bust before winning all the money in the world using the specific plan entered without deviation or resizing for the BR entered. Of course as your BR changes a new RoR can be calculated from that point. This is why RoR tends to catch you early. Your BR should be growing which would decrease your current RoR. If your BR ever doubles the odds that you are in the original RoR percentage has been reduced to almost nothing if RoR were to be calculated for that BR.

For example if you were playing full kelly and doubled your BR the original RoR was 13.5% but a new calculation with the same parameters and new BR would give about a 1 to 2% RoR. Imagine if you played with a reasonable RoR to start with. Also resizing is likely at that point if you were playing at an acceptable RoR to start with and aren't up against an upper boundary like table limit or casino tolerance threshold. Hence the doubling approximation.

[Bodarc]

The "one standard deviation chance" threw me off...still confused as to what that means.

Maybe confusing 1 SD as it relates to N0 with RoR?

[DSchles]

Some clarifications for everyone:

ROR, in its purest sense, means, quite simply, the risk of losing your entire bankroll, expressed as a percentage, or probability. There are NO other constraints. Period. As soon as you begin to impose other constraints, such as "before doubling your bank," or "with constant resizing," or reaching a particular goal, with or without a time constraint, then you are invoking all the other formulas in BJA3 and the calculators that Norm has here for each of them. But, again, as I stated in the book, and as Tthree summarized above, ROR means either you play forever and eventually win all the money in the world, without going broke, or you tap out. Period.

Note that, for "pure" Kelly wagering, in theory, if there were no table limits and chips were infinite divisible, you would be resizing your wagers after every outcome, and your risk of ruin is, theoretically, zero. So, we're NOT interested in expressing that concept.

Finally, the notion of standard deviation does not, in any way, apply to ROR calculations. As mentioned above, it does apply to SCORE and N0, which are reciprocals, once a linear scalar is applied.

More questions? Just ask!

Don

[Cougfan]

I'm getting slightly different results using CVCX. Mine are exactly hitting your rounded numbers 25% chance of losing $6K and a 50% chance of losing $3K. I assumed RSA, so maybe that is the difference.

You can also see this same info using the Risk Widget (second one down on the far right if you have the default view). Just change the Trip Bankroll and look at the percentage risk of trip ruin for an infinite win goal and an infinitely long trip (second row in that widget). I believe that BJA3 also includes a formula showing the likelihood that your BR will drop in half at some point.

Alot of the folks on this site are going to tell you to just calculate your full ROR and not worry about it, but personally I think there is some real value to this type of analysis in helping you to think more fully about the game and your likely results.

Another fun exercise is to look at this activity as an investment opportunity, and consider your likelihood of winning $X or losing $Y over a period of 6 months play. This data can be obtained using the Goals and Risk widgets and can allow you to compare the likely returns from playing BJ versus other possible investments of your time and money (stock market, real estate, etc).

[Three]

Alot of the folks on this site are going to tell you to just calculate your full ROR and not worry about it, but personally I think there is some real value to this type of analysis in helping you to think more fully about the game and your likely results.

Yes if you are going to be resizing at some point after BR shrinks enough the odds of hitting that point is quite relevant when planning your attack on the game. Just pulling arbitrary amounts of partial BR failure are less relevant.

[Cardguy]

Just to clarify and confirm that what I thought/stated previously is correct.
If I artificially set my bankroll to $3,000 in one of the calculators and I find that my risk of ruin is 50% for the game I'm playing for that bankroll, this means the following - there is a 50% chance that at some point in time during my infinitely long "walk" I will hit -$3,000, correct?
Here's why I ask. I've only been playing for a short time (about 750 hands so far) and I'm currently down about $1,400. My actual BR is 20K. Knowing that when I start this walk from zero, my chance of getting to -$3,000 despite perfect play is 50%, makes it a lot easier to stomach my current losses.

[Cougfan]

Just to clarify and confirm that what I thought/stated previously is correct.
If I artificially set my bankroll to $3,000 in one of the calculators and I find that my risk of ruin is 50% for the game I'm playing for that bankroll, this means the following - there is a 50% chance that at some point in time during my infinitely long "walk" I will hit -$3,000, correct?
Here's why I ask. I've only been playing for a short time (about 750 hands so far) and I'm currently down about $1,400. My actual BR is 20K. Knowing that when I start this walk from zero, my chance of getting to -$3,000 despite perfect play is 50%, makes it a lot easier to stomach my current losses.

Yes, at the start of your play, the odds that you would ever be down $3,000 were 50/50. However, the odds right now that your cumulative losses will hit $3,000 or more are much greater than 50%. This is because we now know that you have already had some negative variance that cannot be changed. To use the coin flipping analogy, the odds of flipping two straight tails assuming a fair coin are 25% (50% x 50%). But if you were bemoaning your bad luck and telling me that you had already flipped a tails, then it would be absolutely incorrect for me to tell you not to worry about it because your odds of flipping a second straight tails was only 25%. At that point, you would have a 50% chance of flipping tails.

This assumes that you are actually using a fair coin. The BJ equivalent concept is that you are playing your system perfectly (or with the same error rate you have simmed), that you are not being cheated and that you are not taking any expenses or tips out of your winning sessions.

Also, if your actual BR is really $20K, that means you are willing to lose $20K at this game. If a $1,400 loss is bothering you even a little bit, then your real risk tolerance (aka BR) is probably a lot less than $20K.