risk of ruin question

[sagefr0g]

this is probably a naïve question, but i'm not young and easily confused.
considering the equation for risk of ruin:
ROR = ((1-(ev/std))/(1+(ev/std)))^(bank/std)
if :
bank <= ev
&
ev > std
&
std = bank
does that mean that there is essentially no risk of ruin?
is the equation valid for such circumstances? one gets a negative value for ROR??

edit: sorry incorrectly worded original question, have hopefully corrected it.

 

[DSchles]

this is probably a naïve question, but i'm not young and easily confused.
considering the equation for risk of ruin:
ROR = ((1-(ev/std))/(1+(ev/std)))^(bank/std)
if :
bank <= ev
&
ev > std
&
std = bank
does that mean that there is essentially no risk of ruin?
is the equation valid for such circumstances? one gets a negative value for ROR??

edit: sorry incorrectly worded original question, have hopefully corrected it.

The equation is for per-hand values or per-hour values. if this is blackjack, the bank can't be less than the expectation, nor can the e.v. be greater than the s.d. Something is wrong.

Don

 

[sagefr0g]

The equation is for per-hand values or per-hour values. if this is blackjack, the bank can't be less than the expectation, nor can the e.v. be greater than the s.d. Something is wrong.

Don

yes sir that's correct. it's not for the game of blackjack, but for a game on a play by play basis (similar in nature to per-hand values, I believe).

edit: hmm, perhaps you've pointed me in the right direction. for the game in question, the std is indeed greater than the ev on a play by play basis. but over time (similar to hourly) the std is less than the ev. the equation should still be able to be used for the latter instance, no? and one could set the bank equal to the std (just for computational purposes), right? end edit
further edit: hmm, but then the avg bet would be a wee bit larger than the bank, lol end edit

 

[DSchles]

yes sir that's correct. it's not for the game of blackjack, but for a game on a play by play basis (similar in nature to per-hand values, I believe).

edit: hmm, perhaps you've pointed me in the right direction. for the game in question, the std is indeed greater than the ev on a play by play basis. but over time (similar to hourly) the std is less than the ev. the equation should still be able to be used for the latter instance, no? and one could set the bank equal to the std (just for computational purposes), right? end edit
further edit: hmm, but then the avg bet would be a wee bit larger than the bank, lol end edit

Use the equation on the page of BJA3 following the one on which this formula is found. Give me the numbers.

Don

 

[sagefr0g]

Use the equation on the page of BJA3 following the one on which this formula is found. Give me the numbers.

Don

thank you sir, I hope I didn't mess this up, kinda late night here.

edit: above is on a over time basis for std and ev.
on a play by play basis the numbers are:
ev = 10.03
std = 30.72
end edit.

 

[sagefr0g]

Use the equation on the page of BJA3 following the one on which this formula is found. Give me the numbers.

Don

ok, lemme try this again, late night excuse, no excuse, lol. but what a difference putting parenthesis in the wrong spot makes in excel. my result for the equation ROR = e^-2EV*bank/std^2 was incorrect in my post above. I believe it's now correct below:

still wondering why the problem with the
ROR = ((1-(ev/std))/(1+(ev/std)))^(bank/std) result.
shouldn't the two results agree?

 

[DSchles]

ok, lemme try this again, late night excuse, no excuse, lol. but what a difference putting parenthesis in the wrong spot makes in excel. my result for the equation ROR = e^-2EV*bank/std^2 was incorrect in my post above. I believe it's now correct below:


View attachment 9051

still wondering why the problem with the
ROR = ((1-(ev/std))/(1+(ev/std)))^(bank/std) result.
shouldn't the two results agree?

From where do you get your three values? What time period do they represent? They need to be the basic units. For example, it makes little sense to me that you have a bank of 194 units but an e.v. of 401. The time frame makes no sense to me.

Don

 

[sagefr0g]

From where do you get your three values?

unfortunately, from a mish mash of admittedly convoluted data over a period of about eleven years. but, it's the best source I have as the game doesn't have a useful simulator that I've been able to find. so anyway, from the data I believe I came up with a 'fairly reliable' value for the advantage of the game. using the value for the advantage and the slope of the data I worked out a sort of monte carlo analysis. it comes up with avg. # of plays, average bet, expected value and standard deviation. where the bank value came from, i'll explain below.

What time period do they represent?

eight hours on average for which these particular numbers represent 40 plays. (in a sense similar I believe to how one might figure 100 hands/hour for blackjack, sorta thing).

They need to be the basic units. For example, it makes little sense to me that you have a bank of 194 units but an e.v. of 401. The time frame makes no sense to me.

Don

I sort of think i'm dealing with basic units, not sure about that though. the ev of 401 is what the monte carlo came up with for the 40 plays, or eight hours. but, I purposely set the bank at 194, just for the purpose of matching the value of 194 for the standard deviation derived from the monte carlo. reason being, (which harkens back to my original question, I wanted to see what value one would get for risk of ruin in such an instance as well as the original parameters that I listed in the original question.

edit: thank you again for considering my question. end edit

 

[DSchles]

unfortunately, from a mish mash of admittedly convoluted data over a period of about eleven years. but, it's the best source I have as the game doesn't have a useful simulator that I've been able to find. so anyway, from the data I believe I came up with a 'fairly reliable' value for the advantage of the game. using the value for the advantage and the slope of the data I worked out a sort of monte carlo analysis. it comes up with avg. # of plays, average bet, expected value and standard deviation. where the bank value came from, i'll explain below.

eight hours on average for which these particular numbers represent 40 plays. (in a sense similar I believe to how one might figure 100 hands/hour for blackjack, sorta thing).

I sort of think i'm dealing with basic units, not sure about that though. the ev of 401 is what the monte carlo came up with for the 40 plays, or eight hours. but, I purposely set the bank at 194, just for the purpose of matching the value of 194 for the standard deviation derived from the monte carlo. reason being, (which harkens back to my original question, I wanted to see what value one would get for risk of ruin in such an instance as well as the original parameters that I listed in the original question.

edit: thank you again for considering my question. end edit

There is a different formula for calculating a TRIP ROR as opposed to ultimate risk of ruin. Do you understand the problem? Suppose I asked you to divide your numbers in such a way that, now, they would represent a single hour's worth of play. Your e.v. would be 1/8. Your s.d. would be (1/8)^0.5 = 0.35 of s.d. But, your bank would still be 194 units!

So, we need to get the numbers straight before we do a ROR calculation.

Don

 

[sagefr0g]

There is a different formula for calculating a TRIP ROR as opposed to ultimate risk of ruin. Do you understand the problem? Suppose I asked you to divide your numbers in such a way that, now, they would represent a single hour's worth of play. Your e.v. would be 1/8. Your s.d. would be (1/8)^0.5 = 0.35 of s.d. But, your bank would still be 194 units!

So, we need to get the numbers straight before we do a ROR calculation.

Don

hmmm, just skimmed around a spreadsheet (based on the work in your book with respect to ultimate ror and trip ror) given to me by a friend, and then a brief skim of page 132 of BJA, with respect to the matter of trip ror.
that enlightened me as to how lost in deep murky waters I likely am with respect to my original question and subsequent statements in this thread.
so, I've got some reading to do, lol.
then perhaps I can again delve into the question regarding what if:
if :
bank <= ev
&
ev > std
&
std = bank
sorta thing.

perhaps it's not even a legit question. certainly it's not unless one can like you say, get the numbers straight.
again thank you for your time and consideration.

 

[DSchles]

hmmm, just skimmed around a spreadsheet (based on the work in your book with respect to ultimate ror and trip ror) given to me by a friend, and then a brief skim of page 132 of BJA, with respect to the matter of trip ror.
that enlightened me as to how lost in deep murky waters I likely am with respect to my original question and subsequent statements in this thread.
so, I've got some reading to do, lol.
then perhaps I can again delve into the question regarding what if:
if :
bank <= ev
&
ev > std
&
std = bank
sorta thing.

perhaps it's not even a legit question. certainly it's not unless one can like you say, get the numbers straight.
again thank you for your time and consideration.

Will be happy to help. All of the calculators for trip ROR, goals, etc., are on Norm's site, as well.

Don

 

[sagefr0g]

Will be happy to help. All of the calculators for trip ROR, goals, etc., are on Norm's site, as well.

Don

that's much appreciated sir. perhaps if I get my numbers straight, I can make some sense of them with the calculators on Norm's site, and then perhaps I could ask you if it looks as if my numbers were in fact straight.

one last question, if I may, (and don't worry, I wont jump to conclusions until I get my numbers straight).
supposing one legitimately had a negative risk of ruin, for example say -34%, how would one interpret the meaning of a negative risk of ruin?

 

[gronbog]

Risk of Ruin can not be negative. It's a probability. If you have a "can't lose" situation, then your RoR is zero. Similarly, the highest it can be is 100%.

 

[sagefr0g]

Risk of Ruin can not be negative. It's a probability. If you have a "can't lose" situation, then your RoR is zero. Similarly, the highest it can be is 100%.

so that would imply that the parameters
if :
bank <= ev
&
ev > std
&
std = bank
can not exist.
right?

edit: I removed the examples previously in this edit as an error was present
end edit

 

[gronbog]

Those conditions are consistent, since you have ev >= bank, ev > std, and std = bank.

The second formula can produce a negative result with ev > std. Formulas frequently are quoted with boundary conditions. Perhaps ev <= std is one of the conditions for the validity of the formula. I personally have never seen a situation where ev > std.

 

[sagefr0g]

Those conditions are consistent, since you have ev >= bank, ev > std, and std = bank.

The second formula can produce a negative result with ev > std. Formulas frequently are quoted with boundary conditions. Perhaps ev <= std is one of the conditions for the validity of the formula. I personally have never seen a situation where ev > std.

I also wondered about the idea that there may be boundary conditions. it's been forever since I read over the derivation for the ROR formula, but when I did it was way beyond my complete understanding. I do know that when I tried some really large numbers for ev>std on Norm's calculators that I received an out of range statement instead of a result, but it was for a huge number, so I don't know if that was the problem or if it was a boundary condition, I did receive negative numbers for some inputs.
far as there being a situation where ev>std, I don't really know if it's a legit thing either. I just have my 'hokey' monte carlo set up that's claiming such results, working off of data for which the precision is questionable.
well at any rate, Don's influence has definitely shown me that I need to further read and better understand the situation, so that I can be sure I've got my numbers straight or not.

 

[sagefr0g]

........
I personally have never seen a situation where ev > std.

my monte carlo sort of set up gives me an ev = $401.11 and a std. = $194.29 with respect to a 'typical' session consisting of 40 plays, so on a session basis ev>std. but per play it's ev =$10.03 and std = $30.72, so on a per play basis ev<std.
does that have a "fishy smell", far as the way ev>std. for circa 40 plays, but ev<std. on a per play basis? edit: hmm, maybe not so fishy, just been reading pg 133 BJA where it states, ....if the trip length gets very large, our e.v. will increase much faster than our s.d. .....end edit

 

[DSchles]

my monte carlo sort of set up gives me an ev = $401.11 and a std. = $194.29 with respect to a 'typical' session consisting of 40 plays, so on a session basis ev>std. but per play it's ev =$10.03 and std = $30.72, so on a per play basis ev<std.
does that have a "fishy smell", far as the way ev>std. for circa 40 plays, but ev<std. on a per play basis? edit: hmm, maybe not so fishy, just been reading pg 133 BJA where it states, ....if the trip length gets very large, our e.v. will increase much faster than our s.d. .....end edit

EV is a linear function. The e.v. for 100 hours is 100 times the e.v. for one hour. SD is a square root function. The s.d. for 100 hours is 10 times the s.d. for one hour. You start out with e.v. < s.d. for any typical one play. Eventually, since e.v. increases linearly and s.d. by square root, e.v. catches up to s.d. and then surpasses it. For your ROR calculations, you want the per-play values, not the long run values.

We call the number of plays/hands necessary for e.v. to catch up to s.d. the N0 (N-zero).

Don

 

[sagefr0g]

EV is a linear function. The e.v. for 100 hours is 100 times the e.v. for one hour. SD is a square root function. The s.d. for 100 hours is 10 times the s.d. for one hour. You start out with e.v. < s.d. for any typical one play. Eventually, since e.v. increases linearly and s.d. by square root, e.v. catches up to s.d. and then surpasses it. For your ROR calculations, you want the per-play values, not the long run values.

We call the number of plays/hands necessary for e.v. to catch up to s.d. the N0 (N-zero).

Don

i'm going to do that ror calculation on a per-play value basis, as you say, sir. thank you again.

edit: as an aside with respect to the two equations:
ROR = ((1-(ev/std))/(1+(ev/std)))^(bank/std)
and
ROR ~ e^(-2EV*bank/std^2)
I assume that they should give equal results sometimes, but if not equal then very close results, correct?
end edit.

edit: I like your explanation above with the reference to N0.
it would be really neat if there was a formula that gave the # plays necessary for results to catch up with e.v.
end edit

 

[gronbog]

For per-play values I have found that they yield the same result to within several decimal places.