Risk of Ruin Calculation

As shown previously, the RoR for a given bankroll is exactly double the probability of finishing the session at a loss, provided that the wager follows the standard normal distribution...an example would be a fair coin flip that pays even money. This hasn't actually been proven so it's been named "the Ace2 conjecture".

After crunching some more numbers, it appears that the conjecture is actually true for any wager with no house edge...an example would be betting on a number of a single die that pays 5:1 on a win. I'm quite surprised it works for this scenario since I assumed the reason you double the probability of finishing the session at a loss was related to the symmetry of the standard normal distribution.

The conjecture does not work for any bet with a house edge, but it should be a close approximation for very low-edge bets such as passline with full odds or BJ with perfect strategy (edge under half a percent).

I believe there is a way to calculate the RoR for a bet with an edge but still searching for the method. Since the expectation is for the bankroll to continuously tend down by the wager*edge%, I assume calculus will be required

Interesting. Thanks for cranking the math.

Quote: Ace2

As shown previously, the RoR for a given bankroll is exactly double the probability of finishing the session at a loss, provided that the wager follows the standard normal distribution...an example would be a fair coin flip that pays even money. This hasn't actually been proven so it's been named "the Ace2 conjecture".

After crunching some more numbers, it appears that the conjecture is actually true for any wager with no house edge...an example would be betting on a number of a single die that pays 5:1 on a win. I'm quite surprised it works for this scenario since I assumed the reason you double the probability of finishing the session at a loss was related to the symmetry of the standard normal distribution.

The conjecture does not work for any bet with a house edge, but it should be a close approximation for very low-edge bets such as passline with full odds or BJ with perfect strategy (edge under half a percent).

I believe there is a way to calculate the RoR for a bet with an edge but still searching for the method. Since the expectation is for the bankroll to continuously tend down by the wager*edge%, I assume calculus will be required
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Agreed. As I discussed in this post : https://wizardofvegas.com/forum/questions-and-answers/math/34502-easy-math-puzzles/56/#post847780

mean= 0, variance = X

The question here is how to prove that the risk of bankrupt is DOUBLE* the risk of loss MORE THAN certain units ?

My guess is that when mean=0, and you allow to loss more than(for example, you borrow from your friends) your bankroll before the N rounds, you have 50%* of the chance to recover(partly or fully)from your losses and not bankrupt after end of N rounds. N must be a very large number.

* This explains that why the ROR is DOUBLE compare to player with unlimited bankroll.

Don Schlesinger described this Risk of Ruin phenomenon, which he named the "premature bumping into the barrier syndrome", in his "The Gospel According to Don" column in the March 1994 issue of Blackjack Forum, illustrating the point with a memorable analogy of his falling into the Grand Canyon as a result of a disastrous (but predictable) series of wagers on a coin flipping game.

If you don't happen to have that issue on your nightstand, he reproduced the article in his seminal work Blackjack Attack 3, in "Chapter 8: Risk of Ruin", pages 122-125.

Hope this helps!

Dog Hand

Quote: Ace2

As shown previously, the RoR for a given bankroll is exactly double the probability of finishing the session at a loss, provided that the wager follows the standard normal distribution...an example would be a fair coin flip that pays even money. This hasn't actually been proven so it's been named "the Ace2 conjecture".

After crunching some more numbers, it appears that the conjecture is actually true for any wager with no house edge...an example would be betting on a number of a single die that pays 5:1 on a win. I'm quite surprised it works for this scenario since I assumed the reason you double the probability of finishing the session at a loss was related to the symmetry of the standard normal distribution.

The conjecture does not work for any bet with a house edge, but it should be a close approximation for very low-edge bets such as passline with full odds or BJ with perfect strategy (edge under half a percent).

I believe there is a way to calculate the RoR for a bet with an edge but still searching for the method. Since the expectation is for the bankroll to continuously tend down by the wager*edge%, I assume calculus will be required
link to original post

The ROR hypothesis along with the folly of the "Ace2 Conjecture" basically infers that people who gamble to whatever their end game might be, are mindless idiots who have no self-control or discipline. There is a very small number of those addicted that would fall into such a category, but the vast majority of patrons of casinos gamble as a diversion or recreation.

The testimony of an individual that gambled away his mortage money is sad but like driving a car while stupid and causing an accident, can only fall on the shoulders of the perpetrator. Analysis is probably a waste of time and energy.

tuttigym

Quote: tuttigym

The ROR hypothesis along with the folly of the "Ace2 Conjecture" basically infers that people who gamble to whatever their end game might be, are mindless idiots who have no self-control or discipline. There is a very small number of those addicted that would fall into such a category, but the vast majority of patrons of casinos gamble as a diversion or recreation.

The testimony of an individual that gambled away his mortage money is sad but like driving a car while stupid and causing an accident, can only fall on the shoulders of the perpetrator. Analysis is probably a waste of time and energy.

tuttigym
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If you keep playing long enough, you will lose all your money.
I doubt anybody is disagreeing with that.

As I understand it, the Ace2 Conjecture attempts to address the chances of going broke when you have a number of bet units of money, and wish to play more than that number of games.

If it ever gets figured out, it should be solvable for either "I have 40 money, how many times can I probably play?" or "I want to play 127 times, how many money do I probably need?"

That sort of information can be useful to some people.

Quote: Ace2

You mentioned : ...... probability of finishing the session at a loss......
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I think it should be "probability of finishing the session at a loss MORE THAN a given bankroll".

For example, mean = 0, Var = 1, N = 10000, bankroll = 52.44 units

a) Probability of finishing the session at a loss = P( -52.44 < X < 0 ) = P(Z<0) - P(Z <-0.5244) = 0.5 - 0.3 = 0.2 = 20%
b) Probability of finishing the session at a loss MORE THAN bankroll = P( X < -52.44 ) = P(Z <-0.5244) = 0.3 = 30%

ROR for a given bankroll of 52.44 units = 2 x 30% = 60%, NOT 2 x 20% = 40%.

I am not sure, what do you think ?

Quote: tuttigym

The ROR hypothesis along with the folly of the "Ace2 Conjecture" basically infers that people who gamble to whatever their end game might be, are mindless idiots who have no self-control or discipline. There is a very small number of those addicted that would fall into such a category, but the vast majority of patrons of casinos gamble as a diversion or recreation.

The testimony of an individual that gambled away his mortage money is sad but like driving a car while stupid and causing an accident, can only fall on the shoulders of the perpetrator. Analysis is probably a waste of time and energy.

tuttigym
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RoR is a common metric used in investing and gambling...it doesn't refer to addiction or losing your house. Using several inputs, it measures the risk of losing a specified amount capital/bankroll and is probably the best tool for calculating the bankroll you'll need.

But, as usual, the self-proclaimed "deer-eyed, seasoned citizen" tuttigym just doesn't get it. What's worse, he dilutes a useful thread with his senseless ramblings.

Quote: Ace2

Quote: tuttigym

The ROR hypothesis along with the folly of the "Ace2 Conjecture" basically infers that people who gamble to whatever their end game might be, are mindless idiots who have no self-control or discipline. There is a very small number of those addicted that would fall into such a category, but the vast majority of patrons of casinos gamble as a diversion or recreation.

The testimony of an individual that gambled away his mortage money is sad but like driving a car while stupid and causing an accident, can only fall on the shoulders of the perpetrator. Analysis is probably a waste of time and energy.

tuttigym
link to original post

RoR is a common metric used in investing and gambling...it doesn't refer to addiction or losing your house. Using several inputs, it measures the risk of losing a specified amount capital/bankroll and is probably the best tool for calculating the bankroll you'll need.

But, as usual, the self-proclaimed "deer-eyed, seasoned citizen" tuttigym just doesn't get it. What's worse, he dilutes a useful thread with his senseless ramblings.
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The useless part of your "conjecture" as well as the RoR hypothesis and "math" is that you always seem to forget to mention that the wagers and methods remain identical throughout the exercise which shows that the player must be guilty of GWS*. (Gambling While Stupid)

Have you personally experienced a session of RoR?

tuttigym

Quote: tuttigym

[
Have you personally experienced a session of RoR?

tuttigym
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What does that even mean ?

Quote: tuttigym

Quote: Ace2

Quote: tuttigym

The ROR hypothesis along with the folly of the "Ace2 Conjecture" basically infers that people who gamble to whatever their end game might be, are mindless idiots who have no self-control or discipline. There is a very small number of those addicted that would fall into such a category, but the vast majority of patrons of casinos gamble as a diversion or recreation.

The testimony of an individual that gambled away his mortage money is sad but like driving a car while stupid and causing an accident, can only fall on the shoulders of the perpetrator. Analysis is probably a waste of time and energy.

tuttigym
link to original post

RoR is a common metric used in investing and gambling...it doesn't refer to addiction or losing your house. Using several inputs, it measures the risk of losing a specified amount capital/bankroll and is probably the best tool for calculating the bankroll you'll need.

But, as usual, the self-proclaimed "deer-eyed, seasoned citizen" tuttigym just doesn't get it. What's worse, he dilutes a useful thread with his senseless ramblings.
link to original post

The useless part of your "conjecture" as well as the RoR hypothesis and "math" is that you always seem to forget to mention that the wagers and methods remain identical throughout the exercise which shows that the player must be guilty of GWS*. (Gambling While Stupid)

Have you personally experienced a session of RoR?

tuttigym
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How long of a break do I need to take between dice rolls in order to book a session and quit while ahead? Is the key to have to have some sleep in between? Is a nap enough or does it have to be a new calendar day?

Is it enough to switch tables? Go to the bathroom? Sit out a shooter?

I need to understand this magical concept of a session as it seems the key to knowing what it means to quit ahead so I can be a winner.

Maybe after a meal?

Quote: unJon

How long of a break do I need to take between dice rolls in order to book a session and quit while ahead? Is the key to have to have some sleep in between? Is a nap enough or does it have to be a new calendar day?

Is it enough to switch tables? Go to the bathroom? Sit out a shooter?

I need to understand this magical concept of a session as it seems the key to knowing what it means to quit ahead so I can be a winner.
link to original post

After some very deep philosophical thinking, one could count the chips in their tray, and if that number exceeds their buy-in, color and leave. As the player, one gets to decide when and how much is enough. Simple concept: walking away ahead makes one a winner. Hope that clears it up for you.

tuttigym

Quote: unJon

How long of a break do I need to take between dice rolls in order to book a session and quit while ahead? Is the key to have to have some sleep in between? Is a nap enough or does it have to be a new calendar day?

Is it enough to switch tables? Go to the bathroom? Sit out a shooter?

I need to understand this magical concept of a session as it seems the key to knowing what it means to quit ahead so I can be a winner.
link to original post

After some very deep philosophical thinking, one could count the chips in their tray, and if that number exceeds their buy-in, color and leave. As the player, one gets to decide when and how much is enough. Simple concept: walking away ahead makes one a winner. Hope that clears it up for you.

tuttigym

Sorry for the unintentional duplication.

tuttigym

How does one decide when/if to return?

What if during one’s chip count, one determines that one’s stack does not in fact exceed one’s buy in? Is one allowed in your “system” to leave when down, or must one continue playing until ruin?

Is the deep philosophical thinking a requirement? Would meditation be acceptable? Have you written a book, and if so, where may I purchase said book?

Quote: camapl

How does one decide when/if to return?

What if during one’s chip count, one determines that one’s stack does not in fact exceed one’s buy in? Is one allowed in your “system” to leave when down, or must one continue playing until ruin?

Is the deep philosophical thinking a requirement? Would meditation be acceptable? Have you written a book, and if so, where may I purchase said book?
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Your question on returning after leaving when ahead infers either never or play on until broke. I guess you have no concept of choice or discipline.

For me, leaving when down some after a lengthy amount of play is prudent. Trying to recoup loses when one's play is stagnant, rarely works. So yes, my "system" allows me to leave when down, and that question infers you would probably stay until your bankroll is gone.

As far as "deep philosophical thinking" and "meditation," whatever floats your boat. Book? Yes. Can you purchase it? No, it would make you rich beyond your wildest dreams. I can't have that.

tuttigym

Quote: tuttigym

After some very deep philosophical thinking, one could count the chips in their tray, and if that number exceeds their buy-in, color and leave. As the player, one gets to decide when and how much is enough. Simple concept: walking away ahead makes one a winner. Hope that clears it up for you.

tuttigym
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When playing by the concept, what is your risk of ruin?

Quote: Ace2

Quote: tuttigym

After some very deep philosophical thinking, one could count the chips in their tray, and if that number exceeds their buy-in, color and leave. As the player, one gets to decide when and how much is enough. Simple concept: walking away ahead makes one a winner. Hope that clears it up for you.

tuttigym
link to original post

When playing by the concept, what is your risk of ruin?
link to original post

I do not play by the "concept," so there is no "risk of ruin." Both of those "philosophies" are foreign to me.

tuttigym

Quote: camapl

How does one decide when/if to return?

What if during one’s chip count, one determines that one’s stack does not in fact exceed one’s buy in? Is one allowed in your “system” to leave when down, or must one continue playing until ruin?

Is the deep philosophical thinking a requirement? Would meditation be acceptable? Have you written a book, and if so, where may I purchase said book?
link to original post

Your post seems highly critical, and that is okay. So, perhaps you could enlighten us:
1. Do you indulge in gaming?
2. What forms of gaming take up most of your time when patronizing a casino?
3. Do you have a "system"?
4. What limits do you set, if any, i.e., time, winnings, losses?
5. Do you leave when ahead?
6. How do you know?
7. Does your "system" allow you to leave when down?

Just try to see if I match up to your perceived expectations.

tuttigym

Quote: tuttigym

Your post seems highly critical, and that is okay. So, perhaps you could enlighten us:
1. Do you indulge in gaming?
2. What forms of gaming take up most of your time when patronizing a casino?
3. Do you have a "system"?
4. What limits do you set, if any, i.e., time, winnings, losses?
5. Do you leave when ahead?
6. How do you know?
7. Does your "system" allow you to leave when down?

Just try to see if I match up to your perceived expectations.

tuttigym
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Critical? Yes, but also an attempt at satire… (pot/kettle?)

Since you answered some of my questions, at least partly, I’ll indulge yours, lest we continue inferring incorrectly about one another.

Yes, I place wagers in casinos. It is my sole source of income. I only play when I have a mathematical edge (note the lack of quotation marks). For me, this includes primarily Video Poker and vulturing slots, with occasional Blackjack and keno plays (yes, live keno!). If it can be considered a system, I play when I have as large of an edge as possible, and I stop when the edge drops significantly (sometimes even when it’s still positive, as I usually have a better play elsewhere). As long as my bankroll hasn’t taken too big of a dent, wins/losses during a particular hour, day, week, play are irrelevant no matter what my psyche thinks of them. These things even out the next hour, day, week, play, etc. I have found the math to be reliable. I don’t merely leave or stop simply because I’m ahead or behind, but I do always know how much I gained or lost on each play. I keep track of what I put in and cash out, and I keep accurate records.

tuttigym, I find the majority of your posts to be well written. For someone whose posts tend to reject the math, and those who employ any skill in such, as vehemently as yours do, I am surprised that you would seek responses from me, of all people, in order to see how you match up.

I’ll leave you with a question, as I honestly can’t tell. Do your posts convey your true feelings, or are they merely an attempt to illicit a response? (Feel free to treat this as rhetorical…)

Quote: tuttigym

Being a disturbing force on forums and holding the "math" accountable.

tuttigym
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I guess that answers my question!

Quote: camapl

Quote: tuttigym

Your post seems highly critical, and that is okay. So, perhaps you could enlighten us:
1. Do you indulge in gaming?
2. What forms of gaming take up most of your time when patronizing a casino?
3. Do you have a "system"?
4. What limits do you set, if any, i.e., time, winnings, losses?
5. Do you leave when ahead?
6. How do you know?
7. Does your "system" allow you to leave when down?

Just try to see if I match up to your perceived expectations.

tuttigym
link to original post

Critical? Yes, but also an attempt at satire… (pot/kettle?)

Since you answered some of my questions, at least partly, I’ll indulge yours, lest we continue inferring incorrectly about one another.

Yes, I place wagers in casinos. It is my sole source of income. I only play when I have a mathematical edge (note the lack of quotation marks). For me, this includes primarily Video Poker and vulturing slots, with occasional Blackjack and keno plays (yes, live keno!). If it can be considered a system, I play when I have as large of an edge as possible, and I stop when the edge drops significantly (sometimes even when it’s still positive, as I usually have a better play elsewhere). As long as my bankroll hasn’t taken too big of a dent, wins/losses during a particular hour, day, week, play are irrelevant no matter what my psyche thinks of them. These things even out the next hour, day, week, play, etc. I have found the math to be reliable. I don’t merely leave or stop simply because I’m ahead or behind, but I do always know how much I gained or lost on each play. I keep track of what I put in and cash out, and I keep accurate records.

tuttigym, I find the majority of your posts to be well written. For someone whose posts tend to reject the math, and those who employ any skill in such, as vehemently as yours do, I am surprised that you would seek responses from me, of all people, in order to see how you match up.

I’ll leave you with a question, as I honestly can’t tell. Do your posts convey your true feelings, or are they merely an attempt to illicit a response? (Feel free to treat this as rhetorical…)
link to original post

Sorry, I missed the satire. I guess sometimes I take myself too seriously although most times i try to lighten up.

I, personally could not handle the stress of a sole income from casino or other gaming, so I do admire the special personal traits that can handle that kind of pressure. Other than card counting and without revealing certain trade "secrets," what is the "edge" in video poker or keno? You speak of "the math being reliable." Briefly, what game and what "math," if possible. I guess I am asking is there some special "math" associated with video poker or keno? Keeping accurate records shows focus and discipline -- very commendable.

Most of my posts seek information or knowledge that I do not have, and thanks for the compliment. I do not "reject" the "math." It is that the "math" posed, in most instances, cannot be performed at the tables, and usually has little relevance to actual play at the tables. So that the "disruption" I posted is to hold accountable those who offer the mathematical gymnastics, formulas, and equations they constantly produce. What I am trying to say is that calculations showing miniscule HA/HE numbers are beyond misleading.

tuttigym