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  1. #1
    Double21
    Guest

    Double21: ROR Question

    For who knows how many times---here's a ROR question. Let's say for a particular bank, game, system and betting strategy one plays until their bank is doubled. Assume the starting ROR was 3%. If the winnings are withdrawn and the player starts over---all things else equal---is the ROR (BJA definition of continuing to play until bank is entirely lost) still 3%?

  2. #2
    Don Schlesinger
    Guest

    Don Schlesinger: Re: ROR Question

    > For who knows how many times---here's a ROR
    > question. Let's say for a particular bank,
    > game, system and betting strategy one plays
    > until their bank is doubled. Assume the
    > starting ROR was 3%. If the winnings are
    > withdrawn and the player starts over---all
    > things else equal---is the ROR (BJA
    > definition of continuing to play until bank
    > is entirely lost) still 3%?

    No. Part of the original 3% ROR for the $1,000 starting bank has to consider those times that you'll reach $2,000 or more, and keep all the money in the bank, thereby providing a nice "cushion" for you to go merrily on your way without ever being ruined (losing the $2,000 and slipping all the way to zero). So, if you take that cushion away, and restore the $1,000 bank, you've increased your chances of losing that original $1,000. If you now lose $1,000, you're broke; the other way, you'd still have another $1,000 to play with.

    Don


  3. #3
    Double21
    Guest

    Double21: Re: ROR Question

    > The next question then Don is how long must one go before it is "safe" to remove all winnings and revert back to the starting bankroll playing at the original ROR? Remember the "cards have no memory"!

  4. #4
    Don Schlesinger
    Guest

    Don Schlesinger: Re: ROR Question

    "The next question then Don is how long must one go before it is "safe" to remove all winnings and revert back to the starting bankroll playing at the original ROR? Remember the "cards have no memory"!"

    Technically, it's never safe. If you remove all winnings, by definition, you have the same bank as you started with, and that amount requires that, when you get a lead, you keep the winnings as part of the bank. I don't know if I'm understanding your question properly.

    Maybe what you mean is how much do you need to win such that a portion of your winnings could be removed without having much impact on your original, $1,000 BR ROR? I don't know the answer to that, but it's certain that, if you remove all the winnings and start over again, your ROR can't possibly be the same.

    Again, I may be misunderstanding you. Of ocurse, the cards have no memory. So, if the SECOND time you revert back to $1,000, you no longer plan to siphon off winnings, then, clearly, that's a different situation than if you're always going to siphon them off. I just want to make sure we're communicating properly.

    Don

  5. #5
    double21
    Guest

    double21: Re: ROR Question

    First of all, thanks for taking the time to thoughtfully respond. I think you understand my question---I'm wondering when it's safe (if ever) to spend the winnings and revert back to your original bank, still playing to the starting ROR. If you are playing to support yourself from blackjack then, by definition, at some point you must use the winnings. If by doing so your ROR increases, then eventually you are running a very high probability of going broke! How do people who play for a living make decisions on how much of their winnings to withdraw?

  6. #6
    MathProf
    Guest

    MathProf: Some Answers

    I hope Don will also respond, and give his insights into this question. I have a couple of comments.

    First, many pros play on teams. The team bank is separate from the personal bank. Each player only invests part of his/her fortune in the team bank. If the team bank goes bust, the player still has other capital with which too contribute to the next bank. If your personal fortune is in decline, you could join another team as a non-investing player, and try to raise a new stake from your earnings there.

    Second, 3% RoR is a bit high. If you are betting at the half-Kelly level, your initial RoR is less than 2%. Your RoR is actually much less than that, if your plan is to reduce the stakes after losing a percentage (like half) of the bank.

    Finally, tapping out after doubling many banks may not be that bad. Suppose you start with a 3% RoD (Risk of Ruin before doubling), but after each doubling, you remove the winnings and reset the bank. The probability that you double your first bank is .97. The probability that you will double two banks is (.97)^2 or about 94.1%. The probability that will successfully double N banks is (.97)^N.

    Now suppose that you double 10 banks, but tap out during the eleventh. You will have taken 10 Banks in profit. If you started with a 100K bank, then you would have made 1 Million dollars. This is a very good figure for a career in BJ. As a practical matter, it more likely that you will run out of places to play, than that you will tap out.

    Finally, the initial post I put up on this subject, ended with admonition "Don't quit your day job". The point being, that playing for a living is a lot more risky than many players realize.

    > First of all, thanks for taking the time to
    > thoughtfully respond. I think you understand
    > my question---I'm wondering when it's safe
    > (if ever) to spend the winnings and revert
    > back to your original bank, still playing to
    > the starting ROR. If you are playing to
    > support yourself from blackjack then, by
    > definition, at some point you must use the
    > winnings. If by doing so your ROR increases,
    > then eventually you are running a very high
    > probability of going broke! How do people
    > who play for a living make decisions on how
    > much of their winnings to withdraw?

  7. #7
    ET Fan
    Guest

    ET Fan: Look,

    If you take a bankroll, C, play to a lifetime ROR of X%, double your money to 2C, then make a one time decision to remove C and continue play in the same fashion, then at that point you are playing once again to a ROR of X%. If you're comfortable doing that, then that's what you should do. Of course, in hindsight your ROR was not really X%.

    If you decide ahead of time to remove C every time you reach 2C, and repeat that pattern many times, your ROR is effectively 100%. The saving grace is that your lifetime is not infinite. So you figure out how many times you need to repeat the process to sustain your life style, start with a very low ROR, and use the formulas MathProf provided here and on bj21 to see if you're comfortable with the overall ROR. There are also some posts archived there with very detailed advice re a constant drain on bankroll.

    But don't ask what's "safe." VERY confusing question to put to a mathematician. Gambling for a living is not safe at all! You may not like the numbers the formulas spit out.

    ETF

    > First of all, thanks for taking the time to
    > thoughtfully respond. I think you understand
    > my question---I'm wondering when it's safe
    > (if ever) to spend the winnings and revert
    > back to your original bank, still playing to
    > the starting ROR. If you are playing to
    > support yourself from blackjack then, by
    > definition, at some point you must use the
    > winnings. If by doing so your ROR increases,
    > then eventually you are running a very high
    > probability of going broke! How do people
    > who play for a living make decisions on how
    > much of their winnings to withdraw?

  8. #8
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Look,

    > If you take a bankroll, C, play to a
    > lifetime ROR of X%, double your money to 2C,
    > then make a one time decision to remove C
    > and continue play in the same fashion, then
    > at that point you are playing once again to
    > a ROR of X%. If you're comfortable doing
    > that, then that's what you should do. Of
    > course, in hindsight your ROR was not
    > really X%.

    Yes, that was my point, exactly, that I made above, before reading this post.

    Don

  9. #9
    Neko
    Guest

    Neko: Re: Look,

    ET Fan,

    Thanks for the very clear and understandable reply. I always wondered the same thing that double21 is asking.

    To sum up your answer, at the moment we take out 1C from the 2C bank, our ROR is the original 3%. However, our lifetime ROR is greater. If we keep doing this, our lifetime ROR increases, but when the bank reverts to 1C, the ROR is 3% FOR THAT BANK. How long we can keep doing this is dictated by the lifetime ROR.

    Neko

    > If you take a bankroll, C, play to a
    > lifetime ROR of X%, double your money to 2C,
    > then make a one time decision to remove C
    > and continue play in the same fashion, then
    > at that point you are playing once again to
    > a ROR of X%. If you're comfortable doing
    > that, then that's what you should do. Of
    > course, in hindsight your ROR was not
    > really X%.

    > If you decide ahead of time to remove C
    > every time you reach 2C, and repeat that
    > pattern many times, your ROR is effectively
    > 100%. The saving grace is that your lifetime
    > is not infinite. So you figure out how many
    > times you need to repeat the process to
    > sustain your life style, start with a very
    > low ROR, and use the formulas MathProf
    > provided here and on bj21 to see if you're
    > comfortable with the overall ROR. There are
    > also some posts archived there with very
    > detailed advice re a constant drain on
    > bankroll.

    > But don't ask what's "safe." VERY
    > confusing question to put to a
    > mathematician. Gambling for a living is not
    > safe at all! You may not like the numbers
    > the formulas spit out.

    > ETF

  10. #10
    MathProf
    Guest

    MathProf: Repost (Long)

    Double21 raised this question on another board, and I answered him. Apparently he is dissatisfied by my answer, which is why he is posting it here.

    For those of you who do not read the other board, here are my two previous posts on the subject:

    First Post


    I am not sure what you are trying to say here:


    No less than Don Schlesinger concluded he didn't know at what point it was safe to remove the winnings from your bank and not change the starting ROR. Any idea? The rule of thumb has been after doubling your bank, but Don said that was just a guess. In other words, if you start with a 3% ROR using a specific bank, when can you withdraw winnings and keep the 3% ROR?


    This point has been discussed before. There are some excellent posts on this by myself and by MathBoy in the archives, from about 5 years ago.

    The mathematics of this are relatively simple. Let us say you start with a Bank B with a 3% RoR. Suppose you double it. If you played at the old level with the new bank, your RoR would be 3%*3% = .09%. Now if you remove all the profits, and reset the Bank to B, you will have a 3% RoR on the new bank.

    But note that this is not lifetime RoR of 3%. Your lifetime RoR is actually higher.

    For example, if you play 10 banks, each with an RoR of 3%, then the probability that you will bust one of those banks is almost 30%. (It is actually 1-(.97)^10) = 26.3%.

    Now if you start with a 3% RoR, but your policy is to remove half the winnings after each doubling, then your lifetime RoR becomes the sqrt(.03) = 17%. The only way to keep a lifetime RoR of 3% is to never take out any winnings.

    What is "safe" is a somewhat subjective decision, and may depend on personal circumstances.

    Follow-Up Post


    The Question was


    Could you explain the difference between a bank and lifetime ROR? If I double my bank and then take out the winnings--- in effect starting over--- you state my bank ROR reverts back to the starting percentage. In your example this was 3%. Why is this not also my lifetime ROR? And what is magic about doubling the bank before removing all winnings? Why not after increasing it by 50%? Just curious.


    First, there is nothing "magic" about doubling. You were the one who suggested it, not me. If you play with a large bank and a low bank RoR (which I would recommend) that it will take a long time to double, and it would make sense to take profits much earlier.

    Now as to the difference between lifetime and Bank RoR. I thought you were suggesting the following business plan. Start with Bank B0. Reach a certain level (you said doubling),distribute profits, and from Bank B1. Repeat the process, and form bank B2. Repeat the process, and form Bank B3. etc.

    Now suppose that according to your business plan, the risk of losing each bank is 3%. Imaging that 1000 people try to execute this plan. On average, 30 of them will drop the initial bank, 970 will make it to Bank 1. Of these 970, 3% or about 29 will drop bank 2, and only 940 will get beyond that level. 912 will get beyond the next level, etc. So the probability of making it that level is about 91.2%, the risk of ruined by that point is 8.8%.

    Your lifetime RoR would be the risk that you would be ruined at some point in this process. And for the plan described above, that would be 100%.


  11. #11
    Don Schlesinger
    Guest

    Don Schlesinger: Don't agree

    > The mathematics of this are relatively
    > simple.

    Not to me they aren't. I don't agree with all you've written below, because we may not be describing the same situation.

    > Let us say you start with a Bank B with a 3%
    > RoR.

    Immediately, let's make something clear: 3% ROR has absolutely nothing whatsoever to do with doubling a bank. 3% ROR means 3% chance of tapping out before winning all the money in the world. That's what the ROR formula measures; it has nothing to do with doubling. This is important!

    > Suppose you double it. Now if you
    > remove all the profits, and reset the Bank
    > to B, you will have a 3% RoR on the new
    > bank.

    Only if you plan to play forever with that new bank. If you plan, once again, to siphon off profits once you've doubled, your ROR is greater than 3%.

    Of course, if you have a ROR formula different from the one in BJA, such that you're defining ROR as "risk of losing all your money before doubling the bank," that changes everything. But that's NOT what ROR means.

    Don


  12. #12
    MathProf
    Guest

    MathProf: RoR and Doubling

    There is a very simple relationship between Risk of Ruin Before Doubling, which I will call RoR, and the Risk of Ruin before eternity, which we call RoR. They are related by the following equivalent equations:

    RoD = RoR / (1 + RoR)

    RoR = (RoD)/(1 - RoD)

    Now it wasn't clear to me whether the original poster meant to play with a 3% RoR, or a 3% RoD. But in either case, the answer would be the same, and so I didn't go into that subtlety.

    If he was playing was a 3% RoR, then his RoD would be 2.91%. Now, if we originally playing with a 2.91% RoD, and then he doubled his bank, and removed half the winnings, then we would now have a 2.91% RoD with the new bank, which is a 3% RoR if we played with the new bank until perpetuity.


  13. #13
    Don Schlesinger
    Guest

    Don Schlesinger: Re: RoR and Doubling

    > If he was playing was a 3% RoR, then his
    > RoD would be 2.91%. Now, if we originally
    > playing with a 2.91% RoD, and then he
    > doubled his bank, and removed half the
    > winnings, then we would now have a 2.91% RoD
    > with the new bank, which is a 3% RoR if we
    > played with the new bank until perpetuity.

    Nope, we're still talking at cross purposes. I want to know the HIGHER ROR, above 3%, that the player will incur if he uses the charts from BJA to fashion a 3% ROR but then, at the $2,000 mark (double), withdraws the money.

    I want to state that ROR NOW, before I ever reach the $2,000 mark. So, that ROR is MORE than 3%.

    Am I misstating anything?

    Don

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