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Thread: Double21: ROR Question

  1. #14
    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

  2. #15
    Don Schlesinger
    Guest

    Don Schlesinger: Don't know what else to say

    I'm sorry that this is clear to me but not to you. ET Fan has it right, above, but doesn't give the appropriate ROR.

    Let's try this once more. I play a game with a certain EV and variance such that long-term ROR, as determined by the charts in BJA, is, say 3%. My BR is $1,000. Now, there are some assumptions here. One of them is that I attempt to play forever and do not remove any money from my bank.
    Under these circumstances, ROR = 3% means, "there is 3% chance of my tapping out, and 97% chance that I will win all the money in the world (if I live long enough).

    But, the above is NOT true if I have a secret plan to withdraw all of my winnings and restore my bank to $1,000, should I be lucky enough to reach $2,000 total bank. The original ROR was NOT predicated on that assumption. And, before I start to play, if I state that this is my plan (to withdraw winnings after doubling), ROR is NOT 3% anymore. Or, stated another way, if I want ROR to still be 3%, despite this plan, I need more capital (or, alternatively, need to play a smaller Kelly fraction)!

    I hope this is clear this time.

    Obviously, there reaches a point where the winnings become so massive with respect to original bank that siphoning off a portion of those winnings has no effect on the original long-term ROR. As an example, if I start with $1,000 and state, before playing, that if I were to reach, say, $10,000, I would keep $1,000 and then continue playing with the $9,000, I don't believe I would change my original ROR enough to even discuss the matter.

    But, what I'm saying is that this is NOT the case for removing $1,000 from a $2,000 bank.

    Don

  3. #16
    MathProf
    Guest

    MathProf: I will try again

    Let me restate what I said before


    If you specify the withdrawal strategy, and the goal, we can compute the probability of reaching it.

    If the strategy is to withdraw all winning after every doubling, and to play forever, then there is 0% chance of accomplishing this. This is 100% chance that at some point , one of the banks will go bust.


    I need you to tell me what the "withdrawal strategy" is. By that I mean, when and what will be withdrawn from the bank. It sounds to me like you are saying that we will withdraw after every doubling. If so, then I answered the question above: your RoR is 100%.

    It doesn't matter what your initial RoR is; you will eventually go bust if you adopt this policy.

    Since you were unhappy with answer, I gather that you were asking about another strategy. If you could tell us about more clearly what the policy will be, then we can answer the question.

    >
    > I am sorry, but I still don't quite know
    > what the question is.

    > The player starts with an RoR of 3%. But
    > when he doubles his 2K initial bank, he
    > takes out the 2K in winnings. What does he
    > do then?

    > Repeat the process, and take out 2K in
    > winnings each time he gets to the 4K mark?
    > And what is his goal. To double 10 times. To
    > double 5 times? To play forever.

    > If you specify the withdrawal strategy, and
    > the goal, we can compute the probability of
    > reaching it.

    > If the strategy is to withdraw all winning
    > after every doubling, and to play forever,
    > then there is 0% chance of accomplishing
    > this. This is 100% chance that at some point
    > , one of the banks will go bust.

  4. #17
    Don Schlesinger
    Guest

    Don Schlesinger: Wow, this is weird

    "Since you were unhappy with answer, I gather that you were asking about another strategy. If you could tell us about more clearly what the policy will be, then we can answer the question."

    I can't tell you more clearly. I've run out of ways to make myself any more clear. But, ET Fan understood, above, immediately.

    I stated things in my last post as clearly as I am able to state them. There is NO intention to withdraw winnings after EVERY doubling. But, there is the intention to withdraw $1,000 of the $2,000, should I turn the original $1,000 into $2,000.

    How much does that add to what otherwise would have been a 3% ROR, which assumes NEVER withdrawing any amount, and especially not after simply doubling?

    I'm dumbfounded that this simple question can cause so much confusion. And, one of the reasons is that, unfortunately, too many people think that ROR has something to do with doubling a bank, when, in fact, there is no such concept whatsoever inherent in the term.

    Don

    Don

  5. #18
    Double21
    Guest

    Double21: Re: Wow, this is weird

    You have stated and restated my case with precision! All I'm trying to do is understand what additional ROR (BJA definition) one takes by withdrawing all winnings and reverting back to their original bank after doubling it. If you start with X bank and a 3% ROR (BJA definition), then what is the new ROR after doubling this starting bank and withdrawing the proceeds? This is a practical issue for those of us who rely on blackjack winnings for income! If withdrawing after doubling the bank increases the ROR to an unacceptable level then the obvious solution is to play on until achieving enough winnings where their withdrawal (in whole or part) leaves one with their initial (and presumably maximum acceptable) ROR. If your bankroll is not replaceable this is a very important issue! Help if you can give it will be very much appreciated.

    One poster declared if you start out without the intention of withdrawal after doubling the bank, then revert back to the original bank after doubling it, one retains their initial ROR. However, starting out with that intention and then doing it, increases the ROR. Go figure.

  6. #19
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Wow, this is weird

    > You have stated and restated my case with
    > precision! All I'm trying to do is
    > understand what additional ROR (BJA
    > definition) one takes by withdrawing all
    > winnings and reverting back to their
    > original bank after doubling it.

    This is really too easy for MathProf to not understand, so I don't know what all the fuss is about. I would estimate that the original 3% has to be increased to at least 4-4.5%, and 5% wouldn't surprise me.

    Basically, all we want to know is of the 97% who reach $2,000 and continue forever, how many would have tapped out when their $2,000 slipped back to $1,000, if they had been deprived of the extra $1,000 cushion that they had and went bust instead of bouncing back up and making their fortune.

    VERY simple question, no, MP?

    Don

  7. #20
    MathProf
    Guest

    MathProf: Answer

    If I now understand what you are saying, the player has the following plan. Start with 1000K Bank and play with a 3% RoR. If he doubles the bank, he withdraws the $1000 and starts again. He then continues to play, at the same betting levels, with no further withdrawals.

    The player may go bust in two different ways. First, he may bust before doubling the original bank. If he has a 3% RoR, then the probability that he busts before doubling is 2.91%.

    Now, he succeeds in doubling 97.09% of the time. His new RoR is 3%; this is the conditional probability that he will go broke if he has successfully doubled once. The total is 97.09% * 3%.

    His overall RoR is the sum: 2.91% + (97.09%)* (3%) = 5.83%.

    Note that this is just under 6%, a little less than double the original RoR.

    If there were going to be 2 withdrawals (double, withdraw, double, withdraw, play indefinitely), it would be a little under 9%.

    > "Since you were unhappy with answer, I
    > gather that you were asking about another
    > strategy. If you could tell us about more
    > clearly what the policy will be, then we can
    > answer the question."

    > I can't tell you more clearly. I've run out
    > of ways to make myself any more clear. But,
    > ET Fan understood, above, immediately.

    > I stated things in my last post as clearly
    > as I am able to state them. There is NO
    > intention to withdraw winnings after EVERY
    > doubling. But, there is the intention to
    > withdraw $1,000 of the $2,000, should I turn
    > the original $1,000 into $2,000.

    > How much does that add to what otherwise
    > would have been a 3% ROR, which assumes
    > NEVER withdrawing any amount, and especially
    > not after simply doubling?

    > I'm dumbfounded that this simple question
    > can cause so much confusion. And, one of the
    > reasons is that, unfortunately, too many
    > people think that ROR has something to do
    > with doubling a bank, when, in fact, there
    > is no such concept whatsoever inherent in
    > the term.

    > Don

    > Don

  8. #21
    ET Fan
    Guest

    ET Fan: It may be a simple question ...

    ... but I'm not at all sure Double21 knows what he's asking!

    He said: This is a practical issue for those of us who rely on blackjack winnings for income!

    Since he's relying on winnings for an income, I really don't think he intends to make ONE withdrawal, then play forever after with zero withdrawals! How practical is that? I really think he wants to make withdrawals every time he doubles in perpetuity.

    I completely understand MathProf's caution. This is not discretionary income for D21. He is relying on blackjack winnings for income.

    ETF

    > This is really too easy for MathProf to not
    > understand, so I don't know what all the
    > fuss is about. I would estimate that the
    > original 3% has to be increased to at least
    > 4-4.5%, and 5% wouldn't surprise me.

    > Basically, all we want to know is of the
    > 97% who reach $2,000 and continue forever,
    > how many would have tapped out when their
    > $2,000 slipped back to $1,000, if they had
    > been deprived of the extra $1,000 cushion
    > that they had and went bust instead of
    > bouncing back up and making their fortune.

    > VERY simple question, no, MP?

    > Don

  9. #22
    ET Fan
    Guest

    ET Fan: Tell me where it hurts

    > One poster declared if you start out
    > without the intention of withdrawal after
    > doubling the bank, then revert back to the
    > original bank after doubling it, one retains
    > their initial ROR. However, starting out
    > with that intention and then doing it,
    > increases the ROR. Go figure.

    Why do these two statements seem contradictory to you? Once you've doubled your bank, your ROR is no longer X%, it's much lower. (The original ROR wasn't predicated on the assumption you were surely going to double that bank. Once it's doubled, you have new information to plug into the ROR formula.) If you then take enough to restore the original constraints, the ROR goes back to square one.

    Got it?

    ETF

  10. #23
    Double21
    Guest

    Double21: Re: It may be a simple question ...

    Yes ET I know what Im asking. I'm first of all trying to understand what happens to my initial ROR (BJA definition) if after a certain amount of winnings---in this example an amount equal to the starting bank---I withdraw and start over with the initial bank. Having gotten that data, the next question (as your post suggest) would be what if I do this over and over again? If withdrawal after doubling the bank results in an unacceptable ROR then maybe it has to be winnings of three times the original bank. I'm still uncertain what happens to the starting ROR if you withdraw after doubling the bank. It still seems strange to me that if you take two players (A and B) and A plays until doubling the bank; makes a withdrawal of these winnings and starts over; Player A's ROR is higher than Player's B's who then starts playing for the first time.The cards don't know who's been playing and who's been waiting.

    This seems like a very practical question to me. I can easily imagine people and teams using their winnings at some point on a regular basis.

  11. #24
    Don Schlesinger
    Guest

    Don Schlesinger: Now, you're talking!

    > If I now understand what you are saying,
    > the player has the following plan. Start
    > with 1000K Bank and play with a 3% RoR.

    Well, if it's all right with you, we'll start with $1,000 and not a million! :-)

    > If he doubles the bank, he withdraws the $1000
    > and starts again. He then continues to play,
    > at the same betting levels, with no further
    > withdrawals.

    See, that wasn't so hard, after all! :-)

    > His overall RoR is the sum: 2.91% +
    > (97.09%)* (3%) = 5.83%.

    > Note that this is just under 6%, a little
    > less than double the original RoR.

    Now, you're talking! And, as you can see, above, this is precisely the question that D21 wanted answered and which hasn't been answered until right now. I was a little conservative in my estimate of 4.5%. But, as initial ROR goes up, the difference between the correct new answer and double the original answer is not quite as dramatic as "almost double." So, for 10% ROR, the new answer might be something like 18%.

    Don

  12. #25
    Oldster
    Guest

    Oldster: Re: Wow, this is weird

    If the 3% ROR assumes NEVER removing money from the bankroll, then seems to me more than 97% would reach $2,000 and later suffer a loss so great that they eventually lose everything including the original bankroll.

    Or am I overlooking something?

    Oldster

    > This is really too easy for MathProf to not
    > understand, so I don't know what all the
    > fuss is about. I would estimate that the
    > original 3% has to be increased to at least
    > 4-4.5%, and 5% wouldn't surprise me.

    > Basically, all we want to know is of the
    > 97% who reach $2,000 and continue forever,
    > how many would have tapped out when their
    > $2,000 slipped back to $1,000, if they had
    > been deprived of the extra $1,000 cushion
    > that they had and went bust instead of
    > bouncing back up and making their fortune.

    > VERY simple question, no, MP?

    > Don

  13. #26
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Wow, this is weird

    > If the 3% ROR assumes NEVER removing money
    > from the bankroll, then seems to me more
    > than 97% would reach $2,000 and later suffer
    > a loss so great that they eventually lose
    > everything including the original bankroll.

    > Or am I overlooking something?

    You're not overlooking anything, but your assumption just isn't correct. This is in keeping with the "if they don't get you early, they'll probably never get you" concept I enunciated in BJA. It's a little like escaping the earth's gravitational pull; all the hard work is at the beginning, but once you're free and clear, you don't get pulled back.

    Survive that treacherous early period, on your way to $2,000, and you stand a good chance of "escaping" ruin and never looking back.

    Don

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