Math (simple) Question
January 30th, 2014 at 5:27:21 PM
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What bankroll do I need to have a risk of ruin lower than 1% on a continuous coin flip ? - But lower than 0.1% risk of ruin ?
January 30th, 2014 at 5:30:41 PM
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Not possible with any bankroll
January 30th, 2014 at 5:41:02 PM
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Yes, I see why is not possible, I think I have actually formulated the question wrong. - Will try again:
Say I have a "insignificant" edge, such as when it lands "tails" I win 1.001 and when it lands "heads" I lose 1. And I always bet "tails".
Under this conditions, what bankroll do I need to have a risk or ruin lower than 1% ? But lower than 0.1% ?
Say I have a "insignificant" edge, such as when it lands "tails" I win 1.001 and when it lands "heads" I lose 1. And I always bet "tails".
Under this conditions, what bankroll do I need to have a risk or ruin lower than 1% ? But lower than 0.1% ?
January 30th, 2014 at 5:50:36 PM
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Quote: PlayHunterYes, I see why is not possible, I think I have actually formulated the question wrong. - Will try again:
Say I have a "insignificant" edge, such as when it lands "tails" I win 1.001 and when it lands "heads" I lose 1. And I always bet "tails".
Under this conditions, what bankroll do I need to have a risk or ruin lower than 1% ? But lower than 0.1% ?
When you say "risk of ruin", you you mean that you want to double your bankroll before going broke? Or that you want to bet forever without going broke? (I've seen the term used to mean either, which is why I ask)
January 30th, 2014 at 6:07:23 PM
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Correction, when I exemplified with wining 1.001 that is not really insignificant at all, I should better have said 1.0000001 instead.
When I said risk of ruin, yes I meant to say that I want to bet forever (or close to that - say 100 million bets) without going broke.
When I said risk of ruin, yes I meant to say that I want to bet forever (or close to that - say 100 million bets) without going broke.
January 30th, 2014 at 6:12:35 PM
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Quote: PlayHunterwhat bankroll do I need to have a risk or ruin lower than 1% ? But lower than 0.1% ?
I do not understand this question. "Lower than 1% but lower than 0.1%"?
January 30th, 2014 at 6:15:52 PM
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I think he means between 0.1% and 1%
January 30th, 2014 at 6:21:14 PM
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What I want to really ask is: what bankroll do I need in order to always bet 1 unit "forever" on a coin flip and be "sure" that I will never run out of money ?
Say I will always bet 1 unit on "tails" and when I win, I win 1.0000001 units (50% of the time) and when I lose, I lose 1 unit.
And say I want to place 100 million bets with 100% certainty that I will not lose my bankroll. - What bankroll I would need for this ?
(Disregard my above posts, also disregard the above 1% and 0.1% questions. I think now I was clear with what I wanted to ask.)
Say I will always bet 1 unit on "tails" and when I win, I win 1.0000001 units (50% of the time) and when I lose, I lose 1 unit.
And say I want to place 100 million bets with 100% certainty that I will not lose my bankroll. - What bankroll I would need for this ?
(Disregard my above posts, also disregard the above 1% and 0.1% questions. I think now I was clear with what I wanted to ask.)
February 1st, 2014 at 2:55:22 PM
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to last 100m bets
to be 100% certain you need bank of 100m units ....
to be 99.9999% certain you need bank of ~80k units
if you worry about 99.9999%, then you should not drive a car or catch a plane
to be 100% certain you need bank of 100m units ....
to be 99.9999% certain you need bank of ~80k units
if you worry about 99.9999%, then you should not drive a car or catch a plane
February 2nd, 2014 at 7:34:42 AM
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Umm, thanks newbie49 this really answer my question. No, I am not worried about 00.0001% but I just wanted to know that fact.
So, your answer translates that to survive a 1 million coin flip bets of 1 unit 99.9999% of the time, I need a bankroll of ~800 units.
But this also mean that a bankroll of only 80 units will be enough to survive 99.9999% of the time for 100K coin flip bets of 1 unit?
So, your answer translates that to survive a 1 million coin flip bets of 1 unit 99.9999% of the time, I need a bankroll of ~800 units.
But this also mean that a bankroll of only 80 units will be enough to survive 99.9999% of the time for 100K coin flip bets of 1 unit?
February 3rd, 2014 at 8:38:22 AM
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They don't scale linearly.
Reduce 100m down to 1m coin flip is a factor of 100 times. It only reduce the bankroll requirement by a factor of 10 (SquareRoot(100) = 10). So ~8k units.
Reduce 1m down to 100k coin flip is a factor of 10 times. It only reduce the bankroll requirement by a factor of 3.3 (SquareRoot(10) = 3.3). So ~2.5k units.
Reduce 100k down to 100 coin flip is a factor of 1000 times. It only reduce the bankroll requirement by a factor of 33. So ~74 units.
In any case the above is just an estimation based on standard deviation. I don't know the exact formula.
Reduce 100m down to 1m coin flip is a factor of 100 times. It only reduce the bankroll requirement by a factor of 10 (SquareRoot(100) = 10). So ~8k units.
Reduce 1m down to 100k coin flip is a factor of 10 times. It only reduce the bankroll requirement by a factor of 3.3 (SquareRoot(10) = 3.3). So ~2.5k units.
Reduce 100k down to 100 coin flip is a factor of 1000 times. It only reduce the bankroll requirement by a factor of 33. So ~74 units.
In any case the above is just an estimation based on standard deviation. I don't know the exact formula.
February 3rd, 2014 at 3:34:04 PM
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Thanks I see how it works now. I am amazed what a bitch variance can be. Basically it means that in a pure coin flip game one might (and should even expect) to lose more than 7k units by just betting "heads" for long enough. (Of course it can win the same amount.)
