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A friend of mine mentioned this to me, and I thought I would post it here, because none of us have a life.You have $1,000. A friend says that he will pay you twice your bet amount, every time you flip heads. So, you bet $1, it comes up tails, you lose $1. You bet $1, it comes up heads, you get $2 from him (but lose your original $1). (EDIT: i.e. It's a 2 for 1 payout when you win).However, he decides to make things a bit more interesting. You are required to bet 1% of your bankroll on each of 1 million coinflips, and after 1 million coin-filps, he will pay you an additional bonus of 5% of whatever your current bankroll is. If your bankroll drops below $1.00, the bet is off and you lost $999, but he'll gladly give you the nickel bonus.Assume that 1 million coinflips can be done within a 24 hour period.Assume that the odds of flipping heads is exactly 1 to 1.Do you take the bet?Edited to hopefully be more clear.EDIT AGAIN:There is no trick or con in the betting. It's 1:1 odds. You win, you get a buck, you lose, you pay a buck. I tried to restate this in various ways, but the question itself is not meant to be tricky.

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A friend of mine mentioned this to me, and I thought I would post it here, because none of us have a life.You have $1,000. A friend says that he will pay you twice your bet amount, every time you flip heads. So, you bet $1, it comes up tails, you lose $1. You bet $1, it comes up heads, you get $2 from him (but lose your original $1).However, he decides to make things a bit more interesting. You are required to bet 1% of your bankroll on each coinflip, and after 1 million coin-filps, he will pay you an additional bonus of 5% of whatever your current bankroll is. If your bankroll drops below $1.00, the bet is off and you lost $999, but he'll gladly give you the nickel bonus.Assume that 1 million coinflips can be done within a 24 hour period.Assume that the odds of flipping heads is exactly 1 to 1.Do you take the bet?
Am I missing the downside here?
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my first instinct is not to take the bet as standard deviation would nearly ensure that at some point in a million flips (no matter the time frame) we get get below a point of $1 and hit gambler's ruin.my rough calculations say to go broke we would need a difference of - around 370 flips which my instinct tells me is way within the standard deviation of a million flips and almost guarantees gamblers ruin.so i say i don't take the bet. but what do i know.

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This has absolutely nothing to do with your question, but I had this nice little coin flipping hustle that I would pull of back in high school. Basically you and the mark each pick a sequence of 3 coin flips. The mark must ALWAYS choose first. So for example he'd say HTT. Then you choose your sequence and who ever's sequence comes up first wins.The hustle comes in knowing what sequence to choose that will come up more than 50% of the time, as opposed to your mark's sequence. To do this all you do is take the first two picks of the mark's sequence and add the opposite of the second to the beginning.So if the mark's sequence is HTT you take the first two (HT) and add the opposite of the second to the beginning, thus your sequence is HHT. I have no idea how the math part comes into play in all of this, all I know is it works.

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This has absolutely nothing to do with your question, but I had this nice little coin flipping hustle that I would pull of back in high school. Basically you and the mark each pick a sequence of 3 coin flips. The mark must ALWAYS choose first. So for example he'd say HTT. Then you choose your sequence and who ever's sequence comes up first wins.The hustle comes in knowing what sequence to choose that will come up more than 50% of the time, as opposed to your mark's sequence. To do this all you do is take the first two picks of the mark's sequence and add the opposite of the second to the beginning.So if the mark's sequence is HTT you take the first two (HT) and add the opposite of the second to the beginning, thus your sequence is HHT. I have no idea how the math part comes into play in all of this, all I know is it works.
head asplode
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I have no idea how the math part comes into play in all of this, all I know is it works.
in a series of flips where results are designated as H or T, HTH and THT will come up more often than HTT and THH due to an ability to overlap with the "first" result of the sequence. flip a coin with a piece of paper keeping score and you'll see how this works.edit: in this speech a much smarter statistician than i explains it in better detail. he also explains why this is not the way humans instinctively view this problem.
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in a series of flips where results are designated as H or T, HTH and THT will come up more often than HTT and THH due to an ability to overlap. flip a coin with a piece of paper keeping score and you'll see how this works.
so you are saying that after the first H the coin is due to come up tails right :club:
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in a series of flips where results are designated as H or T, HTH and THT will come up more often than HTT and THH due to an ability to overlap. flip a coin with a piece of paper keeping score and you'll see how this works.
my answer was better.
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of all people you should understand variance :club:
Only putting 1% of your roll on the table at a time, with a 200% ROI?? Seems like good bankroll management to me. And it may just be how he worded it, but I didn't see it as a requirement to take all 1 million flips, just to get the bonus.
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in a series of flips where results are designated as H or T, HTH and THT will come up more often than HTT and THH due to an ability to overlap. flip a coin with a piece of paper keeping score and you'll see how this works.
yea guy who thought me this said something along those lines.all i said was, give me a quarter so i can go start hustlin.
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This has absolutely nothing to do with your question, but I had this nice little coin flipping hustle that I would pull of back in high school. Basically you and the mark each pick a sequence of 3 coin flips. The mark must ALWAYS choose first. So for example he'd say HTT. Then you choose your sequence and who ever's sequence comes up first wins.The hustle comes in knowing what sequence to choose that will come up more than 50% of the time, as opposed to your mark's sequence. To do this all you do is take the first two picks of the mark's sequence and add the opposite of the second to the beginning.So if the mark's sequence is HTT you take the first two (HT) and add the opposite of the second to the beginning, thus your sequence is HHT. I have no idea how the math part comes into play in all of this, all I know is it works.
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so you are saying that after the first H the coin is due to come up tails right :club:
here's a random series of flips:HTHHTHTHTHTHHHHTsay we're looking for HTH. the third result in this series (which completes HTH) also works as a desired result to build a second HTH series. we only need 5 flips to get two HTH series in a row.if we were looking for HTT then we would need at least six flips to get two HTT series in a row.
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Only putting 1% of your roll on the table at a time, with a 200% ROI?? Seems like good bankroll management to me. And it may just be how he worded it, but I didn't see it as a requirement to take all 1 million flips, just to get the bonus.
Under those terms sure. But look at the wording of the original. You get twice your wager but you lose your wager. So you're getting paid 1:1 if you win and not 2:1.Still even without that you'd think that getting 1:1 on a 1:1 proposition should be breakeven and you'd make money from the bonus. But I think the effect is basically like the reverse of compound interest. You wager %1 or $10 and lose. No biggie. Next hand you wager $9.9 and win. But your total is now 999.99 and not 1000. Even though you won 1 and lost 1 your still losing. I did a simulation and you actually lose surprisingly quickly. Usually in around 150K flips. Even though at times you can go on a huge rush and get up over 6K.Edit: under the 2:1 payout it would be a HUGE money maker. I actually couldn't even run it in my sim because the br got too big to calculate. Even you get 1.1 : 1 you'd make billions. At 1.01 : 1 you still win more often than you lose and win by quite a bit when you do win.
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my first instinct is not to take the bet as standard deviation would nearly ensure that at some point in a million flips (no matter the time frame) we get get below a point of $1 and hit gambler's ruin.my rough calculations say to go broke we would need a difference of - around 370 flips which my instinct tells me is way within the standard deviation of a million flips and almost guarantees gamblers ruin.so i say i don't take the bet. but what do i know.
Good call!Not fully believing it myself, I wrote a computer simulation. Somewhere before 1,000,000 flips, you are basically guaranteed to go broke. I guess it's possible that I wrote the simulation incorrectly, but I really don't think so. After doing 1 million flips 100,000 times, I went broke every single time. But in the short term (around 100,000 flips), I would occasionally get some HUGE bankrolls, even though I was still more likely to lose than not. In other words, somewhere between 100,000 and 1,000,000 filps, it switches from +EV to -EV.I'm not an actuary by any means, so perhaps at infinity it becomes a wash, or maybe I've just proven some conjecture. Beats the heck out of me.Why this is relevant to poker players (Bankroll management):If you start with, say, $1,000,000, and the payout ratio is 1.01 to 1 (in your favor), you will still come out behind more often than not, when betting 1% of your bankroll, even with say, 1,000 flips. Switch it to 0.9% of your bankroll, and you will come out ahead more often than not. Regardless, your Net will be bigger as a result of the 1.01 payout, but you only have one bankroll.So if your ROI is 10% at any particular game, you should be putting less than 10% of your bankroll at risk when you play it. To be safer, make it about 5%.
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in a series of flips where results are designated as H or T, HTH and THT will come up more often than HTT and THH due to an ability to overlap with the "first" result of the sequence. flip a coin with a piece of paper keeping score and you'll see how this works.edit: in this speech a much smarter statistician than i explains it in better detail. he also explains why this is not the way humans instinctively view this problem.
I will bet you on that if you give odds .
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here's a random series of flips:HTHHTHTHTHTHHHHTsay we're looking for HTH. the third result in this series (which completes HTH) also works as a desired result to build a second HTH series. we only need 5 flips to get two HTH series in a row.if we were looking for HTT then we would need at least six flips to get two HTT series in a row.
I'm willing to bet that is not a random sequence of coin flips and that instead you made it up to look random.
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I will bet you on that if you give odds .
okay, lets have a agreed upon poster flip a coin and create a sequence of 50 results. every time it comes up HTH in the sequence i get $200 from you and every time it comes up HTT you get $150 from me. how's that?
I'm willing to bet that is not a random sequence of coin flips and that instead you made it up to look random.
how much?i used a $1 gold coin with John Adams' face on it.
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Under those terms sure. But look at the wording of the original. You get twice your wager but you lose your wager. So you're getting paid 1:1 if you win and not 2:1.Still even without that you'd think that getting 1:1 on a 1:1 proposition should be breakeven and you'd make money from the bonus. But I think the effect is basically like the reverse of compound interest. You wager %1 or $10 and lose. No biggie. Next hand you wager $9.9 and win. But your total is now 999.99 and not 1000. Even though you won 1 and lost 1 your still losing. I did a simulation and you actually lose surprisingly quickly. Usually in around 150K flips. Even though at times you can go on a huge rush and get up over 6K.Edit: under the 2:1 payout it would be a HUGE money maker. I actually couldn't even run it in my sim because the br got too big to calculate. Even you get 1.1 : 1 you'd make billions. At 1.01 : 1 you still win more often than you lose and win by quite a bit when you do win.
Can I ask how you're running these mathematical simulations? Same goes to the other guy. Just out of interest.
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Can I ask how you're running these mathematical simulations? Same goes to the other guy. Just out of interest.
$br = 1000;$max = 0;for ($i = 0; $i < 1000000 && $br > 1; $i++){	$wager = $br * 0.01;	if (rand (0,1)) {		$br = $br + $wager;	} else {		$br = $br - $wager;	}	if ($br > $max) $max = $br;}if ($br < 1) {	echo 'you lose after '.$i." flips. Your max was $max\n";} else {	echo "remaining br = ".$br." with bonus = " .$br*1.05."\n";}

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