Flipping coin challenge
August 5th, 2022 at 7:04:43 PM
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Hi to all, I have a question that is around my head in the last weeks. Imagine that you have (a very strange) challenge with a friend of yours. The challenge is to flip the coin 1.000 times. If the coin is head you win 10 dollars and if the coin is tail your friend win 10 dollars. After 800 flips there were 500 heads and 300 tails, you are 2.000 dollars up. Your friend say to you "dude, I have very bad luck, do you want to switch the selection in this last 200 flips?"
If you change, when the coin is head your friend is going to win 10 dollars and if is tail you are going to win 10 dollars.
What would you do? Stay in head or switch to tail?
Thanks.
If you change, when the coin is head your friend is going to win 10 dollars and if is tail you are going to win 10 dollars.
What would you do? Stay in head or switch to tail?
Thanks.
August 5th, 2022 at 7:22:30 PM
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Quote: Cristobal
What would you do? Stay in head or switch to tail?
Thanks.
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I am probably OK to switch.
I don't think the coin is biased.
May the cards fall in your favor.
August 5th, 2022 at 7:53:31 PM
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He’s your friend. He’s down. He wants to switch. You should switch.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
August 5th, 2022 at 8:12:18 PM
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If it's a US coin the coin is biased. All US coins are heavier on the heads (obverse) side.
So how is the flip conducted?
So how is the flip conducted?
August 5th, 2022 at 9:11:53 PM
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Quote: unJonHe’s your friend. He’s down. He wants to switch. You should switch.
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hahahahahaa you have a point.
August 5th, 2022 at 9:14:24 PM
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Quote: AlanMendelsonIf it's a US coin the coin is biased. All US coins are heavier on the heads (obverse) side.
So how is the flip conducted?
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Let´s say the coin is not biased. You have exact the same possibility to have head or tail. Would you switch with your friend?
In my case I would switch.
August 5th, 2022 at 9:29:56 PM
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Math warning.
500 or more heads in 800 flips is 7.07 deviations to the right of expectations, roughly a 1 in 600 billion chance
I wouldn’t worry about it. You’re about 2.000 times more likely to win the Powerball jackpot tomorrow
Being up 50 to 30 is a more realistic scenario. Still only about a 1 in 78 chance
As long as you know it’s a fair coin, there’s no reason to switch. Dice and coins have no memory. Believing otherwise is called gambler’s fallacy, probably the most common fallacy in gambling, hence the name
500 or more heads in 800 flips is 7.07 deviations to the right of expectations, roughly a 1 in 600 billion chance
I wouldn’t worry about it. You’re about 2.000 times more likely to win the Powerball jackpot tomorrow
Being up 50 to 30 is a more realistic scenario. Still only about a 1 in 78 chance
As long as you know it’s a fair coin, there’s no reason to switch. Dice and coins have no memory. Believing otherwise is called gambler’s fallacy, probably the most common fallacy in gambling, hence the name
It’s all about making that GTA
August 5th, 2022 at 9:57:37 PM
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Quote: Ace2Math warning.
500 or more heads in 800 flips is 7.07 deviations to the right of expectations, roughly a 1 in 600 billion chance
I wouldn’t worry about it. You’re about 2.000 times more likely to win the Powerball jackpot tomorrow
Being up 50 to 30 is a more realistic scenario. Still only about a 1 in 78 chance
As long as you know it’s a fair coin, there’s no reason to switch. Dice and coins have no memory. Believing otherwise is called gambler’s fallacy, probably the most common fallacy in gambling, hence the name
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Thanks, Ace2. And yes, maybe I exaggerate with the percentage. But my point is after seeing and recording in an excel more than 50.000 hands in Baccarat it´s that the variance of the player or banker can go 5%-10% up or down but then always but always return to their natural point (44.6-45.9). It´s difficult to me to think that´s is only a coincidence.
August 5th, 2022 at 10:54:11 PM
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After 50,000 hands, only about a 1 in 1,000,000 chance your wins will differ from expectations by more than 1%. One standard deviation is roughly 1/5th of one percentQuote: CristobalQuote: Ace2Math warning.
500 or more heads in 800 flips is 7.07 deviations to the right of expectations, roughly a 1 in 600 billion chance
I wouldn’t worry about it. You’re about 2.000 times more likely to win the Powerball jackpot tomorrow
Being up 50 to 30 is a more realistic scenario. Still only about a 1 in 78 chance
As long as you know it’s a fair coin, there’s no reason to switch. Dice and coins have no memory. Believing otherwise is called gambler’s fallacy, probably the most common fallacy in gambling, hence the name
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Thanks, Ace2. And yes, maybe I exaggerate with the percentage. But my point is after seeing and recording in an excel more than 50.000 hands in Baccarat it´s that the variance of the player or banker can go 5%-10% up or down but then always but always return to their natural point (44.6-45.9). It´s difficult to me to think that´s is only a coincidence.
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Expectation increases linearly with trials but SD increases by square root of trials. That’s why you can see a lot of variance with few trials but very little with many trials. Also why you can beat the casino in the short term but they will always get their house edge with a long enough term
That last bit, though it’s basic statistics that can be proven, is vehemently denied by several forum members
It’s all about making that GTA
August 6th, 2022 at 1:00:59 AM
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Quote: AlanMendelsonIf it's a US coin the coin is biased. All US coins are heavier on the heads (obverse) side.
So how is the flip conducted?
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I should have said that I do not think the coin's intrinsic irregularity is not the dominant cause of the bias in the results.
edit: brain malfunction. Added strikethrough on errant "not".
Last edited by: Dieter on Aug 6, 2022
May the cards fall in your favor.
August 6th, 2022 at 1:02:36 AM
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Quote: Cristobal
Thanks, Ace2. And yes, maybe I exaggerate with the percentage. But my point is after seeing and recording in an excel more than 50.000 hands in Baccarat it´s that the variance of the player or banker can go 5%-10% up or down but then always but always return to their natural point (44.6-45.9). It´s difficult to me to think that´s is only a coincidence.
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Cristobel, Do you misunderstand reversion to the mean like so many gamblers do?
As you add more to your sample, then the percentage heads: tails or Banker: Player WILL tend towards the expected ratio, even while the numerical difference might well increase.
So: For example, take your coin flip situation
You might start with 1 head and 0 tails
Percentage Heads=1/1 = 100% heads and 0% Tails. Numerical Difference = 1 - 0 = 1
You reach 500 Heads and 300 Tails.
Percentage Heads=500/800 = 62.5% heads and 37.5% Tails. Numerical Difference = 500 - 300 = 200
Now flip some more and end up with a reasonable situation of 1600 Heads and 1300 Tails. Let's observe that you still get another 100 more 'extra' heads than tails! The gap widened!!!
Percentage Heads=1600/2900 = 55.2% heads and 44.8% Tails. Numerical Difference = 1600 - 1300 = 300
See how you have tended towards 50% (going from 100% to 62.5% to 55.2%) while the numerical difference has increased from 1 to 200 to 300
Regression to the mean is of the proportion, not of the numerical difference. You don't get 'catching up' or evening out.
Psalm 25:16
Turn to me and be gracious to me, for I am lonely and afflicted.
Proverbs 18:2
A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
August 6th, 2022 at 1:03:07 AM
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You confirm his thinking and let him know the only possible way to get even AND WIN is by switching. Then you charge him a 10% vig per flip for switching.Quote: CristobalHi to all, I have a question that is around my head in the last weeks. Imagine that you have (a very strange) challenge with a friend of yours. The challenge is to flip the coin 1.000 times. If the coin is head you win 10 dollars and if the coin is tail your friend win 10 dollars. After 800 flips there were 500 heads and 300 tails, you are 2.000 dollars up. Your friend say to you "dude, I have very bad luck, do you want to switch the selection in this last 200 flips?"
If you change, when the coin is head your friend is going to win 10 dollars and if is tail you are going to win 10 dollars.
What would you do? Stay in head or switch to tail?
Thanks.
link to original post
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
August 6th, 2022 at 2:29:04 AM
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On the matter of a biased flip:
Gamblers Take Note: The Odds in a Coin Flip Aren’t Quite 50/50 Tip of the hat to Mr. Mendelson for pointing out the weight difference as one factor.
Gamblers Take Note: The Odds in a Coin Flip Aren’t Quite 50/50 Tip of the hat to Mr. Mendelson for pointing out the weight difference as one factor.
“You don’t bring a bone saw to a negotiation.” - Robert Jordan, former U.S. ambassador to Saudi Arabia
August 6th, 2022 at 6:18:49 AM
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Quote: unJonHe’s your friend. He’s down. He wants to switch. You should switch.
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I agree but I would also try and charge him for the switch. I would ask for $5 either flat for the switch or $10.25 when I win and only $9.75 when he wins.
You can't know everything, but you can know anything.
August 6th, 2022 at 6:33:10 AM
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Quote: CristobalQuote: AlanMendelsonIf it's a US coin the coin is biased. All US coins are heavier on the heads (obverse) side.
So how is the flip conducted?
link to original post
Let´s say the coin is not biased. You have exact the same possibility to have head or tail. Would you switch with your friend?
In my case I would switch.
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I too am interested in how the coin flip is being conducted.
Unless I hear otherwise, I assume that the players alternate tosses, using the same coin, to land on the ground or floor, landing edge (or vertically in a crevice) is a re-toss, players have free choice of set and toss method.
I would also be inclined to allow the contest to end early, if one player falls way behind.
May the cards fall in your favor.
August 6th, 2022 at 6:55:13 AM
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Quote: Ace2500 or more heads in 800 flips is 7.07 deviations to the right of expectations, roughly a 1 in 600 billion chance
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I was going to make this same point. I would be very suspicious of the coin after those results and want to change sides too.
However, if we assume it's a fair coin and flip, then switching sides would not affect the odds. It should be also noted that even with a fair coin, the flip itself is biased towards the side that started face up, especially if the coin is caught in the hand. I had an Ask the Wizard question about this recently.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 6th, 2022 at 7:20:02 AM
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He's down 2k, and believes in mumbo jumbo. You can charge more, and he will pay. You can probably add in a -20% carnival side bet.Quote: DRichQuote: unJonHe’s your friend. He’s down. He wants to switch. You should switch.
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I agree but I would also try and charge him for the switch. I would ask for $5 either flat for the switch or $10.25 when I win and only $9.75 when he wins.
link to original post
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
August 6th, 2022 at 7:25:11 AM
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Quote: AxelWolfHe's down 2k, and believes in mumbo jumbo. You can charge more, and he will pay. You can probably add in a -20% carnival side bet.Quote: DRichQuote: unJonHe’s your friend. He’s down. He wants to switch. You should switch.
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I agree but I would also try and charge him for the switch. I would ask for $5 either flat for the switch or $10.25 when I win and only $9.75 when he wins.
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Feels like you all missed the key part of the the hypo. The word, friend.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
August 6th, 2022 at 7:27:20 AM
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How many Yo's in a row before you would start betting it? Apparently, 17 isn't enough to phase some people, I think my number is probably 5 before I'm like WTF is going on?Quote: WizardQuote: Ace2500 or more heads in 800 flips is 7.07 deviations to the right of expectations, roughly a 1 in 600 billion chance
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I would be very suspicious of the coin after those results and want to change sides too.
We have a guy here somewhere who's claiming he is beating baccarat with something like 8 standard deviations above.
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
August 6th, 2022 at 7:29:45 AM
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Quote: unJonQuote: AxelWolfHe's down 2k, and believes in mumbo jumbo. You can charge more, and he will pay. You can probably add in a -20% carnival side bet.Quote: DRichQuote: unJonHe’s your friend. He’s down. He wants to switch. You should switch.
link to original post
I agree but I would also try and charge him for the switch. I would ask for $5 either flat for the switch or $10.25 when I win and only $9.75 when he wins.
link to original post
link to original post
Feels like you all missed the key part of the the hypo. The word, friend.
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That is why I offered $5. If it wasn't a friend the vig would be much higher.
You can't know everything, but you can know anything.
August 6th, 2022 at 7:44:57 AM
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Oh, I forgot it was a friend. You should call it even, or charge him triple unless he promises to never gamble again since he didn't change out the obviously biased coin or call foul long before that. He is obviously prone to mumbo jumbo voodoo.Quote: DRichQuote: unJonQuote: AxelWolfHe's down 2k, and believes in mumbo jumbo. You can charge more, and he will pay. You can probably add in a -20% carnival side bet.Quote: DRichQuote: unJonHe’s your friend. He’s down. He wants to switch. You should switch.
link to original post
I agree but I would also try and charge him for the switch. I would ask for $5 either flat for the switch or $10.25 when I win and only $9.75 when he wins.
link to original post
link to original post
Feels like you all missed the key part of the the hypo. The word, friend.
link to original post
That is why I offered $5. If it wasn't a friend the vig would be much higher.
link to original post
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
August 6th, 2022 at 7:49:04 AM
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"Expectation increases linearly with trials but SD increases by square root of trials. That’s why you can see a lot of variance with few trials but very little with many trials. Also why you can beat the casino in the short term but they will always get their house edge with a long enough term".
I agree with the first part of that, the variance that I mention of 5%-10% was in the first hundred of hands, when I pass the first 1.000 and either the % was lower and lower. But in the road always when the player or banker was underreated around 1% always come back to his natural point, every single time.
If you have play 90.000 of 100.000 hands and you see that player is underreated in 500 hands (39.662 instead of 40.162). Do you think that the probability of having a player in this last 10.000 hands is what shoul be (0.446247) or is a little higher? For me, is a little higher, something around 0.45XXXX.
And that is not gambler´s fallacy, it´s simple law of large numbers.
I agree with the first part of that, the variance that I mention of 5%-10% was in the first hundred of hands, when I pass the first 1.000 and either the % was lower and lower. But in the road always when the player or banker was underreated around 1% always come back to his natural point, every single time.
If you have play 90.000 of 100.000 hands and you see that player is underreated in 500 hands (39.662 instead of 40.162). Do you think that the probability of having a player in this last 10.000 hands is what shoul be (0.446247) or is a little higher? For me, is a little higher, something around 0.45XXXX.
And that is not gambler´s fallacy, it´s simple law of large numbers.
August 6th, 2022 at 10:21:25 AM
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There seems to be very strong proof that this is not a fair coin. If after 800 flips there were 500 heads and 300 tails, I would assume the coin was biased towards heads. So, I would switch towards heads.
1. Weighted coins do exist.
2. You are not in a regulated situation.
3. The probability of a 500/300 split with a fair coin was explained by a previous poster.
4. People do cheat. On school tests. In marriage. In business. At cards/gambling. On IRS returns. That is life. Keep your eyes wide open and think, dammit.
1. Weighted coins do exist.
2. You are not in a regulated situation.
3. The probability of a 500/300 split with a fair coin was explained by a previous poster.
4. People do cheat. On school tests. In marriage. In business. At cards/gambling. On IRS returns. That is life. Keep your eyes wide open and think, dammit.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
August 6th, 2022 at 1:39:35 PM
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https://www.omnicalculator.com/statistics/coin-flip-probability Probability 0.000000000000763
If I had that exact result I would be fairly certain that the coin is not a fair coin. You can use your binomial function in a spreadsheet or the above link to show that 500 out of 800 is exceedingly unlikely with a 50/50 coin.AT 444/356 you are already looking at a 1 in 1000 fluke with a fair coin. I would have quit way before 500/300.
If I had that exact result I would be fairly certain that the coin is not a fair coin. You can use your binomial function in a spreadsheet or the above link to show that 500 out of 800 is exceedingly unlikely with a 50/50 coin.AT 444/356 you are already looking at a 1 in 1000 fluke with a fair coin. I would have quit way before 500/300.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
August 6th, 2022 at 2:08:33 PM
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I ran a bot on a coin flip site (hedon io) using all these variants mentioned in the comments, it only really works if you apply some sort of martingale in the method, which essentially gives you free flips, and cutting while you're up, starting when there's many reds in a row, and many other factors affect the outcomes.
August 6th, 2022 at 3:58:44 PM
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Thanks Mental for your opinion and the link. What do you think about what I put above?
"If you have play 90.000 of 100.000 hands and you see that player is underreated in 500 hands (39.662 instead of 40.162). Do you think that the probability of having a player in this last 10.000 hands is what shoul be (0.446247) or is a little higher? For me, is a little higher, something around 0.45XXXX."
For sure Baccarat is a -EV game if you play ALL the hands, and now I am trying to figure it out if you can have a little edge (about 0.20%) if only you play certain hands. I have an excel with a little more than 52.000 hands with good results but is still a small sample to have conclusions.
Thanks.
"If you have play 90.000 of 100.000 hands and you see that player is underreated in 500 hands (39.662 instead of 40.162). Do you think that the probability of having a player in this last 10.000 hands is what shoul be (0.446247) or is a little higher? For me, is a little higher, something around 0.45XXXX."
For sure Baccarat is a -EV game if you play ALL the hands, and now I am trying to figure it out if you can have a little edge (about 0.20%) if only you play certain hands. I have an excel with a little more than 52.000 hands with good results but is still a small sample to have conclusions.
Thanks.
August 6th, 2022 at 4:04:07 PM
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Hang on...
are you talking about baccarat, or flipping coins?
They are very different.
are you talking about baccarat, or flipping coins?
They are very different.
May the cards fall in your favor.
August 6th, 2022 at 4:26:40 PM
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Really both, and I don´t feel there are very different, in fact they have a lot in common. But if it is a problem you can edit my last comment and centre in flip coins. No problem for me.
August 6th, 2022 at 4:34:22 PM
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Quote: CristobalReally both, and I don´t feel there are very different, in fact they have a lot in common. But if it is a problem you can edit my last comment and centre in flip coins. No problem for me.
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The math looks vaguely similar, so I understand the confusion.
In actual practice... no.
I've never shuffled coins and dealt them from a shoe, for instance. Nor have I flipped a card to determine heads or tails.
If your interest is in baccarat outcomes, you should probably disregard my opinions on coins as irrelevant.
May the cards fall in your favor.
