Flipping coin challenge

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.

Quote: Cristobal

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.
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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.

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.

Quote: unJon

He’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.

Quote: Cristobal

Quote: AlanMendelson

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?
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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.
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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.

Quote: Ace2

500 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.

Quote: DRich

Quote: unJon

He’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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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: AxelWolf

Quote: DRich

Quote: unJon

He’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

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.
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Feels like you all missed the key part of the the hypo. The word, friend.

Quote: Wizard

Quote: Ace2

500 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.

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?

We have a guy here somewhere who's claiming he is beating baccarat with something like 8 standard deviations above.

Quote: unJon

Quote: AxelWolf

Quote: DRich

Quote: unJon

He’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

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.
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.