Cristobal
Cristobal
Joined: Jul 21, 2022
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August 5th, 2022 at 7:04:43 PM permalink
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.
Dieter
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Dieter
Joined: Jul 23, 2014
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Thanks for this post from:
Cristobal
August 5th, 2022 at 7:22:30 PM permalink
Quote: Cristobal


What would you do? Stay in head or switch to tail?

Thanks.
link to original post



I am probably OK to switch.
I don't think the coin is biased.
May the cards fall in your favor.
unJon
unJon
Joined: Jul 1, 2018
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Thanks for this post from:
pwcrabb
August 5th, 2022 at 7:53:31 PM permalink
Heís your friend. Heís 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.
AlanMendelson
AlanMendelson
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August 5th, 2022 at 8:12:18 PM permalink
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?
Cristobal
Cristobal
Joined: Jul 21, 2022
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August 5th, 2022 at 9:11:53 PM permalink
Quote: unJon

Heís your friend. Heís down. He wants to switch. You should switch.
link to original post



hahahahahaa you have a point.
Cristobal
Cristobal
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August 5th, 2022 at 9:14:24 PM permalink
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?
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.
Ace2
Ace2
Joined: Oct 2, 2017
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August 5th, 2022 at 9:29:56 PM permalink
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 wouldnít worry about it. Youíre 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 itís a fair coin, thereís no reason to switch. Dice and coins have no memory. Believing otherwise is called gamblerís fallacy, probably the most common fallacy in gambling, hence the name
Itís all about making that GTA
Cristobal
Cristobal
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August 5th, 2022 at 9:57:37 PM permalink
Quote: Ace2

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 wouldnít worry about it. Youíre 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 itís a fair coin, thereís no reason to switch. Dice and coins have no memory. Believing otherwise is called gamblerís fallacy, probably the most common fallacy in gambling, hence the name
link to original post



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.
Ace2
Ace2
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August 5th, 2022 at 10:54:11 PM permalink
Quote: Cristobal

Quote: Ace2

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 wouldnít worry about it. Youíre 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 itís a fair coin, thereís no reason to switch. Dice and coins have no memory. Believing otherwise is called gamblerís fallacy, probably the most common fallacy in gambling, hence the name
link to original post



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.
link to original post

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 percent

Expectation increases linearly with trials but SD increases by square root of trials. Thatís 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 itís basic statistics that can be proven, is vehemently denied by several forum members
Itís all about making that GTA
Dieter
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Dieter
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August 6th, 2022 at 1:00:59 AM permalink
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?
link to original post



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.

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