"I am playing a fair even money game flipping coins.
My opponent cannot quit. I intend to quit any time I
get one bet ahead. Do I have an advantage?"

Bard:
Yes, you do have an advantage in this scenario. Here's why:
Limited downside: Since you are guaranteed to quit after winning
one bet, your maximum possible loss is limited to losing your initial bet.
Unlimited upside: Your potential winnings, on the other hand, are
unlimited. As long as you keep winning individual flips, you can
keep doubling your money.

Probability still in your favor: Each coin flip is still a 50/50 chance
of winning, favoring you just like even-money odds suggest. So,
statistically speaking, you're more likely to win any individual flip
than lose it.

--
Rich

On 12/30/23 3:50 PM, Rich D wrote:
> "I am playing a fair even money game flipping coins.
> My opponent cannot quit. I intend to quit any time I
> get one bet ahead. Do I have an advantage?"
>
> Bard:
> Yes, you do have an advantage in this scenario. Here's why:
> Limited downside: Since you are guaranteed to quit after winning
> one bet, your maximum possible loss is limited to losing your initial bet.
> Unlimited upside: Your potential winnings, on the other hand, are
> unlimited. As long as you keep winning individual flips, you can
> keep doubling your money.
>
> Probability still in your favor: Each coin flip is still a 50/50 chance
> of winning, favoring you just like even-money odds suggest. So,
> statistically speaking, you're more likely to win any individual flip
> than lose it.
>
>
> --
> Rich

The one issue is that if you do not have an unlimited bankroll, you may
be forced to quit due to running out of money to make bets, with a loss
of your full bankroll. This must be taken into account to compute your
advantage. Of course, if you have unlimited funds, you can reduce the
chance of losses to effectively zero, but it also means that you
winnings, which will be just 1 bet, are an infintesimal fraction of your
bankroll.

You need to do the maths to see if the small chance of losing everything
(or you max losing you are willing to lose) out ways the large chance of
winning the single bet value.

Note, your winnings are limited to a single bet, as your strategy is to
quit after a net winning of just 1 bet. Yes, you might be able to play
again, but that reinstalls the chance of total loss, even of what you
have just won.

I seem to remember, that the maths work out that if you have an N bet
bankroll, and a 50-50 game, there is a 1/(N+1) chance of losing N net
bets before being up 1 bet (and thus an N/(N+1) chance of winning) so
your "advantage"" is 1 * N/(N+1) - N * 1/(N+1) = N(N+1) - N/(N+1) = 0

Thus, as long as you have a finite bankroll, you have no advantage with
this stratagy, which has been used MANY times (when the odds were
slightly against you) to the demise of much money. The Casinos do not
mind this sort of stratagy, as the small wins provide the dopamine hit
to make the people try again, and the house gets to eventually keep the
money.

On December 30, Richard Damon wrote:
>> "I am playing a fair even money game flipping coins.
>> My opponent cannot quit. I intend to quit any time I
>> get one bet ahead. Do I have an advantage?"
>> Bard:
>> Yes, you do have an advantage in this scenario. Here's why:
>> Limited downside: Since you are guaranteed to quit after winning
>> one bet, your maximum possible loss is limited to losing your initial bet.
>> Unlimited upside: Your potential winnings, on the other hand, are
>> unlimited. As long as you keep winning individual flips, you can
>> keep doubling your money.
>> Probability still in your favor: Each coin flip is still a 50/50 chance
>> of winning, favoring you just like even-money odds suggest. So,
>> statistically speaking, you're more likely to win any individual flip
>> than lose it.
>
> The one issue is that if you do not have an unlimited bankroll, you may
> be forced to quit due to running out of money to make bets, with a loss
> of your full bankroll. This must be taken into account to compute your
> advantage. Of course, if you have unlimited funds, you can reduce the
> chance of losses to effectively zero, but it also means that you
> winnings, which will be just 1 bet, are an infintesimal fraction of your
> bankroll.
> Note, your winnings are limited to a single bet, as your strategy is to
> quit after a net winning of just 1 bet. Yes, you might be able to play
> again, but that reinstalls the chance of total loss, even of what you
> have just won.
> Thus, as long as you have a finite bankroll, you have no advantage with
> this stratagy, which has been used MANY times (when the odds were
> slightly against you) to the demise of much money.

um, fascinating.
Did you actually read the question, and answer?
Try again, slowly and carefully -

--
Rich

On 12/30/23 5:59 PM, Rich D wrote:
> On December 30, Richard Damon wrote:
>>> "I am playing a fair even money game flipping coins.
>>> My opponent cannot quit. I intend to quit any time I
>>> get one bet ahead. Do I have an advantage?"
>>> Bard:
>>> Yes, you do have an advantage in this scenario. Here's why:
>>> Limited downside: Since you are guaranteed to quit after winning
>>> one bet, your maximum possible loss is limited to losing your initial bet.
>>> Unlimited upside: Your potential winnings, on the other hand, are
>>> unlimited. As long as you keep winning individual flips, you can
>>> keep doubling your money.
>>> Probability still in your favor: Each coin flip is still a 50/50 chance
>>> of winning, favoring you just like even-money odds suggest. So,
>>> statistically speaking, you're more likely to win any individual flip
>>> than lose it.
>>
>> The one issue is that if you do not have an unlimited bankroll, you may
>> be forced to quit due to running out of money to make bets, with a loss
>> of your full bankroll. This must be taken into account to compute your
>> advantage. Of course, if you have unlimited funds, you can reduce the
>> chance of losses to effectively zero, but it also means that you
>> winnings, which will be just 1 bet, are an infintesimal fraction of your
>> bankroll.
>> Note, your winnings are limited to a single bet, as your strategy is to
>> quit after a net winning of just 1 bet. Yes, you might be able to play
>> again, but that reinstalls the chance of total loss, even of what you
>> have just won.
>> Thus, as long as you have a finite bankroll, you have no advantage with
>> this stratagy, which has been used MANY times (when the odds were
>> slightly against you) to the demise of much money.
>
> um, fascinating.
> Did you actually read the question, and answer?
> Try again, slowly and carefully -
>
> --
> Rich

Yes, it said:

"I am playing a fair even money game flipping coins. My opponent cannot
quit. I intend to quit any time I get one bet ahead. Do I have an
advantage?"

So, the question says the player INTENDS on quiting if they get one bet
ahead, but of course, if they run out of money, they will need to quit,
even if they didn't intend to.

Also, since they intend to quit when they get one bet ahead, the game
WILL stop then.

Ignoring the chance of running out of money has caused many real people
to run out of money.

So, your idea of a limited downside is FALSE, as if they lose the first
bet, either they give up then, and have lost that bet (effectively
saying their bankroll is just one bet), or they continue, and need to
put in another bet, and thus their potential downside increases.

There potential Upside is NOT unlimited, as the strategy says they will
stop when they are up one.

So in truth, they have a strictly limited upside, and a downside limited
only by the max they are willing to lose, as which point they must stop
even though that wasn't in their plan.

On 12/30/23 5:59 PM, Rich D wrote:
> On December 30, Richard Damon wrote:
>>> "I am playing a fair even money game flipping coins.
>>> My opponent cannot quit. I intend to quit any time I
>>> get one bet ahead. Do I have an advantage?"
>>> Bard:
>>> Yes, you do have an advantage in this scenario. Here's why:
>>> Limited downside: Since you are guaranteed to quit after winning
>>> one bet, your maximum possible loss is limited to losing your initial bet.
>>> Unlimited upside: Your potential winnings, on the other hand, are
>>> unlimited. As long as you keep winning individual flips, you can
>>> keep doubling your money.
>>> Probability still in your favor: Each coin flip is still a 50/50 chance
>>> of winning, favoring you just like even-money odds suggest. So,
>>> statistically speaking, you're more likely to win any individual flip
>>> than lose it.
>>
>> The one issue is that if you do not have an unlimited bankroll, you may
>> be forced to quit due to running out of money to make bets, with a loss
>> of your full bankroll. This must be taken into account to compute your
>> advantage. Of course, if you have unlimited funds, you can reduce the
>> chance of losses to effectively zero, but it also means that you
>> winnings, which will be just 1 bet, are an infintesimal fraction of your
>> bankroll.
>> Note, your winnings are limited to a single bet, as your strategy is to
>> quit after a net winning of just 1 bet. Yes, you might be able to play
>> again, but that reinstalls the chance of total loss, even of what you
>> have just won.
>> Thus, as long as you have a finite bankroll, you have no advantage with
>> this stratagy, which has been used MANY times (when the odds were
>> slightly against you) to the demise of much money.
>
> um, fascinating.
> Did you actually read the question, and answer?
> Try again, slowly and carefully -
>
> --
> Rich

And, I will point out that posting bad advice from an AI without comment
isn't a good idea.

As I said, many people have lost a lot of money believing that sort of
lie, and I wouldn't want to be "guilty" of propagating such a misconception.

There are enough idiots in this group, you might get one of them to lose
a lot of money.