Hilarious. Bard AI is as confused as Pickle
From
Bill Vanek@21:1/5 to
All on Tue Dec 19 19:18:07 2023
Holy shit! And people are afraid of AI? The text in quotes is my questions,
and the rest is Bard’s responses. There are also some comments by me, but
you can figure out which is which:
"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?"
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.
However, it's important to note a few caveats:
Unpredictability:While the statistics favor you, each flip is still
independent and there's no guarantee of winning any specific flip. You could encounter a string of losses before getting ahead.
Risk aversion:This strategy carries some risk, as you could potentially lose multiple flips in a row before winning. For risk-averse players, the uncertainty might outweigh the potential gains.
Psychological considerations:The emotional rollercoaster of potentially
winning big quickly followed by potential losses can be intense. Maintaining discipline and sticking to your quitting strategy during potential losing streaks is crucial.
Overall, quitting after one win in a fair coin flip game with even money odds provides an advantage in terms of limiting potential losses and maximizing potential gains. However, it's essential to be aware of the inherent risks
and potential for emotional challenges before adopting this strategy.
Please let me know if you have any further questions or if you'd like me to expand on any of these points.
...
"I said that i quit after i get one bet ahead. how are my potential gains unlimited? also, the bets are limited to one bet unit every flip."
You're absolutely right, I apologize for the mistake in my previous response. In the scenario you described where you quit after getting one bet ahead with
a limited bet size of one unit per flip, your potential gains are not mathematically unlimited. Even though you could theoretically win an infinite number of flips in a row, your actual winnings would be capped at a finite amount due to the fixed bet size.
Here's a breakdown of how your winnings would be calculated:
First win:You win one bet unit.
Second win:You win another bet unit, bringing your total to two units.
Third win:You win one more unit, totaling three units.
And so on...
As you can see, even with a string of consecutive wins, your winnings would
be steadily increasing but ultimately limited by the constant one-unit bet size.
However, even though your total potential gains are not mathematically unlimited, quitting after one win still offers several advantages:
Limited downside:As before, your maximum possible loss is still limited to
one bet unit, regardless of how many flips you lose in a row.
Favorable expected value:In the long run, the even-money odds of each flip
give you a slightly positive expected value, meaning you can expect to win
more than you lose on average.
Psychological benefit:Quitting after one win can help you avoid the emotional trap of chasing losses and potentially overextending yourself.
Therefore, while your potential gains wouldn't be literally unlimited in this specific scenario, quitting after one win can still be a sound strategy with several benefits compared to playing indefinitely.
I hope this clarification is helpful! Please let me know if you have any
other questions.
...
"i said i quit after i am ahead. how are my losses limited to one bet unit?"
You're right, I apologize for the continued confusion! In the scenario where you quit the coin flip game after gaining any advantage, regardless of the size, your potential losses are indeed not limited to just one bet unit.
Here's a breakdown of why:
Variable Win and Loss Points: By quitting whenever you're ahead,the point at which you stop playing varies depending on the outcome of each flip. You
could win on the first flip and quit immediately, minimizing your loss to
just one unit. However, you could also encounter several losing flips before finally winning,accumulating losses beyond a single unit.
Compounding Losses:If you experience a string of losing flips before winning, your losses can snowball.Imagine losing 5 flips in a row before winning;
you'd be down 5 bet units by the time you quit. So,while your maximum loss
per flip remains one unit,your total potential loss can be much higher depending on your luck in the sequence of flips.
Unlimited Play Duration:Since you quit after gaining any advantage, the game can theoretically continue indefinitely. The longer you play, the higher the chances of encountering losing streaks and accumulating larger losses.
Although quitting after any lead offers strategic advantages in terms of maximizing potential gains and controlling the downside to some extent, it's crucial to understand that it doesn't guarantee limiting your losses to just one bet unit.
Here's an analogy to illustrate the point:Imagine playing a game where you
roll a die. On a 1-3, you lose one point. On a 4-5, you gain one point. On a 6,you win and quit. While the average outcome over many rolls favors gaining points, a single unlucky roll of consecutive 1-3s can result in losing more than just one point.
I hope this explanation clarifies the concept.Please let me know if you have any further questions or if you'd like me to elaborate on any specific
aspects.
*****
Okay this is me now. I asked for some math, and Bard provided some below. Tim will know if this is the correct approach to the problem, but Bard at least comes right out and says it is 0 EV.
*****
...
"are you claiming that i would have a positive mathematical expectation? if
so, please show that math."
I apologize for the confusion I caused. My previous answers contained inaccuracies and inconsistencies. To answer your question accurately, I need more information about the specific rules of the coin flip game you're
playing. Here are some additional details that would help me:
Win conditions:How do you determine a "win" in this game? Is it just gaining any lead, regardless of its size, or achieving a specific win target (e.g., doubling your initial bet)?
Stopping rule:Do you have the option to quit at any point during the game, or only after attaining a win?
Bet size:Is the bet size fixed at one unit per flip, or can it dynamically change based on the game state?
Once I have a clearer understanding of these details, I can properly
calculate the mathematical expectation of your strategy and answer your question about whether it has a positive expectation.
Please provide the missing information, and I'll be happy to help you with
the calculations and explanations.
...
"being ahead one bet is a win. i always quit when i am ahead one bet. i can quit at any time, but my opponent cannot quit ever. the bet size cannot change."
Thank you for the additional information! With the clarified rules, we can
now analyze the mathematical expectation of your strategy.
Here's how we can calculate it:
1. Defining States and Probabilities:
States:We can define two states:Ahead (W)andBehind (L).You win (W) by being
one bet ahead,and you lose (L) if you're behind or even.
Probabilities:Each flip is a Bernoulli trial with a 50% chance of heads (win) and 50% chance of tails (loss).
2. Transition Matrix:
The transition matrix shows the probabilities of moving between states in one flip:
Current State
Next State (Heads)
Next State (Tails)
Ahead (W)
Stay Ahead (W)(50%)
Behind (L)(50%)
Behind (L)
Ahead (W)(50%)
Stay Behind (L)(50%)
3. Expected Value per Flip:
Win Value:You win one bet unit when you transition from L to W (50% chance). Loss Value:You lose one bet unit when you transition from W to L (50%
chance).
Expected Value per Flip:E = (Win Value * Win Probability) + (Loss Value *
Loss Probability) = (1 * 0.5) + (-1 * 0.5) =0.
4. Long-Term Average:
Since the expected value per flip is 0,your average winnings or losses over a large number of flips will also be 0.
This means that in the long run,neither player has a mathematical
advantage,and the game is essentially fair.
However, it's important to consider some additional factors:
Variance:While the expected value is 0,there can be significant fluctuations
in winnings and losses in the short term due to the random nature of coin flips.You could have winning streaks or losing streaks that deviate from the average.
Risk Aversion:Even though the expected value is neutral,some players might be averse to the volatility of potential losses and prefer a more stable,albeit potentially lower,return.
In conclusion, although your strategy of quitting after getting ahead one bet offers some psychological and strategic benefits, it does not have a positive mathematical expectation in the long run. Over a large number of flips, you
can expect to break even on average.
I hope this analysis clarifies the situation and provides you with a better understanding of the mathematical implications of your strategy.
--- SoupGate-Win32 v1.05
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From
da pickle@21:1/5 to
Bill Vanek on Wed Dec 20 08:36:03 2023
On 12/19/2023 7:18 PM, Bill Vanek wrote:
Holy shit! And people are afraid of AI? The text in quotes is my questions, and the rest is Bard’s responses. There are also some comments by me, but you can figure out which is which:
I am only "afraid" that AI is causing a lot of lost jobs ...
In conclusion, although your strategy of quitting after getting ahead one bet offers some psychological and strategic benefits, it does not have a positive mathematical expectation in the long run. Over a large number of flips, you can expect to break even on average.
I hope this analysis clarifies the situation and provides you with a better understanding of the mathematical implications of your strategy.
I agree ... in the "long run" (actually over and over again) "you" wind
up even ... ... ... and then you start over again!
[But only if "you" never get +1 along the way.]
I really enjoyed your "results" ... it reminds me of a short story long
ago that I cannot find ... maybe you have read it or can find it.
If I remember correctly, the basic story is about the whole world
finally deciding to build a giant computer and put it in orbit so it can
solve all the problems in the world. It becomes all "powerful" along
the way (it gain control of everything) and answers questions from
earth. One day along the way, one of the operators asks a simple
question ... "Is there a God?" [Those may not be a quote, just what I remember.] A pause and then an answer: "NOW, there is!" [Also may be
slightly different words.]
I have searched and received a lot of stories (especially Asimov) but
not the one I remember. Maybe some AI will work ... what does "it" say
is the answer to that question?
--- SoupGate-Win32 v1.05
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From
da pickle@21:1/5 to
VegasJerry on Wed Dec 20 16:57:32 2023
On 12/20/2023 3:38 PM, VegasJerry wrote:
On Wednesday, December 20, 2023 at 1:12:17 PM UTC-8, da pickle wrote:
On 12/20/2023 3:10 PM, VegasJerry wrote:
On Tuesday, December 19, 2023 at 5:18:14 PM UTC-8, Bill Vanek wrote:
Holy shit! And people are afraid of AI? The text in quotes is my questions,
and the rest is Bard’s responses. There are also some comments by me, but
you can figure out which is which:
"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?" >>>>
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.
However, it's important to note a few caveats:
Unpredictability:While the statistics favor you, each flip is still
independent and there's no guarantee of winning any specific flip. You could
encounter a string of losses before getting ahead.
Risk aversion:This strategy carries some risk, as you could potentially lose
multiple flips in a row before winning. For risk-averse players, the
uncertainty might outweigh the potential gains.
Psychological considerations:The emotional rollercoaster of potentially >>>> winning big quickly followed by potential losses can be intense. Maintaining
discipline and sticking to your quitting strategy during potential losing >>>> streaks is crucial.
Overall, quitting after one win in a fair coin flip game with even money odds
provides an advantage in terms of limiting potential losses and maximizing >>>> potential gains. However, it's essential to be aware of the inherent risks >>>> and potential for emotional challenges before adopting this strategy.
Please let me know if you have any further questions or if you'd like me to
expand on any of these points.
...
"I said that i quit after i get one bet ahead. how are my potential gains >>>> unlimited? also, the bets are limited to one bet unit every flip."
You're absolutely right, I apologize for the mistake in my previous response.
In the scenario you described where you quit after getting one bet ahead with
a limited bet size of one unit per flip, your potential gains are not
mathematically unlimited. Even though you could theoretically win an infinite
number of flips in a row, your actual winnings would be capped at a finite >>>> amount due to the fixed bet size.
Here's a breakdown of how your winnings would be calculated:
First win:You win one bet unit.
Second win:You win another bet unit, bringing your total to two units. >>>> Third win:You win one more unit, totaling three units.
And so on...
As you can see, even with a string of consecutive wins, your winnings would
be steadily increasing but ultimately limited by the constant one-unit bet >>>> size.
However, even though your total potential gains are not mathematically >>>> unlimited, quitting after one win still offers several advantages:
Limited downside:As before, your maximum possible loss is still limited to >>>> one bet unit, regardless of how many flips you lose in a row.
Favorable expected value:In the long run, the even-money odds of each flip >>>> give you a slightly positive expected value, meaning you can expect to win >>>> more than you lose on average.
Psychological benefit:Quitting after one win can help you avoid the emotional
trap of chasing losses and potentially overextending yourself.
Therefore, while your potential gains wouldn't be literally unlimited in this
specific scenario, quitting after one win can still be a sound strategy with
several benefits compared to playing indefinitely.
I hope this clarification is helpful! Please let me know if you have any >>>> other questions.
...
"i said i quit after i am ahead. how are my losses limited to one bet unit?"
You're right, I apologize for the continued confusion! In the scenario where
you quit the coin flip game after gaining any advantage, regardless of the >>>> size, your potential losses are indeed not limited to just one bet unit. >>>>
Here's a breakdown of why:
Variable Win and Loss Points: By quitting whenever you're ahead,the point at
which you stop playing varies depending on the outcome of each flip. You >>>> could win on the first flip and quit immediately, minimizing your loss to >>>> just one unit. However, you could also encounter several losing flips before
finally winning,accumulating losses beyond a single unit.
Compounding Losses:If you experience a string of losing flips before winning,
your losses can snowball.Imagine losing 5 flips in a row before winning; >>>> you'd be down 5 bet units by the time you quit. So,while your maximum loss >>>> per flip remains one unit,your total potential loss can be much higher >>>> depending on your luck in the sequence of flips.
Unlimited Play Duration:Since you quit after gaining any advantage, the game
can theoretically continue indefinitely. The longer you play, the higher the
chances of encountering losing streaks and accumulating larger losses. >>>>
Although quitting after any lead offers strategic advantages in terms of >>>> maximizing potential gains and controlling the downside to some extent, it's
crucial to understand that it doesn't guarantee limiting your losses to just
one bet unit.
Here's an analogy to illustrate the point:Imagine playing a game where you >>>> roll a die. On a 1-3, you lose one point. On a 4-5, you gain one point. On a
6,you win and quit. While the average outcome over many rolls favors gaining
points, a single unlucky roll of consecutive 1-3s can result in losing more
than just one point.
I hope this explanation clarifies the concept.Please let me know if you have
any further questions or if you'd like me to elaborate on any specific >>>> aspects.
*****
Okay this is me now. I asked for some math, and Bard provided some below. Tim
will know if this is the correct approach to the problem, but Bard at least
comes right out and says it is 0 EV.
*****
...
"are you claiming that i would have a positive mathematical expectation? if
so, please show that math."
I apologize for the confusion I caused. My previous answers contained
inaccuracies and inconsistencies. To answer your question accurately, I need
more information about the specific rules of the coin flip game you're >>>> playing. Here are some additional details that would help me:
Win conditions:How do you determine a "win" in this game? Is it just gaining
any lead, regardless of its size, or achieving a specific win target (e.g.,
doubling your initial bet)?
Stopping rule:Do you have the option to quit at any point during the game, or
only after attaining a win?
Bet size:Is the bet size fixed at one unit per flip, or can it dynamically >>>> change based on the game state?
Once I have a clearer understanding of these details, I can properly
calculate the mathematical expectation of your strategy and answer your >>>> question about whether it has a positive expectation.
Please provide the missing information, and I'll be happy to help you with >>>> the calculations and explanations.
...
"being ahead one bet is a win. i always quit when i am ahead one bet. i can
quit at any time, but my opponent cannot quit ever. the bet size cannot >>>> change."
Thank you for the additional information! With the clarified rules, we can >>>> now analyze the mathematical expectation of your strategy.
Here's how we can calculate it:
1. Defining States and Probabilities:
States:We can define two states:Ahead (W)andBehind (L).You win (W) by being
one bet ahead,and you lose (L) if you're behind or even.
Probabilities:Each flip is a Bernoulli trial with a 50% chance of heads (win)
and 50% chance of tails (loss).
2. Transition Matrix:
The transition matrix shows the probabilities of moving between states in one
flip:
Current State
Next State (Heads)
Next State (Tails)
Ahead (W)
Stay Ahead (W)(50%)
Behind (L)(50%)
Behind (L)
Ahead (W)(50%)
Stay Behind (L)(50%)
3. Expected Value per Flip:
Win Value:You win one bet unit when you transition from L to W (50% chance).
Loss Value:You lose one bet unit when you transition from W to L (50%
chance).
Expected Value per Flip:E = (Win Value * Win Probability) + (Loss Value * >>>> Loss Probability) = (1 * 0.5) + (-1 * 0.5) =0.
4. Long-Term Average:
Since the expected value per flip is 0,your average winnings or losses over a
large number of flips will also be 0.
This means that in the long run,neither player has a mathematical
advantage,and the game is essentially fair.
However, it's important to consider some additional factors:
Variance:While the expected value is 0,there can be significant fluctuations
in winnings and losses in the short term due to the random nature of coin >>>> flips.You could have winning streaks or losing streaks that deviate from the
average.
Risk Aversion:Even though the expected value is neutral,some players might be
averse to the volatility of potential losses and prefer a more stable,albeit
potentially lower,return.
In conclusion, although your strategy of quitting after getting ahead one bet
offers some psychological and strategic benefits, it does not have a positive
mathematical expectation in the long run. Over a large number of flips, you
can expect to break even on average.
I hope this analysis clarifies the situation and provides you with a better
understanding of the mathematical implications of your strategy.
.
Interesting interaction. I’ve programed but this AI programming is astounding. (But then, I was dazzled by Facial Recognition). I can’t begin to think the programming necessary. But your interaction shows some of this AI’s difficulty when you
must bring attention to its errors. There seems to be a depth (my word) problem. But then, it’s been stated the AIs available to us are more shallow (my word) than their advanced ones.
When I signed up to play with Chatbot AI, it said they could not guarantee what Chatbot may do with my name and information as their control of it isn’t absolute. It’s been noted that it will lie. (It will cite non-existent sites as sources of
proof). Apparently learned by seeing people lie. (“Lying is acceptable, so I, too, can lie.”) These errors you encountered may be an offshoot of that, in that it admits to errors it should have known by calling them ‘confusion, inaccuracies and
inconsistencies.’
Thanks for posting that..
.
I agree ... it was very interesting.
.
I still don’t understand the ‘fear’ of AI. As a cartoon once showed a person standing by a cord coming from a big AI computer, and them simply “pulling the plug out of the wall socket.”
The gloom and doom seem overblown and meant for attention (and perhaps, investors). As for job losses, computers (and automation) have been doing that for years. I remember when there were Elevator Operators. And I remember one of them remarking how
happy she was that they put in a folding-down seat for her to sit on.
“Floor please?” went the same way as our telephone operator that used to request, “Number please?” (Yet my job with Western Electric was installing step-dialing systems).
On the high end, they wring their hands at AI taking over the power system and blacking out the country. As I’ve pointed out before, I use to run the Western Grid. (Bonneville Power Administration @ Vancouver Washington). Even I could not black out
the system, it is too well protected and would automatically drop into isochronous systems.
Now in the middle, it seems script writers worry about inventive complex story lines. And (as a filed writer myself) there may be something to that. The inventive mind doesn’t necessarily need to be human…
Very interesting comments. I agree the internet and now AI are
contributing to the loss of many jobs. It is hard now to find a
"person" top talk to ... the robot wants to answer all your questions.
I too remember telephone operators and party line and extensions.
The power of an "education" is changing too ... the "education" is
changing too. STEM does not seem as important as it once was.
Do you think we should morn the lost of handwriting? And knowing your multiplication tables? And many other lost pieces of education.
It is nice to discuss something so interesting without the rancor.
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