Giveaway Help me with GTO giveaway stats (1 Viewer)

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casinochipper22

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OK, so I can't stop thinking about this. I know I'm not smart enough to answer myself, so maybe someone out there can help me with the math or strategy (if there is one) @BlueMerle was kind enough to do this giveaway. https://www.pokerchipforum.com/threads/i-am-giving-away-free-beaver.86822/

Rules...
1. A random number between 1-100 is established.

2. To win you have to be the first to guess the random number between 1 and 100, and then game is over

3. Players make their guess one at a time.

Question, you have the option to choose when you make your guess. First or last or somewhere in the middle. What is best?


This was an amazing twist to a giveaway and did anyone else go down the rabbit hole of what is the optimum time to make a guess (I didn't comment on the OP bc I didn't need the chips. But I was puzzled at when I should guess if I was trying to win) If you guess first, you are guaranteed first crack at winning, but your odds are 1x100 or 1%. If you wait, and guess 20th, then your odds are 1.25%. If you wait to guess at fifty, your odds are doubled to 2%. But you risk the other 49 guesses coming up winners.

What is the math here? If any. And when would you make your guess if you had a choice? Lets say there is a million on the line...do you guess first? or 20th? or when is the best time to throw your hat in the ring???

I will giveaway two live vegas one dollar chips. Shipped free in CONUS. I'll leave this post up for 24 hours. Any comment will get you an entry into this drawing. But I'm really just looking for some good will hunting type answer to this. I won't be able to sleep at night if I don't do this.
 
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casinochipper22

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it feels like the risk of letting someone guess before you doesn't outwiegh the benefits of one less number out of the pool to guess from. I'm leaning towards first. but I still don't know.
 

khp

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I think the odds of being able to guess is calculated like this:

If you guess second, you have a 99/100 chance of being allowed to guess.

If you guess third, you have a 99/100 x 98/99 chance of being allowed to guess and so on.

There’s also psychology to consider - people, in general, are less likely to choose 1 and 100, or even 1-5, and 96-100. If you weight these in then the math is a bit different and not pure anymore.

Given these, I would venture that it’s optimal to make your guess somewhere when you have a ~70% chance of being allowed to guess. Better statisticians please chime in!


Lastly, if you know anything about the poster, say the year he was born, or the year in which his wife/kids were born, you also have a higher than expected shot of getting the number right. (Or the year in which his favourite team last won a championship, etc etc)
 
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I don't understand how one's odds improve with other people taking numbers. Certainly there are fewer numbers available, but one doesn't have any idea whether one of the existing guesses is the correct answer.
 

casinochipper22

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I don't understand how one's odds improve with other people taking numbers. Certainly there are fewer numbers available, but one doesn't have any idea whether one of the existing guesses is the correct answer.
well it would just end and you loose and don't even have a chance to guess. That is the risk you are taking by not guessing first.
 

khp

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I don't understand how one's odds improve with other people taking numbers. Certainly there are fewer numbers available, but one doesn't have any idea whether one of the existing guesses is the correct answer.
Let’s say there are two numbers. I guess 1. The game hasn’t ended because a winner hasnt been declared. What are your odds of winning if you make the next guess?
 

ktran

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I figure it's better to guess early. If you wait someone else could guess it and outweighs the slight increase of odds. Even if you get better odds other waiters will get the odds too. It's exponential gets worse I believe to wait and pick. Factors of waiting depends too. Well in this case, there would be potential more than 100 guessing so it's probably better to guess first. If it's not a limited number of people, it's just a race of who can post it. If it's a guess of #1-100 and there's 100 people limited guessing, I could see waiting to be better.
 

TheOffalo

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I don't understand how one's odds improve with other people taking numbers. Certainly there are fewer numbers available, but one doesn't have any idea whether one of the existing guesses is the correct answer.
I think it depends on the format of the game. If people are just picking numbers and the winning number is declared at the end then there’s no advantage (that I can think of off the top of my head), but if the game is over once someone guesses the right answer then it’s a balance of a higher chance of guessing correct vs a higher chance of the game ending before you can guess, as the OP describes.
 

khp

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I think the odds of being able to guess is calculated like this:

If you guess second, you have a 99/100 chance of being allowed to guess.

If you guess third, you have a 99/100 x 98/99 chance of being allowed to guess and so on.

There’s also psychology to consider - people, in general, are less likely to choose 1 and 100, or even 1-5, and 96-100. If you weight these in then the math is a bit different and not pure anymore.

Given these, I would venture that it’s optimal to make your guess somewhere when you have a ~70% chance of being allowed to guess. Better statisticians please chime in!


Lastly, if you know anything about the poster, say the year he was born, or the year in which his wife/kids were born, you also have a higher than expected shot of getting the number right. (Or the year in which his favourite team last won a championship, etc etc)

I just “mapped” this in excel because I was curious and now I think I might be wrong.

So you have a 99/100 chance of being allowed to guess second and a 98/99 x 99/100 chance of being allowed to guess third. But actually this just means you have a 98% chance to guess third, 97% chance to guess fourth, etc. Each guess made decreases the chance you’re allowed to guess by 1%.

Then, as you’ve noted, if the number was truly chosen at random, then you have an increasing chance to guess it correctly.

However, if you calculate expected value as % chance you’re allowed to guess multiplied by the increasing probability of guessing correctly as there are fewer numbers, you actually get back to an EV of 1%, implying it doesn’t matter when you guess.
 

khp

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I just “mapped” this in excel because I was curious and now I think I might be wrong.

So you have a 99/100 chance of being allowed to guess second and a 98/99 x 99/100 chance of being allowed to guess third. But actually this just means you have a 98% chance to guess third, 97% chance to guess fourth, etc. Each guess made decreases the chance you’re allowed to guess by 1%.

Then, as you’ve noted, if the number was truly chosen at random, then you have an increasing chance to guess it correctly.

However, if you calculate expected value as % chance you’re allowed to guess multiplied by the increasing probability of guessing correctly as there are fewer numbers, you actually get back to an EV of 1%, implying it doesn’t matter when you guess.
Examples:
(Chance you’re allowed to guess) x (Chance of getting it right)


If you guess second:
(99/100)(1/99) = 1%

If you guess third
[(99/100)(98/99)](1/98) = 1%

If you guess 21st
(99/100)(98/99)….(1/80) = 1%
 

casinochipper22

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I think it depends on the format of the game. If people are just picking numbers and the winning number is declared at the end then there’s no advantage (that I can think of off the top of my head), but if the game is over once someone guesses the right answer then it’s a balance of a higher chance of guessing correct vs a higher chance of the game ending before you can guess, as the OP describes.
Sorry I didn't make it clear. To win you have to guess the random number (1-100 first.) Guesses are made one at a time. There are 100 people total. You have the option to pick any number you want, and you also have the option to pick when you make your pick. That is the question I'm asking. With those rules, it's it best to pick first. It wait until others have made their picks.
 

casinochipper22

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I think it depends on the format of the game. If people are just picking numbers and the winning number is declared at the end then there’s no advantage (that I can think of off the top of my head), but if the game is over once someone guesses the right answer then it’s a balance of a higher chance of guessing correct vs a higher chance of the game ending before you can guess, as the OP describes.
And yes. When number is hit. Game is over
 

casinochipper22

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I just “mapped” this in excel because I was curious and now I think I might be wrong.

So you have a 99/100 chance of being allowed to guess second and a 98/99 x 99/100 chance of being allowed to guess third. But actually this just means you have a 98% chance to guess third, 97% chance to guess fourth, etc. Each guess made decreases the chance you’re allowed to guess by 1%.

Then, as you’ve noted, if the number was truly chosen at random, then you have an increasing chance to guess it correctly.

However, if you calculate expected value as % chance you’re allowed to guess multiplied by the increasing probability of guessing correctly as there are fewer numbers, you actually get back to an EV of 1%, implying it doesn’t matter when you guess.
You only get one guess. I'm just asking when would be the best time to guess if you had a choice.
 

TheOffalo

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Interesting, so it’s neither live guesses nor a wait-until-end reveal, but rather the guesses are processed in (requested?) order? But you can’t request first to guess last, can you?

Or you’re picking your spot in line basically.
 

casinochipper22

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Interesting, so it’s neither live guesses nor a wait-until-end reveal, but rather the guesses are processed in (requested?) order? But you can’t request first to guess last, can you?

Or you’re picking your spot in line basically.
Sorry. I updated the op with rules. I didn't make it clear. I just was going off the rules for the original giveaway
 

khp

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I know. I’m saying it doesn’t matter when you guess - the expected value is always 1%
@casinochipper22 your question in the OP is a bit more complicated than meets the eye.

If no one has guessed yet, and you’re asking when is the best time to guess, then I would say it doesn’t matter - any strategy has an EV of 1% - whether you guess first or 21st or last (because there’s a low probability that the game makes it that far).

If people have already guessed, then the EV would still be the same whether you wait or guess immediately, though the EV would be higher than 1% because there are now fewer numbers. This is balanced by the “risk” you took by waiting to guess.
 
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casinochipper22

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I figure it's better to guess early. If you wait someone else could guess it and outweighs the slight increase of odds. Even if you get better odds other waiters will get the odds too. It's exponential gets worse I believe to wait and pick. Factors of waiting depends too. Well in this case, there would be potential more than 100 guessing so it's probably better to guess first. If it's not a limited number of people, it's just a race of who can post it. If it's a guess of #1-100 and there's 100 people limited guessing, I could see waiting to be better.
Random # generator came up with #7.
Thanks for the input everyone.
 
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