quick poll

[The_Ditto]

I'm just doing a quick study of something and wanted to gather a good sample of responses .. hoping if you are interested, it's a simple, 1 question poll ..

http://www.easypolls.net/poll.html?p=5dd692d1e4b033f78236d9af


Would appreciate any contributions!

Thank you! ;)

[DeTess]

This question is a bit vague. I assume it's about dice?

[Eldan]

I have no idea what you're asking here. I mean, this depends entirely on the items in question. If I'm offered to get either five or two items, and I don't want any of them, I'l ltake the two, so it's less effort to throw them away. If all the items are valuable, I'll take all five, as even the less good ones still add value.
This question needs more information, is what I'm saying.

[Ninja_Prawn]

Yeah, I can't answer that either. What pool of possible items are these random items drawn from? Do I want all of the possible items or only some? What's the probability of getting a 'good' item? Who decides which two are 'best'? Is there any cost to drawing from this randomiser?

It's gonna depend on what the items are, for sure. If I'm pulling chocolates from a box of Quality Street, I'll keep all five because I can give away the caramels to other people. But if I'm pulling video game weapons from a gacha, I'll keep the two because I don't need low-tier trash cluttering up my inventory. You know?

[The_Ditto]

Consider the items of a class that you are interested in and can use . regardless of their actual type.

Just that some are more valuable than others.

Let's consider trading card game, for example (ie Magic, or Pokemon, etc.) ... think along those lines to make it simpler.

[The_Ditto]

I also posed it on Stack exchange Math forum as a pure Probability question:

https://math.stackexchange.com/questions/3445296/probability-of-a-number-being-larger-than-previous-number

Gives some insight to the actual odds of the difference .. *shrug* :)

[Jay R]

It depends on what kind of items. If it's gemstones or anything else primarily valued for monetary value, then quite probably the five items will be worth more total than the best two of six.

But if it's something that I value some of but not all, like books or games, then I probably have no use for the bottom half, and it would be better to take the best two of six.

----------

Thought experiment: the set of five is chosen by choosing the set of six, and then randomly removing one of them. This is equivalent to choosing five at random, since the sample space is the same, and chosen at the same probabilities.

Then there's a 66.7% probability that I would get my favorite two anyway, plus three more, and I would certainly get at least one of my favorite two (plus four more). So there is a 2/3 probability that choosing the set of five is inherently better than picking two from the set of six.

The remaining 1/3 probability? It's also better if the remaining four items is worth at least as much as my first or second choice.

So I would probably go for the set of five, unless there is a high probability that the #1 or #2 item is worth vastly more than the other four combined. [This would happen if the value of the items to me (which is not inherently the same as its monetary value) has a highly skewed distribution.

Example1: You are choosing from a set of nickels or dimes. Then the value of five of them is always worth more than the value of the best two. I would choose the set of five.

Example2. You are choosing from a set of ten pennies and a $10,000 ruby. I would choose the set of 6, to improve my probability of getting the ruby.

[137beth]

What if the items in question are vague forum polls? Would you rather have the two best vague forum pools, or any five?

[The_Ditto]

Example1: You are choosing from a set of nickels or dimes. Then the value of five of them is always worth more than the value of the best two. I would choose the set of five.

Example2. You are choosing from a set of ten pennies and a $10,000 ruby. I would choose the set of 6, to improve my probability of getting the ruby.

absolutely fair point .. I think that's what I'm seeing in the results to .. mostly it's coming out to a 50:50 split on the options and it's probably based on your examples above .. depends on how people think about it or view it . :)

[Ninja_Prawn]

What if the items in question are vague forum polls? Would you rather have the two best vague forum pools, or any five?

That one's easy: best two. Ain't no one got time for five vague forum polls.

[The_Ditto]

Ok, so interesting results .. not what I expected, however, based on the comments from a few above, I believe it's due to just that .. because some will assume inconsistent values of the rewards ..
That's cool ..

It's basically a 50:50 split ..

https://imgur.com/a/moJ0t8a

[Jay R]

absolutely fair point .. I think that's what I'm seeing in the results to .. mostly it's coming out to a 50:50 split on the options and it's probably based on your examples above .. depends on how people think about it or view it . :)

Yes, well, I’m a statistician. The first thing I did was consider what probability distribution would lead to each choice being optimal.

I suspect most people didn’t analyze it mathematically, but went with their first unconscious assumption about the distribution.

[Knaight]

There's also the matter of resale and how utility distributions don't necessarily line up with value, along with the matter of maintenance costs. For instance, I emphatically do not need five houses. The best 2 of six is one thing (though tax season is still going to hurt), but five? They're hard to offload, they're expensive to be given, they have disgusting maintenance costs, and the way out of that dilemma looks suspiciously like "become a slumlord", which I have some ethical qualms with.

[Eldan]

Yes, well, I’m a statistician. The first thing I did was consider what probability distribution would lead to each choice being optimal.

I suspect most people didn’t analyze it mathematically, but went with their first unconscious assumption about the distribution.

I mean, I attempted a statistical analysis too, but without any values, there's not much point, is there? What were your results?

[Jay R]

I mean, I attempted a statistical analysis too, but without any values, there's not much point, is there? What were your results?

I gave them above. In a distribution with little relative difference between the best and worst outcomes (nickels and dimes), then getting five random results is superior to getting the best two of six random results (a minimum of 25 cents is better than a maximum of 20 cents). In that case, it's better to take the full set of five.

But in a highly skewed distribution, where the highest value is far higher than average values (choosing from ten pennies and a $10,000 ruby), then getting the top two of six values is better, because it has a higher chance of including the ruby. Taking the top two of six random results has an expected value of $5,454.56, while taking all of five random results has an expected value of $4,545.47. For a more spectacular difference, consider the median. If you take the best two of six random results, it's $10,000.01, while the median of taking all of a set of five is $0.05.

[Peelee]

Thought experiment: the set of five is chosen by choosing the set of six, and then randomly removing one of them. This is equivalent to choosing five at random, since the sample space is the same, and chosen at the same probabilities.

Then there's a 66.7% probability that I would get my favorite two anyway, plus three more, and I would certainly get at least one of my favorite two (plus four more). So there is a 2/3 probability that choosing the set of five is inherently better than picking two from the set of six.

The remaining 1/3 probability? It's also better if the remaining four items is worth at least as much as my first or second choice.

So I would probably go for the set of five, unless there is a high probability that the #1 or #2 item is worth vastly more than the other four combined.

OK, but what if I said that you could now keep those five, or you could trade them for first choice in opening up one of three doors?

[Jay R]

OK, but what if I said that you could now keep those five, or you could trade them for first choice in opening up one of three doors?

I know it was a flip comment, but there’s a serious answer:

It depends. Am I currently holding five dimes or a $10,000 ruby?

I won’t trade away a great prize for the unknown.

[Peelee]

I know it was a flip comment, but there’s a serious answer:

It depends. Am I currently holding five dimes or a $10,000 ruby?

I won’t trade away a great prize for the unknown.

You don't know, because that's how Monty do. :smalltongue:

[Ninja_Prawn]

A goat is a blessing that just keeps on giving! As long as you like goat's milk...

[Tarmor]

A goat is a blessing that just keeps on giving! As long as you like goat's milk...
I don't want five goats or the best two! Chickens maybe...