A Paulson color puzzle to pass the pandemic time

One Eyed Dollar

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Maybe this has been answered before, but I didn't find it in a quick search.

Counting base colors and edge spots, what is the fewest number of sample chips you would need to buy to get 1 of each Paulson color?

Which chips would you need?

Just wondering if any of the experts here have assembled a list like that before, out of curiosity.
 

markleteenie

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Maybe this has been answered before, but I didn't find it in a quick search.

Counting base colors and edge spots, what is the fewest number of sample chips you would need to buy to get 1 of each Paulson color?

Which chips would you need?

Just wondering if any of the experts here have assembled a list like that before, out of curiosity.
What's a sample chip?
Real chips, or made up?

If you could make this chip in different configurations, that's 9 colors each....so 10 chips.
1586479149479.png


Unless you can individually configure each of the bear claw spots, then that's 13, so 7.
 
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allforcharity

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I'm pretty sure he means real chips with edge spots, in enough variety to represent all (84? 85?) colours available on the Paulson palette.

To be honest, I have no idea. You might be able to pare it down to about 35 chips or so, if you're lucky?
 

One Eyed Dollar

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Right, like how many individual chips would it take? I guess I mean singles, not samples. Using actual chips.
 

BGinGA

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What's a sample chip?
Real chips, or made up?

If you could make this chip in different configurations, that's 9 colors each....so 10 chips.
View attachment 437279

Unless you can individually configure each of the bear claw spots, then that's 13, so 7.
^^ Correct answer. Although given the thickness of 1/4" spots vs 1/8", I'd say that a set of ten 8a14-spotted chips would be vastly better to represent all 89 colors. Or eleven chips, if you want the base color to be identical on all of them (probably best for actual use).
 

allforcharity

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I highly doubt that there are 11 different existing chips that have all 89 colours represented. I was assuming you were trying to get actual casino chips that could represent all colours through their base colours and edgespots.
 

One Eyed Dollar

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I highly doubt that there are 11 different existing chips that have all 89 colours represented. I was assuming you were trying to get actual casino chips that could represent all colours through their base colours and edgespots.
Right, using existing Paulson chips: casino, fantasy, NAGB, etc.
 

BGinGA

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actual casino chips that could represent all colours through their base colours and edgespots
That's probably closer to 25 total chips. Figure a combination of three-color and four-color chips, covering 89 unique colors.
 

FDLmold

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This is a computation-heavy mathematics problem. Needs lots of inputs too, and a computer.
 

12thMan

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I wonder what the least amount you could do to represent all colors with base colors and spots on chips that are existing right now, not making new ones. Like the big top 5s would knockoff these colors, and maybe a boat chip would knock off some others, and so on until you have all Paulson colors represented over a whole bunch of different casino/fantasy chips.

Would be like a chipper scavenger hunt to have the most unique chips to represent all the different colors.
 

justsomedude

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That's probably closer to 25 total chips. Figure a combination of three-color and four-color chips, covering 89 unique colors.

AS is a good example.

I'm not certain, but I do not think there were any repeating colors in that set. If true, you'd have 26 unique colors spread across 8 chips. Extrapolating that to 89, you should be able to get every Paulson color in 27 chips or so. Which is right in @BGinGA's ballpark.

There are probably more efficient ways of doing it, I was just using AS as an example...

1586495091596.png
 

allforcharity

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AS is a good example.

I'm not certain, but I do not think there were any repeating colors in that set. If true, you'd have 26 unique colors spread across 8 chips. Extrapolating that to 89, you should be able to get every Paulson color in 27 chips or so. Which is right in @BGinGA's ballpark.

There are probably more efficient ways of doing it, I was just using AS as an example...

View attachment 437431

But can you guarantee that there exists another 19 chips that have exactly the missing 63 colours you need spread among them, without duplicates at all? I highly doubt it. Just looking at the sheer number of blue shades alone, there's no way you could avoid duplications of other colours if you could collect every shade in a real chip. That's why I allowed for some slippage when I guessed in mid-30s, and something tells me you may need a few more than that, because some rare colours might be only in a 2- or 3- combo chip that combines with more common colours.
 

justsomedude

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But can you guarantee that there exists another 19 chips that have exactly the missing 63 colours you need spread among them, without duplicates at all?

Really not trying to guarantee anything. I was merely spitballing with the first set that came to mind.

Just looking at the sheer number of blue shades alone, there's no way you could avoid duplications of other colours if you could collect every shade in a real chip.

I dunno; it could be possible. Again, look at AS... there are 6 different shades of blue in that set. Pretty impressive given there are only 8 chips. There are also 3 yellows, 5 pinks, and 4 grays/beiges.
 

redwine

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I spent WAY too much time on this, but I was able to use a greedy approach to get to my current best answer of 39 chips.

I was able to achieve 73 unique colors with just 24 chips, but the next 15 colors each took 1 incremental chip, as I did not have any chip in my database that had 2 or more of those remaining 14 colors.

My database is laughably incomplete derived mostly from this link and various posts on this forum. Obviously, if I had more color information this number will go down. I think the theoretical lower bound would be 22 chips, as a paulson chip can have at most 4 colors(?) and 88/4 = 22.

So the answer is somewhere between 22 and 39.

1597900345979.png


the 15 colors to be represented by an incremental chip: DayBlue, HawaiiFlower, LimeGreen, DolphinBlue, IceBlue, DarkRed, OceanBlue, PastelGreen, ShowboatGrey, DesertFlower, Carrot, Bronze, DarkBrown, LemonGreen, Sunrise
 

FDLmold

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Impressive. Improving your result would require taking those 15 "single" colors and getting an exhaustive list of casino chips they are on, then calculating if you can eliminate any of the first 24 chips as a result.
 

JustDave

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AS is a good example.

I'm not certain, but I do not think there were any repeating colors in that set. If true, you'd have 26 unique colors spread across 8 chips. Extrapolating that to 89, you should be able to get every Paulson color in 27 chips or so. Which is right in @BGinGA's ballpark.

There are probably more efficient ways of doing it, I was just using AS as an example...

View attachment 437431
This is a big part of why i bought a sample.
 

redwine

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Impressive. Improving your result would require taking those 15 "single" colors and getting an exhaustive list of casino chips they are on, then calculating if you can eliminate any of the first 24 chips as a result.

Yes, that would definitely be one way to improve the result.

The overall problem is basically a set-cover optimization problem which is computationally hard. As I gather more color data over time, I'll be monitoring whether I can get the number lower... If I had to guess, the true minimum is probably in the upper-20s.
 

CrazyEddie

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Now cross-index against a database of singles market prices and then re-optimize for price rather than number of chips. :)

I wonder whether the answer turns out to be more expensive than just buying a color sample set off of ebay (or PCF!).
 

allforcharity

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Now cross-index against a database of singles market prices and then re-optimize for price rather than number of chips. :)

I wonder whether the answer turns out to be more expensive than just buying a color sample set off of ebay (or PCF!).

Well, the underside of the going rate for a complete Paulson sample set is $400, so if you needed, say, 40 chips to get all the colours, and you can get them for less than $10 each on average, then you could be good to build your own.

Me, I'd rather have the Paulson set.
 

JustDave

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Well, the underside of the going rate for a complete Paulson sample set is $400, so if you needed, say, 40 chips to get all the colours, and you can get them for less than $10 each on average, then you could be good to build your own.

Me, I'd rather have the Paulson set.
I wanted one until I saw the price.

Made me sad.
 

redwine

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Progress. Found several 38 chip solutions (previous: 39) by adding PNY chips and searching more combinations. One such:

1598063054629.png


the 14 colors to be represented by an incremental chip: DolphinBlue, NavyBlue, BahamaBlue, DarkRed, OceanBlue, PastelGreen, LemonGreen, DesertFlower, Carrot, Bronze, DarkBrown, Maroon, Sunrise, Beige
 
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