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Subject: How high can a Geek count? rss

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Drake Storm
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How much math in a game is too much?

I'm tweaking a card game I designed and I'm wondering if I need to simplify the numbers. Basically you are trying to collect sets (nothing original here) and the incremental value of each additional card increases.

Originally for various sets I had numbers like:

1, 4, 9, 16, 25, 36...
4, 16, 36, 64, 100, 144...
9, 36, 81, 144, 225, 324...

In a typical game you probably get 4-7 sets that need to be added up 3 different times. So 1 round would be adding something like 4+64+81+144+25+108. Not the quickest thing to do in your head.

So in my version #2, I rounded all numbers to the nearest 5, and smoothed out the progressions. So now you get series of numbers like:

5, 10, 15, 25, 35, 45
5, 15, 30, 50, 75, 105
10, 35, 75, 130, 200

Now you have to add something like 10+35+75+130+45. Its easier, but is it too much still?

My next option is to round everything to the nearest 10. That will cause some series of numbers to be very similar (which I was trying to avoid), but should make adding easier. And then if I round to the nearest 10, should I just divide everything by 10 so the numbers are smaller? Is it easier to add 4+8+12+15+7 than 40+80+120+150+70?

When all said and done, if it makes any difference, the game probably won't be appealing to very lite gamers or heavy gamers, but rather more medium weight gamers (whatever that means).

Any suggestions appreciated.
 
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Jason Sadler
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Make it money and people can do the math easier. I do have to admit that it seems like a lot of addition for what seems like a very simple sort of game.

Is there any reason that the sets have to be those numbers? Could they match other ways and have smaller point values added to them. Are you adding them together for a score?
 
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Eric
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If you're targetting medium weight gamers, as you say, I wouldn't include anything too complex math-wise, this will divert from the game. If you need something to calculate the value, I'd go like Carcassonne/Tikal/TtR and have a board where you move your counter for the amount of points to add.

I think that most people won't like to calculate that much, even your simpler example seems a bit too much.

I'd say to keep a fast pace game (at least one that doesn't require a calculator), you'd need to keep the total value to be added under 20-25 at most. Not that people won't be able to count more than than, but most people don't thrust themselves to count. Just the other day, I went to the grocery and bought for 3.61$, paid with a 5$ the clerk typed in 55$, so the return indicated 51.39$. She DID brought out the calculator to see really how much I should get back. shake She couldn't even say "OK, I've typed in 50$ over, let's reduce the amount by 50$ and that's it!", she had to bring the calculator. This is depressing!

Unless your game is for math-freaks, don't do anything too complex math-wise, you'll loose most players.

Again, include money for the counter (let's says you use something like poker chips) and that become easier.
 
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Drake Storm
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I kinda assumed people could do SOME math.

Look at Lost Cities - that is for lite gamers and is very popular. Of course that gives me a headache sometimes... 5+7+9+10-20*2... but my game only has addition not subtraction and multiplication! Now that I think of it, do lite/medium gamers use a calculator for Lost Cities?

My game is purely a card game, so adding money doesn't really make sense. Lost Cities comes with a board that isn't really needed, so I guess I could add some kind of board that helps with the scoring somehow.
 
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David Fair
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DrakeStorm wrote:
Originally for various sets I had numbers like:

1, 4, 9, 16, 25, 36...
4, 16, 36, 64, 100, 144...
9, 36, 81, 144, 225, 324...


Is there a reason that the second line should have the 5th set worth 25 times the value of the first one? That's a pretty huge jump. The third line is proportionatly identical (100/25=4 & 225/25=9). Should the values really ramp up that fast?

If no, I recommend the time-honored pyramidial numbers. Players of Coloretto, Amun-re and Hare & Tortoise have these memorized already:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, etc

(if the progression is not obvious, it is the number of units in a pyramid stack where the size of the bottom row is equal to the position in the order of the list. Thus, for the 5th number, the value is equal to th number of units in a pyramid with 5 units in the bottom row, or 5+4+3+2+1=15, and the next number simply adds 6 to that (15+6=21) and so on.)
 
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Jason Sadler
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Sounds like my money theory was dead on arrival.

Aljovin wrote:
If you're targetting medium weight gamers, as you say, I wouldn't include anything too complex math-wise, this will divert from the game. If you need something to calculate the value, I'd go like Carcassonne/Tikal/TtR and have a board where you move your counter for the amount of points to add.

I think that most people won't like to calculate that much, even your simpler example seems a bit too much.

I'd say to keep a fast pace game (at least one that doesn't require a calculator), you'd need to keep the total value to be added under 20-25 at most. Not that people won't be able to count more than than, but most people don't thrust themselves to count. Just the other day, I went to the grocery and bought for 3.61$, paid with a 5$ the clerk typed in 55$, so the return indicated 51.39$. She DID brought out the calculator to see really how much I should get back. shake She couldn't even say "OK, I've typed in 50$ over, let's reduce the amount by 50$ and that's it!", she had to bring the calculator. This is depressing!

Unless your game is for math-freaks, don't do anything too complex math-wise, you'll loose most players.

Again, include money for the counter (let's says you use something like poker chips) and that become easier.
 
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Bandit Ripshawd
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1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, ... are called triangular numbers, for the record.

The formula for generating the x-th triangular number is (x+1)*(x/2). Thus, the 22nd triangular number would be (22+1)*(22/2) = (23)*(11) = 253.

Sorry, being a math major, I needed to adress this.
 
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Scott Borton
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DrakeStorm wrote:
Now that I think of it, do lite/medium gamers use a calculator for Lost Cities?

I've actually written a Palm program for calculating Lost Cities scores. Not because I'm slow or because I don't have any math skills, but because for some problems a machine is simply faster. But in this case the program is faster only because it knows the rules for scoring and only needs to know which cards are on a player's board, which can be entered quickly enough by using the pen interface.

If I had to use a standard 4-function calculator for LC, I believe that it would be slower-- the overhead of actually typing the numbers would erase any speed benefit the calculator would provide, and I would still have to write down any intermediate steps.
 
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Peter Vrabel
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DrakeStorm wrote:
Or

...

5, 10, 15, 25, 35, 45
5, 15, 30, 50, 75, 105
10, 35, 75, 130, 200

...



All of these numbers are divisible by 5. Is there any reason why you can't divide everything by five, making the numbers smaller and easier to add up?

1, 2, 3, 5, 7, 9
1, 3, 6, 10, 15, 11
2, 7, 15, 26, 50
 
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Scott Borton
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After thinking some more about this, I realized that there are some (many?) "old lady" games which require frequent counting. For example, the French variant of rummy that I'm used to playing only allows players to meld cards if the first set of melds the player makes has a total face value of at least 51, so players are calculating their hand on practically every turn. And this hasn't caused any problems.

My own counting strategy may or may not be efficient (and maybe everyone does this, but I haven't actually needed to discuss it with anyone before now): I first scan the entire series, trying to find combinations that I have internalized. Taking one of your examples, but changing the order for emphasis:

1, 4, 16, 25, 9, 36...

I can immediately spot that 1 + 9 = 10 and 16 + 4 = 20, so I would be able to count 1, 4, 9, and 16 almost instantly. I would then easily calculate that 30+25=55 simply by knowing that adding 10 to anything increases the tens digit of a number. Then it's just matter of breaking down 36 to 30+6, and that results in 55+30+6. I know that 5+6=11, so 55+6 becomes 50+11=61, and 61+30=60+30+1=91. Of course, all this happens at the "hardware" level-- I don't consciously do those calculations.

This strategy begins to fail with numbers like 367 and 123. It's still easy to quickly add those two, but extra steps are needed to break it down into smaller calculations.

The point is that if I were to design a series of numbers that could be quickly added, I would choose numbers that either were part of, or that could quickly be broken down into, the set of mathematical equalities that I have already internalized. One- or two-digit numbers, or numbers that are multiples of 5, would be good candidates for this.
 
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Angus the Bull
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Well, I started counting when I first saw your post. I've gotten to 63,240. I had been able to count 3 to 4 numbers each second at the begining but now with the number being so large it takes me a full second just to say it. I'll let you know high I can count, but I'm going to need to sleep soon.
63,241
63,242
63,243
63,244......

 
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