Charlie Sundt
United Kingdom London
www.fictionontheweb.co.uk

Not all patches are created equal.
This thread has a good analysis of how to maximise your quiltmaking efficiency. Building on that, I did a quick analysis of the highest and lowest value pieces in a couple of different ways.
There are other factors to consider as well as the value of the pieces, such as what shapes work best for you, and how to create opportunities for yourself and limit opportunities for your opponent. But hopefully some of you will find this of interest.
This first image shows relative value of patches (space covered minus button cost), sorted without factoring in button income or time spent  so the patches in the top left are more or less the best ones to buy in the endgame, and the ones in the bottom right are the worst. Click here to see it full size.
The second image shows maximum potential value of patches factoring in time spent (space covered minus button cost minus time spent plus button income x 9)  so top left patches are more or less the best to buy at the start of the game, and bottom right are the worst. Click here to see it full size.

Frazer Eden
United Kingdom Cheshire

Some quite interesting analysis you have made. I always put more value into time than button cost so for example, out of your three "2" value tiles I would rate the cheaper time tile higher

Vincent White
United States Chestnut Hill Massachusetts

The x9 is a little deceptive as some of these you likely can't afford until you are past the first payout already. Curious how the values change if you x9 if cost 5 or less and x8 if more than 5.

Charlie Sundt
United Kingdom London
www.fictionontheweb.co.uk

vinniebrasco wrote: The x9 is a little deceptive as some of these you likely can't afford until you are past the first payout already. Curious how the values change if you x9 if cost 5 or less and x8 if more than 5.
If you factor in affordability at the beginning of the game, the maximum potential value of the patches only changes by one so the general picture looks very similar.
The best two pieces that are affordable right at the beginning of the game are in the bottom left of the second picture  the spaceinvadershape worth 21, and the crossshape worth 19.

Devin Smith
England Southampton Hampshire

Minus time spent isn't the the relevant mathematical operation. You want divided by time, instead: points per unit time.



If you only count each unit of time as equivalent to one button, you're significantly undervaluing time.

Adam Frandsen
United States Eagle Mountain UT

Excalabur wrote: Minus time spent isn't the the relevant mathematical operation. You want divided by time, instead: points per unit time.
Exactly right. It's unfortunate to have to undermine the original poster's efforts, but the above pictures are completely meaningless.
Look at the highestrated patch, for example (the topleft in the second picture, costing 8 buttons and 6 time). In reality, this highestrated patch is less valuable than several others. Its true maximum value is 39÷6, or 6.5 points per unit of time spent.
For comparison, one of the other patches can earn a whopping 12 points per unit of time spent! Yet it was given a mediocre rating in the second picture (bottom center patch costing 7 buttons, 1 time). I don't know for sure, but I think that one might be the "true" mvp (most valuable patch). However, don't be deceived: the real weakness of this patch is that it costs a lot of buttons (for early/mid game), yet doesn't move you very far on the time track. So if you aren't careful when you buy it, you can easily run low on buttons and still be several spaces away from your next income space. (Your options will be severely limited, especially against a canny opponent, and you'll probably have to jump ahead on your next move, earning a measly 1 point per unit of time spent, which will undermine the good return you got on this patch in the first place.)
In other words, even the "best" patch is not truly the best. In my estimation, if you want to play well, you shouldn't rate patches based on numerical calculations alone. This game has a lot more subtlety than that. Don't miss all of its juicy brilliance by getting too hung up on numbers! It pays to think more abstractly, or in other dimensions.
P.S. If anyone does decide to recalculate the maximum values of the patches, pay attention to the patches costing 10 buttons. As an earlier poster has said, it's impossible to earn their button income all 9 times.

Frederik Verf
Netherlands

Dear commenters. I have another alternative view. I would not say points per time is the best way to calculate the best pieces. I think that will overrate time as importance in deciding which pieces are best. For example a tile will be twice as bad if it costs two time instead of 1, and will only be half as bad if the tile costs 3 time instead of 2. Therefore i measured a rating of time as 1:1.66. Altough this rating is arbitrary i think it is better than both mentioned options since 1:1 is bad since time is more costly than buttons and points divided by time overrates the importance of time and gives it a weird nonlinear scale. The rating of 1:1.66 is made by dividing the most costly button price of 10 by the most costly time price of 6. I know this is not perfect and arbitrary but I think it is fairly accurate. I also think the maximum potential value is flawed and therefore just took the average of 5. (9! Divided by 9 is five) If you do this you get the following formula
Relative value= 2 times amount of tiles plus 5 times amount of buttons minus button costs minus 1.66 times amount of time costs.
You then get the following values, with three photos, of the best third, the medium third and the worst third: (in opposite arrangement, i clicked the wrong photo first haha)

neko flying
Germany Berlin Berlin

freekhoorn wrote: Relative value= 2 times amount of tiles plus 5 times amount of buttons minus button costs minus 1.66 times amount of time costs.
Subtracting time from points does not make any sense. The reason you want to divide by time is that the game is about converting time into points. Hence why you want to take the ratio. Two tiles that take T time each and give P points each are equivalent to a single tile that takes 2*T time and gives 2*P points. If your formula says otherwise, it is wrong.
(In addition, buttons are not worth 5 points each. They are worth much more at the beginning of the game and much less at the end.)



I still like the method I worked out:
https://boardgamegeek.com/article/24701397#24701397
It is almost exactly the same as the thread linked above: https://boardgamegeek.com/thread/1307009/patchworktacticma...
The key difference is the pause I take for "net yield" before diving by time. It quickly helps me spot both an efficient piece, but also a BIG GAIN piece. When choosing between relatively close alternatives, it's important to recognize which ones are of close efficiency (and good), but get you more gain.
I suppose if I played enough I would just have the pieces memorized, and know which are the best ones. My method helps me spot them as if I have no prior knowledge.

Grant
United States Cuyahoga Falls Ohio
One of the best gaming weekends in Ohio since 2010. Search facebook for "BOGA Weekend Retreat" for more info!

freekhoorn wrote: For example a tile will be twice as bad if it costs two time instead of 1 A tile that costs 2 time IS twice as bad as an identical tile that costs 1 time. I think you may have approached this whole exercise with a faulty premise.

Frederik Verf
Netherlands

I do not agree, since there are a lot of other things that also factor in effectiveness of a tile. However even if you do agree with that, you wont agree that the difference between 2 and 3 should be less than the difference between 1 or 2 or do you?

neko flying
Germany Berlin Berlin

freekhoorn wrote: the difference between 2 and 3 should be less than the difference between 1 or 2
If the value in victory points of the tiles is the same, say 12 points, and they cost 1, 2, and 3 time, then the value of a tile per time unit is:
12 VP / (1 t) = 12 VP/t 12 VP / (2 t) = 6 VP/t 12 VP / (3 t) = 4 VP/t
Therefore, there is a bigger difference between the tile the costs 1 and the tile that costs 2 than between the tile that costs 2 and the tile that costs 3.

Frederik Verf
Netherlands

Thats what i mean. I meant to say with that that time is overrated in this equation and also has a nonlinear scale. Do you really want to say that you cannot measure the cost of one step of time? I know your maths, but doesnt it feel weird and makes time too important in this measurement (that is already arbitrary anyway)?

Grant
United States Cuyahoga Falls Ohio
One of the best gaming weekends in Ohio since 2010. Search facebook for "BOGA Weekend Retreat" for more info!

freekhoorn wrote: Thats what i mean. I meant to say with that that time is overrated in this equation and also has a nonlinear scale. Do you really want to say that you cannot measure the cost of one step of time? I know your maths, but doesnt it feel weird and makes time too important in this measurement (that is already arbitrary anyway)? Time and buttons are both quantifiable, and they're also both different units of measure. You can't just add and subtract them from each other. What does "overrated" or "too important" mean in this context? You're trying to have a mathematical discussion but you're using illdefined terms and gut feeling rather than obviously true equations. You can't just arbitrarily combine things in illogical ways until you think they "feel right."

Grant
United States Cuyahoga Falls Ohio
One of the best gaming weekends in Ohio since 2010. Search facebook for "BOGA Weekend Retreat" for more info!

freekhoorn wrote: I do not agree, since there are a lot of other things that also factor in effectiveness of a tile. Who are you saying you don't agree with here? I suggest you start using quotes so people can tell who you're talking to. If you're replying to me, I was clearly talking about identical tiles that only differed in their time cost, so no, there are NOT "a lot of other things that also factor in effectiveness" in that scenario.
Quote: However even if you do agree with that, you wont agree that the difference between 2 and 3 should be less than the difference between 1 or 2 or do you? The differences are exactly what the equations show them to be, as neko illustrated. I don't understand what you even mean by what they "should" be. There's no "should" in math, just "is" and "isn't".

neko flying
Germany Berlin Berlin

freekhoorn wrote: Thats what i mean. I meant to say with that that time is overrated in this equation and also has a nonlinear scale.
Overrated with respect to what? The utility of the "value per time" metric is that you can use it to estimate your points as:
Points = (time elapsed) x (average tile value/time) + bonuses  157.
Since the time elapsed is always the same (except on the very last move), you basically have:
Points at endgame = (5460) x (average tile value/time) + bonuses  157.
Which is a useful equation: Obviously the "average tile value/time" is the main factor determining how many points you will score at the end.
Your metric of "value minus time" does not relate in any clear way to your final score at the end of the game.


