Points per time?

[Sombra rose]

I read this somewhere and as a new player to patch work I'd like to know what the experts mean by this to try and push to the 400s
Ty

[Suoivax]

it refers to how many points you are getting compared to how far you move on the "time/turn" board.

[adeodatus243]

The game can be divided into three phases: opening, middle, and end. These are related to the three primary restrictions on taking & placing pieces: button limitations, time limitations, and space limitations. In the opening you're button-restricted. You have limited income, so you'll probably pass for buttons several times. This means time is interchangeable for buttons. To evaluate pieces in the opening, divide the sum of the button cost and the time cost by the button income they give. This gives the payback time—how many button incomes will it take to recoup your investment in that piece. In the early game, the 3-6 and the 7-2 are about the same value—they each give two button income and cost nine buttons+time, for a payback time of 4.5. This doesn't mean you ignore patch size completely—always take the largest patch for the value, and occasionally I'll take a really good 0-button piece for a reason other than just getting to a valuable piece, but that's the guiding factor. This usually ends around the fourth income space. At that point you should mostly be able to buy the pieces you want without much passing for buttons.

The second phase is the middle game. Here the value function is a bit more complicated, since it incorporates both the squares covered and the income stages left. The function is (2×spaces_covered+button_income×income_events_left–button_cost)/time_cost, and you should factor in any patches you grab or give up into the spaces covered amount. For example, the 7-2 taken with 5 income spaces left and where the patch isn't a consideration would be worth (2×6+2×5-7)/2=15/2=7.5. Here pieces with low time costs thrive, since here the main restriction is time. If you're not efficient in the middle game you can run out of time before your board gets full (and before you get many points). This stage usually ends around the eighth button income.

The end game starts when you see that you're going to run out of space. The value function is a merger of the early and middle game value functions, 2×spaces_covered+button_income×income_events_left–button_cost-time_cost, again incorporating patches but also incorporating the effect of the game ending reducing the time cost. You're essentially comparing taking the piece to the value of passing, and while every piece is worth more than passing, this evaluation guides your tactics—yes, taking this piece is better than passing, but it'll give my opponent a better piece. Large pieces with low button costs and little or no button income but high time costs thrive here.

Sometimes there won't be an endgame, usually if the players passed back and forth for a long time early on. Close to the end it's possible to evaluate all possible lines of play to pick the best one.

If you learn to evaluate pieces based on the game phase, you can incorporate those values into your tactical decisions. Sometimes it's better to take a less valuable piece if it forces your opponent to take a much less valuable piece. Remember, it's not solitaire, you're not aiming for a high score, you're trying to beat your opponent.

[Stu_1977_SEmelb]

An excellent rundown, adeodatus243, but one thing with which I would disagree is the claim that all pieces are worth more than passing.

I've occasionally found that I'm actually better off passing than taking any of the three pieces in front of the pawn (and yes, they could all potentially fit on my board and I calculated the costs and returns for each piece separately); this can also be irrespective of whether or not that affects my opponent's choices (sometimes the opponent is already finished and I have the final move of the game, for instance).

[johnoldboy33]

Personally, I don't really look at points per time. I try and and start off by getting cheap buttons I.e. a 1/5 1/4. If layout allows. I also try to build corners to opposite corner (diagonal) and fill the gaps in. Generally for me the more weider the shape like the big 2/1 or the 1/2 help fill the board quicker.

[brh2113]

Something to keep in mind: in patchwork you are *not* trying to maximize your points; you're trying to score more points than your opponent. A 10 - 3 win is just as good as a 25 - 3 win and is better than a 25 - 27 loss!

If you're strictly trying to maximize your points, you'd usually want to play pieces on every turn, since the pieces are generally worth more points than the time. But if playing a +points piece for yourself unlocks a ++points piece for your opponent, it's often better to just pass.

[adeodatus243]

An excellent rundown, adeodatus243, but one thing with which I would disagree is the claim that all pieces are worth more than passing.

I've occasionally found that I'm actually better off passing than taking any of the three pieces in front of the pawn (and yes, they could all potentially fit on my board and I calculated the costs and returns for each piece separately); this can also be irrespective of whether or not that affects my opponent's choices (sometimes the opponent is already finished and I have the final move of the game, for instance).

You're right, I spoke too hastily. After the eighth button income the 10-3, the 7-6, and the 6-5 are all worth less than passing if you have to pay the full time price and don't get a patch. The 4-6 and the 10-5 are net-zero under those same conditions.

[Stu_1977_SEmelb]

An excellent rundown, adeodatus243, but one thing with which I would disagree is the claim that all pieces are worth more than passing.

I've occasionally found that I'm actually better off passing than taking any of the three pieces in front of the pawn (and yes, they could all potentially fit on my board and I calculated the costs and returns for each piece separately); this can also be irrespective of whether or not that affects my opponent's choices (sometimes the opponent is already finished and I have the final move of the game, for instance).

You're right, I spoke too hastily. After the eighth button income the 10-3, the 7-6, and the 6-5 are all worth less than passing if you have to pay the full time price and don't get a patch. The 4-6 and the 10-5 are net-zero under those same conditions.

Only those three? Really? Hmm... I guess it's quite possible that once the pool is considerably reduced those three could sometimes end up clustered together and in front of the pawn. (I do also remember occasionally calculating values which work out exactly the same as passing.)

Wow, you seem to really know all the numbers very well. I don't remember any of the stats, I'm always just calculating values on the fly.

[adeodatus243]

An excellent rundown, adeodatus243, but one thing with which I would disagree is the claim that all pieces are worth more than passing.

I've occasionally found that I'm actually better off passing than taking any of the three pieces in front of the pawn (and yes, they could all potentially fit on my board and I calculated the costs and returns for each piece separately); this can also be irrespective of whether or not that affects my opponent's choices (sometimes the opponent is already finished and I have the final move of the game, for instance).

You're right, I spoke too hastily. After the eighth button income the 10-3, the 7-6, and the 6-5 are all worth less than passing if you have to pay the full time price and don't get a patch. The 4-6 and the 10-5 are net-zero under those same conditions.

Only those three? Really? Hmm... I guess it's quite possible that once the pool is considerably reduced those three could sometimes end up clustered together and in front of the pawn. (I do also remember occasionally calculating values which work out exactly the same as passing.)

Wow, you seem to really know all the numbers very well. I don't remember any of the stats, I'm always just calculating values on the fly.

I forgot the 10-4 as well. Basically, expensive pieces with lots of button income but little space-filling ability compared to their cost.