HOME WORLD FORUMS WIKI VIDEOS
9580 members and stacking!
     Welcome guest, please login or sign up

3 Pages V < 1 2 3 >  
Reply to this topicStart new topic
> Downstacker's Guide to the Galaxy, Some techniques I do when I downstack
Rating  4
post Sep 28 2011, 01:52 PM
Post #16




Posts: 0
Joined: --



Here is a shorter and simpler explanation of what I was said in the last post. Somehow I think this post would also become too long, but I will relegate the musings, which are after the dashed line, after clearing up the main point.

Just take these conditions for the game (3 and 4 in the last post).
- the game starts with no garbage
- garbage position doesn’t matter for the argument
- all garbage is sent with one hole, as is the case with most normal versus modes
- there is no garbage blocking

These are all normal conditions, although some variants can have differences. But the main condition that is different is this:
- the game ends immediately when the garbage lines reaches the top but the player may place as many tetrominos above the playing field as they want to (just imagine something like 0G play with ghost). That is, for example, players can’t lose a game by quickly pressing down to drop blocks and end the game.

Now this is why when with this particular condition is imposed a player, in this particular variant, will only lose when the garbage blocks exceed a certain value. I assumed 180 in my first post but it doesn’t matter, you can assume 189 (that is garbage reaches 21st row) if you want to.

Now here is the thing. Now think of all the variables in terms of point blocks (or one fourth of a tetromino). It doesn’t really matter because eventually you can just divide your result by 4 to get the intuitive result in terms of tetrominos. It would help to understand the variables involved as I mentioned in the last post.

G = Total “garbage” blocks sent by the player (since the start of the game)
D = Total “garbage” blocks cleared by the player (since start of the game)
B = Total “non-garbage” blocks cleared by the player (since start of the game)

For example suppose someone made two tetrises at the start of a game. First one was obviously made with all non-garbage blocks. Assume that the second one was made using one garbage line and three non-garbage lines. Now what would be the values of G, D and B up till that point in the game? If you can understand this, the rest of the post is not difficult to understand.

G = (4+5) incomplete lines = 9 incomplete lines = 9*(9) =81
D = 1 incomplete line = 1*(9) =9
B = 7 complete lines + 1 = 7*(10) +1 = 71

Remember the garbage lines are sent with one hole, and the downstacked lines also contain 9 blocks (since it is simply the garbage sent by the other player). Now the last variable left to define is K.
K= number of non-garbage blocks (coloured blocks) in player’s field at any given time

For example, if all the blocks in the field at a given time were garbage blocks then K=0.

Now it is helpful to understand the exact values of TPM, LPM and APM in terms of values defined above. Let t be time in minutes. Then:

TPM = [ (B+K) / t ] / 4
LPM = [ (B+D) / t ] / 10
APM (in unit of lines) = [ G / t ] / 9

Now these values G, B and D are obviously only increased (and they can only be increased) when a move such as single, double, triple, tsd etc. is made. After all, only a placement that clears a line will increase B (necessarily) and D (sometimes). And only a move that sends garbage to the other player will increase G.

Now of course both players have separate pairs of values. Let us define G1,B1 and D1 for the first player and G2, B2, D2 for the second player. Now here is the main point of introducing all these variables and stuff. At the end of the game the player that wins (in this particular variant) the game will “always” have a higher value G+D. In other words if the first player won at the end of the game then:

G1+D1 > G2+D2

Of course you could multiply or divide both sides of this inequality by any number. Now (G+D)/9 is simply the variable “garbage lines downstacked + garbage sent”.

We could also account for speed by calculating (G+D)/t or (G+D)/(9*t) for this matter.

So you could think of this “G+D” variable to be constantly fluctuating for both players during the game. Sometimes it goes higher for one player and sometimes for the other. But in the “end” the player that wins will always have higher value of “G+D”. This is due to simplified conditions for the game ending. But if you can ignore the effect of non-garbage blocks present in the field when the game ends (in a real game), this measure would be fairly useful as a statistic. I hope this clarifies some of the confusion.

Note that it doesn’t matter whether the game uses b2b, spins, combos etc. What you just need is to detect them and use correct values for g, b and d accordingly. But garbage blocking does change things because in that case garbage sent is not equal to attack.

The purpose of all this discussion was to give some justification to the statistic. Actual playing or downstacking strategies are a completely different matter.

=====================================================================

1- Another interesting thing is that these variables can be used to give a better picture of efficiency. It is obviously subjective to a certain extent, but still useful. For example, in our variant of the game, suppose the second player wins from the first but the first player claims that the opponent just won because he was faster not because he was more efficient. We have:
E=(G+D)/B

We can rewind the game a bit for the player (and rewind only for that player) who 'used' more blocks (for lines) to the point where the blocks 'used' were equal and then compare the efficiency.

Also note that if we consider the quantity [4*(G+D)]/[9*B] it gives us a quantity that would read like “garbage lines downstacked plus the garbage sent per tetromino”.

2- Another analogy of G+D factor in context of a completely different scenario could be this. This is a rough example but I still think it is interesting, although it has hardly any relevance to the real discussion. Consider a sort of a racing game between two players where two players race around the same lap over and over. The exact nature or complexity of racing game doesn’t matter at all.

Let the lap length be 100, for example. Now suppose the objective of the game is to maximize the distance traveled after say, one minute mark. Obviously the player who has traveled more distance at the end of the game will always win.

But suppose we add another two conditions. A player can win by:
1- overlapping the other player (the game is won instantly)
2- or the distance doesn’t increase by more than 50. That is at each minute it is checked whether the player that is leading doesn’t have a lead of more than 50. If it is more than 50 then this check is relegated for another one minute. If the lead is within 50 then the leading player wins.

Now the second check happens at the end of every minute, unless the game is decided by condition 1. Even though we can clearly see that distance traveled in this case has some similarity to G+D factor, in that the winning player will always have more of this quantity, it doesn’t mean that it is always wise to increase it without any judgment. For example, if a player had a lead of 40 at 50 seconds mark, wouldn’t it be wiser for that player to slowdown a bit and then anticipate and react, in contrast to going on full speed (and hence missing an opportunity of winning the game).
User is offlinePM
Go to the top of the page
+Quote Post
Ravendarksky
post Oct 14 2011, 12:05 PM
Post #17


Tetris Professional
Group Icon
Posts: 813
Joined: 23-July 09



Having taken the time to read through your post Annon there is one fundamental thing I do differently... Probably because I'm not as good as you and I don't play blockbox!

When digging my tactic is just to have as flat a stack as possible, as long as this doesn't block one of the next 4 garbage holes.

I try and place I pieces horizontally to this affect. I've nabbed two of your fumens to show this. The main thinking is that clearing a single with an I piece creates 3 lines above my stack. Horizontal placement creates 0 or 1.
I treat ALL blocks needing cleared on screen as garbage, so I don't really see the difference between a garbage single and a non garbage single...





I'm only talking about digging from a purely staying alive perspective. Otherwise I'd try and Tspin over my garbage.

I think this approach works better in games like Cultris 2 where you can't predict what pieces come next. Having flat I pieces usually leads to more placements for all other pieces too. As part of my wider "Play horizontally, not vertically" strategy.

Also in one of your examples I don't see why this isn't the best option:


Thanks for taking the time to post your guide... I find it very informative. Especially when I can compare where I would do different things and see that I end up with more lines left on my screen.

Feel free to tell me why and how I'm wrong!


--------------------
User is offlinePM
Go to the top of the page
+Quote Post
B1ink
post Oct 14 2011, 03:05 PM
Post #18


Tetris Novice
Group Icon
Posts: 58
Joined: 2-August 09



One of the main differences in how you two downstack is anon is doing it from a multiplayer perspective and not a single player perspective(although his ideas work well in both scenarios). He is not trying to get to the bottom the fastest way possible. Instead he places the pieces to change his field height the most relative to the other player's field. By playing this way, the longer the game goes on, the better position he will be in to win. That is why one of his core ideas is to only clear singles involving garbage. When you clear non garbage singles, you have wasted pieces and time, because you neither lowered your field nor raised your opponents field during that time. You could have been doing nothing and still be in the same position you started in. The reason garbage is significant is because it allows him to place less pieces on the field while sending more garbage, but this difference is only notable in multiplayer.
User is offlinePM
Go to the top of the page
+Quote Post
Anonymous
post Oct 14 2011, 06:37 PM
Post #19


Tetris Professional
Group Icon
Posts: 595
Joined: 29-June 09



QUOTE(Ravendarksky @ Oct 14 2011, 08:05 AM) *

When digging my tactic is just to have as flat a stack as possible, as long as this doesn't block one of the next 4 garbage holes.

I try and place I pieces horizontally to this affect. I've nabbed two of your fumens to show this. The main thinking is that clearing a single with an I piece creates 3 lines above my stack. Horizontal placement creates 0 or 1.
I treat ALL blocks needing cleared on screen as garbage, so I don't really see the difference between a garbage single and a non garbage single...

I'm only talking about digging from a purely staying alive perspective. Otherwise I'd try and Tspin over my garbage.

I think this approach works better in games like Cultris 2 where you can't predict what pieces come next. Having flat I pieces usually leads to more placements for all other pieces too. As part of my wider "Play horizontally, not vertically" strategy.


Yep, pretty much what B1ink said. You're right, you can place the I piece horizontally and it will help your stack become flatter and thus easier to stack on. However, your I piece can do stuff that other pieces can't do, like fit into 3 (or greate) deep holes. Other pieces can't do this which is why I'd rather use the I piece for a Tetris in this situation. On the other hand, there are many pieces that can be used to get that single and lower your field/make it not as messy/stuff (probably won't be as clean as using an I piece, but they can still do it).

Also, my goal when downstacking is to not get any singles because when you get regular singles, it means you spent time to place 2.5 pieces to build up a line and then you get a single which means you don't send any lines. In other words, those 2.5 pieces don't do anything. However, you could have used them to do something for instance a garbage double.

If you do an analysis on pieces used vs (lines sent and lines downstacked)

your fumen:


my fumen


In your fumen, you use 6 pieces. However, since your O block and S block didn't get cleared, I'll say you used 4 pieces. Anyways, you downstacked 2 lines and sent one line. So:
(lines downstacked + lines sent) / pieces used = (2 + 1) / 4 = .75
So your ratio of lines sent/downstacked to pieces is .75

In my fumen, I use 6 pieces, I downstack one line and send 4 lines, so:

(lines downstacked + lines sent) / pieces used = (4 + 1) / 6 = .8333
So my ratio of lines sent/downstacked to pieces is .8333

Comparing our ratios, Making that Tetris instead of using the I piece for a single would probably make you better off. If you're near the top though, then you'd most likely want to downstack the two lines rather than get the Tetris though.


These downstacking lines blur in games like TOJ/TF though. Efficiency in downstacking isn't as important because you can make up for inefficient downstacking by making T-spins and combos. If you build 3 lines and get a garbage Tetris, is it more efficient than if you get a single and a T-spin double?

However, I would like to point out that I've seen a lot of people play Blockbox and they're terrible man! just terrible! Their downstacking skills are only mediocre. And, these downstacking skills transfer over to when they play on TF and Nullpomino. I'm sure many players could increase their apm by at least 5 or even more if they could downstack properly and not get so many singles (and these singles aren't part of combos, so they aren't anything except wasted lines).

QUOTE

Also in one of your examples I don't see why this isn't the best option:



original fumen


Also, for the last fumen, if you have a T piece, sure, go ahead and put it in. I was just saying that to be a good player, you have to see all three possibilities. Most beginner players only see that the T piece fits in. Advanced players can see that a T or an L piece can fit in. Mega pro players can see that you can put the L piece in before you complete the line (the last situation). The T piece probably is the best piece to use, however it's good to know all three possibilities. And by knowing the other situations, you can save your T piece for a T-spin or fix your stack, or other purposes.

And for anyone who hasn't realized this yet, I update the original post about once or twice a week, so check periodically c:


--------------------
My awesome downstacking guide, last updated (Jan 29, 2013): Downstacker's Guide to the Galaxy
Tired of the same old Tetris games? Read my idea for a revamped Tetris game! The Next Evolution of Tetris
User is offlinePM
Go to the top of the page
+Quote Post
larrytetris
post Oct 19 2011, 08:18 AM
Post #20


Tetris Professional
Group Icon
Posts: 935
Joined: 23-May 10



Fantastic stuff.


Side note: I was amused seeing "2 User(s) are reading this topic (0 Guests and 1 Anonymous Users)" hehehe anonymous users :3

Sticky request.


--------------------

Hate cannot drive out hate, only love can do that.
~Martin Luther King Jr.

IPB Image

QUOTE(DarthDuck @ Oct 19 2011, 09:14 PM) *

Larry can polymer spin and reinvent tetris itself while he plays
User is offlinePM
Go to the top of the page
+Quote Post
Paradox
post Oct 19 2011, 10:01 AM
Post #21


Tetris Grand Master
Group Icon
Posts: 1,841
Joined: 2-November 10



oh I forgot to mention I attempted to make a formula to calculate the best downstack option in each situation Wink.png

its a bit limited. It is only for the current situation + current piece. It doesn't account for next piece or hold piece.

Here is an example of how it rates pieces, lower numbers are more favorable positions:




so to address that previous fumen:



Hopefully I can make it so it can calculate for up to 3 next pieces but it requires a bit of math that I suck at.


--------------------
IPB Image
User is offlinePM
Go to the top of the page
+Quote Post
Anonymous
post Oct 21 2011, 06:53 PM
Post #22


Tetris Professional
Group Icon
Posts: 595
Joined: 29-June 09



QUOTE(Paradox @ Oct 19 2011, 06:01 AM) *

oh I forgot to mention I attempted to make a formula to calculate the best downstack option in each situation Wink.png

its a bit limited. It is only for the current situation + current piece. It doesn't account for next piece or hold piece.

Here is an example of how it rates pieces, lower numbers are more favorable positions:



Can you show us the formula you used to calculate those numbers? Seems like it could be useful.


--------------------
My awesome downstacking guide, last updated (Jan 29, 2013): Downstacker's Guide to the Galaxy
Tired of the same old Tetris games? Read my idea for a revamped Tetris game! The Next Evolution of Tetris
User is offlinePM
Go to the top of the page
+Quote Post
coolmaninsano
post Oct 21 2011, 11:38 PM
Post #23


Tetris Novice
Group Icon
Posts: 0
Joined: 29-March 10



Yeah, [citation needed] Paradox. That really seems useful.

Seconding the sticky request.
User is offlinePM
Go to the top of the page
+Quote Post
Paradox
post Oct 21 2011, 11:53 PM
Post #24


Tetris Grand Master
Group Icon
Posts: 1,841
Joined: 2-November 10



So basically it scores a single garbage line clear based on how much residue is left over the rest of the holes afterwards.

https://docs.google.com/spreadsheet/ccc?key...Xc&hl=en_US

its not really meant to be a guide on downstacking but its a 1st stage attempt of figuring out how exactly we should downstack. Its a really limited slice of what we should take into account while downstacking.

If anyone is interested I'd like to make a flow chart for downstacking. I just haven't been able to come up with all of the factors to take into consideration as you go from piece to piece.



--------------------
IPB Image
User is offlinePM
Go to the top of the page
+Quote Post
caffeine
post Oct 24 2011, 03:28 PM
Post #25


Tetris Grand Master
Group Icon
Posts: 1,752
Joined: 27-June 09



I'm really enjoying this article so far, anon. Keep up the good work!

The idea behind the "predicting your hole" is true and everything, and it's a good solution. I just thought the scenario was interesting, so I wanted to also show these:

This is about equal, I'd think:


This one's probably worse for multiplayer, but the endgame is actually a little faster for dig 18 mode:
User is offlinePM
Go to the top of the page
+Quote Post
Paul676
post Oct 24 2011, 05:01 PM
Post #26


Tetris Grand Master
Group Icon
Posts: 2,491
Joined: 22-July 09





--------------------
User is offlinePM
Go to the top of the page
+Quote Post
myndzi
post Oct 24 2011, 08:54 PM
Post #27


Tetris Grand Master
Group Icon
Posts: 1,932
Joined: 26-June 09



QUOTE(Paul676 @ Oct 24 2011, 05:01 PM) *




lol.

Re: quantifying downstack efficiency, it seems to me that it is pretty easy. The problem is branching choices, but you can prune branches with an algorithm for example based on how bad you will allow it to get in the interests of future awesomeness. You might even find the fastest/best solution first, then loosen the criteria to see if it's just a local minimum.

The crux of the problem is that there is a fairly easy-to-quantify best position for a single piece, but it changes depending on the next pieces. The way you can quantify that is by how many minos must be filled after your placement (and this looks something like what Paradox did, though maybe not from quite the same angle) by putting that piece in that position.



This solution is awful because it requires you to fill 27 minos (=7 pieces) before you can downstack further into the column the I was placed in.



This, on the other hand - while not a likely situation in dig race, demonstrates that the same piece placement can be much better depending on the circumstance. In this case, 0 minos are added to your load and 4 lines are cleared - pretty much the best you can do.

In general, it's okay to add minos over holes so long as they will be removed by the time you reach those holes. Depending on the pieces coming up and the efficiency, it can be better to add a little spike over a hole when you know you can remove it - because if you are going to wind up building up a larger stack around the place you want to keep low, then you will have to fill it in with new pieces later to clear those lines.

The balance, then, is not adding to your workload by creating lines that get in your way later, but gradually filling in your residue so that it gets gracefully cleared out. The best solution will always leave the next garbage hole accessible, preferably by the exact piece you have ready at that point, and it will leave your residue in places that it won't interfere in the upcoming lines.

This is pretty easy to quantify with math, really, but the problem is that it's so completely dependent on all the other pieces that it's useless to try and score any given piece itself. Whether a placement is good or bad depends on what you can do with the next N pieces - however many that is to completely remove the residue from the piece you dropped.


--------------------
User is offlinePM
Go to the top of the page
+Quote Post
Anonymous
post Oct 24 2011, 09:53 PM
Post #28


Tetris Professional
Group Icon
Posts: 595
Joined: 29-June 09



QUOTE(myndzi @ Oct 24 2011, 04:54 PM) *

In general, it's okay to add minos over holes so long as they will be removed by the time you reach those holes. Depending on the pieces coming up and the efficiency, it can be better to add a little spike over a hole when you know you can remove it - because if you are going to wind up building up a larger stack around the place you want to keep low, then you will have to fill it in with new pieces later to clear those lines.


tru dat. That's why, when downstacking, I say "don't stack over the holes, but if you do, stack flat" rather than "don't stack over the holes". It's okay to stack over the holes to an extent because eventually by the time you get to the hole, you'll have cleared those pieces from previous clears (or you should have), like you said.

QUOTE

This is pretty easy to quantify with math, really, but the problem is that it's so completely dependent on all the other pieces that it's useless to try and score any given piece itself. Whether a placement is good or bad depends on what you can do with the next N pieces - however many that is to completely remove the residue from the piece you dropped.


Yep, pretty much. That's why I give a lot of theoretical downstacking ideas rather than concrete, "if you're in this position, do this" kind of stuff. There's just way too many factors to consider to map every possible piece placement when downstacking, like current garbage hole placement, future garbage holes, piece order, number of previews, etc.


--------------------
My awesome downstacking guide, last updated (Jan 29, 2013): Downstacker's Guide to the Galaxy
Tired of the same old Tetris games? Read my idea for a revamped Tetris game! The Next Evolution of Tetris
User is offlinePM
Go to the top of the page
+Quote Post
post Oct 24 2011, 11:07 PM
Post #29




Posts: 0
Joined: --



Anon your calculation on the previous page isn't quite correct, at least in my opinion! You calculated the values 0.75 and 0.83 for the upper and lower diagram respectively. Here is how I think the calculation would be. When you are comparing two placements from the same initial field position and using the same pieces, I think roughly what you are trying to do is that how well you use 'all' the pieces (that were placed within that particular stretch) for adding and downstacking lines.

There is a bit of danger with using efficiency for unequal pieces used. It is as a reasonably helpful averaging measure but not necessarily a correct one. And especially when the fractional difference between pieces used is very high it becomes more unreliable. In any case, perhaps throughput is a better word than efficiency because the word 'efficiency' can perhaps give a wrong impression at times. That is, an efficient player would rather finish a game when he clearly sees the opportunity to do so.

But leaving aside all this, lets come to the diagrams on the last page. Unlike previously I will just use lines and tetrominos to calculate E this time. Also assumed standard attack for singles, doubles (1), triples (2), tetris (4), b2b (5) and so on. For the first diagram:
sent = 1
downstack = 2
tetrominos = 2 (you can see that there were actually 8 blocks used in lines)
So we have E1 = (1+2)/2 = 1.5

For the second diagram:
sent = 4
downstack = 1
tetrominos = 3.5 (14 blocks used in lines)
we have E2 = (4+1)/3.5 = 1.429

But there are two serious problems with doing a calculation like this one.
1-- It would give unnecessary credit to placements in the sense that a lot of the clears were done using blocks that were already there before any placements were made. Mathematically what we would want is that efficiency adds up properly from one point to next.

If we were to change the blocks used values by calculating 'all' the non-garbage blocks cleared, surely the adding up would be correct. But using a weighted average concept would be more balanced in this case I feel. Also notice that if you compare the values below to the ones calculated from using efficiency of individual clears (single, doubles, tetris), you get a good sense of comparison. Unlike above, these values are more intuitive.

I 'think' that one of the solutions is to use proportional representation to blocks placed within a clear. It is a bit difficult to explain in words clearly and briefly so I will just write the numbers and hope it becomes clear. I have written e value in front of every clear. These can be verified easily.

First Diagram:

Clear Type -- u value -- e value (efficiency value of that particular clear)

single (0 garbage line) --- 1.25 --- 0
double (1 garbage line) --- 0.5 --- 0.727
single (1 garbage line) --- 0.25 --- 4

Notice that if you look carefully the used column (2nd one) only counts the blocks that were used by our placements and not the ones that were already there before.

Calculating the value sum(u*e)/sum(u) = 0.682

Second Diagram:

b2b tetris (1 garbage line) --- 3.5 --- 0.645

Calculating the value sume (u*e)/sum(u) = 0.645

2-- This still doesn't account at all for how well the pieces that are left can potentially contribute to the cause. We need a decent guess for that to make a more confident statement about which sequence of placements is better in most cases.

For that consider this: the first placement, at best, sets you up for a tetris without any garbage line while the second sets you up for a b2b tetris with one garbage line. Now the E values for these are:
e1(tetris with no garbage line) = (4+0)/10 = 0.4
e2(b2b tetris with one garbage line) = (5+1)/7.75 = 0.774

Now both players used 6 tetrominos. With this in mind we estimate the efficiency in terms of, for example, "on average how well the blocks placed were used for attack or downstacking".

Modified E1 = (0+0.364+1+4*0.4)/6 = 0.494
Modified E2 = (2.258+2.5*0.774)/6 = 0.699

I think that this modification gives a better picture of comparing two diagrams in terms of piece placements, starting with same field position and using exactly the same tetrominos. It's a bit unfortunate that the calculation becomes so clumsy and probably very time consuming to do by hand. But the first step can be automated without much difficulty. The second part depends on foresight, especially more so if the game involves spins.

EDIT: Made a major correction. Didn't see it before.
User is offlinePM
Go to the top of the page
+Quote Post
Paradox
post Oct 24 2011, 11:11 PM
Post #30


Tetris Grand Master
Group Icon
Posts: 1,841
Joined: 2-November 10



How would we take into account next pieces though + other factors? It seems really complicated. I wish someone made an AI that could downstack amazingly (Ryan Heise >:( )

I think its possible to make a methodical guide to downstacking which is kind of what I personally want to figure out and/or know.


--------------------
IPB Image
User is offlinePM
Go to the top of the page
+Quote Post

3 Pages V < 1 2 3 >
Reply to this topicStart new topic
1 User(s) are reading this topic (1 Guests and 0 Anonymous Users)
0 Members:

 

©2009-2014 Hard Drop Community & Forum
harddrop.com is not sponsored or endorsed by The Tetris Company or its subsidiaries.