Condensed pentomino set

Thread in 'Discussion' started by jujube, 23 Nov 2008.

  1. jujube

    jujube Unregistered

    i made a gameplay video of a clone game with modified pieces and a 13x26 playing field:
    http://www.youtube.com/watch?v=kWDr05urawg

    there are 7 pieces, which i think makes it feel a lot like tetris. after playing with this specific set of pieces for a couple days i was able to survive for a while in the highest level of the game, but not too easily. i think i found a good balance of difficulty in decision making vs playability at high speeds. there are also some simple twists that work because of the basic rotations of the pieces (not unlike ARS), but there's no lock delay in this game, so i couldn't really showcase these twists in the higher levels (although there is one at 1:35). but i wanted a video of the higher levels anyway, to demonstrate how the gameplay could mimic the high speed action of tetris.

    any thoughts?

    edit: on a sidenote, youtube did not resize my video [​IMG]
     
  2. DIGITAL

    DIGITAL Unregistered

    At first glance, it looks like one of those cheap knockoffs made in China where it's almost like the real thing but there's certainly a defect in one way or another. [​IMG][​IMG][​IMG]

    The pieces look vaguely similar to the ones we're familiar with first of all. But there is something bastardized about the way they look. [​IMG]

    I mean, the L, J, S, and Z must have hit puberty or something because there's something not proportional going on there. And that T, what the hell, it grew a mole on it's hip!

    On another note, I was waiting on the I when I noticed the colors were ARS like. What came out was another mole creature! Ok ok, that was forgiven because there had to be a mirror piece for that T. But then what took my breath away was the boomerang O! (hint hint: I think it makes more sense to switch the color of the I and the O [​IMG] )
     
  3. jujube

    jujube Unregistered

    yeah lol.

    yeah that's a good point. i had made the boomerang piece yellow like the O tet because it's a stupid damn piece that always comes at the wrong time and messes up your stack [​IMG] except of course when you have a good place for it. then you're very happy to see it.

    i'm trying a 12x24 well and it's only a bit more challenging. i think i'll stick with these dimensions. it's still playable at the highest level, but you really want to keep your stack low and plan effectively.
     
  4. is this your own game? looks like something i would like to try, if you have a link. nice work.
     
  5. kapat

    kapat Unregistered

    um ...i'm no mathmatition . but it hink the "original" piece where so universal, cuase they where "palindromic", or the line of symmatry was so applying in most ways.
    i think in order to design a 7-block-piece game you'd need to design new pieces.

    in order to make it as appicible.
     
  6. Screw the game. The MIDI version of Voodoo Chile is fantastic.
     
  7. Ai

    Ai

    Woah that definitely looked weird! I would love to give the game a try too.
     
  8. jujube

    jujube Unregistered

    well, i don't know about designing new pieces that would be simple enough for this to work.

    there is sort of a way of classifying the pentominoes i used, into two classes.

    all pentominoes (and mirrors if they produce unique 2D rotational states) which contain 2 segments, and these segments are joined on their ends so that they form a single corner.
    Code:
     O    O  O O O
     O    O  O
     O    O  O
     O O  O O
    all pentominoes (and mirrors if they produce unique 2D rotational states) which contain 2 segments, and these segments are at least 2 blocks in length, and they run parallel to each other.
    Code:
    O    O  O    O
    O    O  O O  O O
    O O  O O  O O  O O
     O  O
    this might look abstract, and it probably is. but it's just a way of condensing the group of pents, and there is some logic behind the methods of reduction. of course it would be easier with tets, which can include no more than 7 pieces, including mirrored pieces. but these aren't the only ways to condense the full pentomino set.

    using a full pent set makes it really hard to leave room for each piece in your stack if the well is playably narrow. if you make the well too wide, it can be hard to get pieces lined up correctly where you want them when the gravity is fast. herc had an interesting way of handling the problem in a mode in gravytris, with multicolored pents and tetris + puyo + cascade style gameplay.

    isn't it? [​IMG] i couldn't help but laugh when i first heard it, because it sounds really cheesy. but i felt bad because i know somebody spent a lot of time making it.

    there are all kinds of free midi files here:
    http://www.mididb.com/


    deepdorp and Ai: i didn't design the game. it's called "unlimited". there's a piece set modifier in the game, and you can design up to 12 pieces per set. it's hard to figure out what to do though, so send me a pm if you need help.
     
  9. DIGITAL

    DIGITAL Unregistered

    Hmm, here are my thoughts on each pentomino. The scores are a little biased towards flat stacking, meaning that certain pieces will score more in certain areas even through the width of the orientation states are the same.

    Code:
    O    O 
    O    O  
    O    O  
    O O  O O
    
    These two might not be versatile enough for the set. Their horizontal states are unusable most of the game because they require too wide of a specific terrain type. That leaves us with the two vertical states. The upright vertical states provide for many placement opportunities. However, the downright vertical state is limited to a column that is 3 rows deep.

    States - 4/4
    Upright Horizontal - 1.5 for usability
    Downright Horizontal - 1.5 for usability
    Upright Vertical - 4 for usability
    Downright Vertical - 2 for usability
    Score - 9/20

    Code:
    O    O 
    O    O 
    O O  O O 
     O  O
    
    The vertical states of these are a little more balanced than the first two but their horizontal states are still pretty much useless if not more.

    States - 4/4
    Upright Horizontal - 2 for usability
    Downright Horizontal - 2 for usability
    Upright Vertical - 3.5 for usability
    Downright Vertical - 3 for usability
    Score - 10/20

    Code:
    O
    O
    O O O
    
    This one is a bit of a compromise of the first two. The horizontal states are more usable but the vertical states become less flexible. However, the vertical states suffer an additional penalty due to acquiring the more horizontal characteristic.

    States - 4/4
    Upright Horizontal - 3 for usability
    Downright Horizontal - 3 for usability
    Upright Vertical - 1.5 for usability
    Downright Vertical - 1.5 for usability
    Score - 9/20

    Code:
    O    O
    O O  O O
    O O  O O
    
    Usable States - 4/4
    Upright Horizontal - 3 for usability
    Downright Horizontal - 3.5 for usability
    Upright Vertical - 4 for usability
    Downright Vertical - 4 for usability
    Score - 14.5/20

    In terms of flexibility, it's obvious that the last two are the best. Their flexibility resembles that of tetrominoes actually. That led me to wonder what pentominoes would be the most flexible.

    Code:
     O
    O O O
     O
    
    This is like the inverse of an O. It doesn't fit too well on flat areas but it's extremely versatile on step structures.

    Usable States - 1/1
    Upright Horizontal - 2.5 for usability
    Downright Horizontal - 2.5 for usability
    Upright Vertical - 2.5 for usability
    Downright Vertical - 2.5 for usability
    Score - 10/20

    Code:
    O O O O O
    
    This acts very much like the I tetromino in that it sacrifices its horizontal usability to have the highest vertical placement opportunities in the game. This does the job of the downright J/L/S/Z pentominoes and does it better than any one of them could.

    Usable States - 2/2
    Upright Horizontal -1 for usability
    Downright Horizontal - 1 for usability
    Upright Vertical - 5 for usability
    Downright Vertical - 5 for usability
    Score - 12/20

    Code:
    O O
    O O O
    
    This is like a hybrid of a T and a J/L/O. The horizontal states carry over the properties of the T albeit a bit backwards. The vertical states are flexible like the J/L/O on flat areas although there's just that weird notch you have to worry about.

    Usable States - 4/4
    Upright Horizontal -3 for usability
    Downright Horizontal - 2.5 for usability
    Upright Vertical - 3.5 for usability
    Downright Vertical - 3.5 for usability
    Score - 12.5/20

    Code:
    O
    O O
     O O
    
    This pentomino is to the even L-ish pentomino (third one discussed aside from mirrors) as the S/Z tetromino is to the J/L.

    States - 4/4
    Upright Horizontal - 3.5 for usability
    Downright Horizontal - 3.5 for usability
    Upright Vertical - 1.5 for usability
    Downright Vertical - 1.5 for usability
    Score - 10/20
     
  10. jujube

    jujube Unregistered

    adjusting the well width can greatly help with the horizontal usability of pieces. and when playing with pentominoes instead of tetrominoes, it's not only more fair to make the well wider, but it's a bit of a necessity. if you consider that an L tet sits horizontally 3-wide and an L pent sits 4-wide, then the ratio should be 4:3 for pent vs tet well width, which would give you ~13 for pents. another thing to consider is the I (5:4), which would need a well width of 12-13. the method i used for finding a good well width was to simply use the 5:4 ratio taken from the number of ominos in a piece.

    another important thing is how the pieces interact with each other, and you can imagine that the usability ratings for pieces would fluctuate depending on which other pieces you have to work with. an extreme example would be if you had a randomizer that only gave I pieces, allowing you to place any piece vertically or horizontally in most situations without ill effects. but a more practical example is how the L and S tets interact with each other. the same works with the puberty L and S pents (they have grown proportionally to each other [​IMG]).

    this is the only point you made that i strongly disagree with. while i probably use them a little more often vertically, i've found them to be very useful for horizontal placements. they can sit in either a 2-wide or 3-wide space, and in a 3-wide space you have the option of placing it so that it has a 1- or 2-block overlap on adjacent blocks, or you can consider placing 2-wide in a 3-wide space to leave a favorable shape behind with 1 remaining hole (depending on the next piece). and this also goes back to how the pieces fit with each other. if you can place the L horizontally, you can continue stacking flat with an S.

    i agree 100%. these pieces could fit somehow within any piece set. they're the easy ones. they have similar properties with the O tet but can be placed downright vertical on a messy stack, and they can be twisted like a T or S. i've never had any difficulty deciding where to put one of these, unless there was more than one excellent place.

    this one could be just fine in a game with lock delay, so that if you had to place it in a flat area you could easily fill the overhang(s).

    i really don't like the upright horizontal properties of this one. unless you have a perfect 2-0-0-0-2 (stack height by column left to right) shape in your stack (or received the correct pieces to fit that way around it), it can cause you to place several pieces vertically around it, and you may have to stack up 3 or 4 rows just to flatten out your stack again.

    this is another piece i don't like too much. it's fine if you have a perfect step shape to put it on, but otherwise you'll need just the right pieces to fit around it. this piece has always felt awkward to me in falling pentomino games.
     
  11. DIGITAL

    DIGITAL Unregistered

    Concerning the ratio of the piece to the well height, I don't think that's too much of an issue. The problem is that the ease in placing the piece does not scale because you now have to worry about the shape of four column surfaces which is a lot harder than three. If we take the ratio of the horizontal state's width and the vertical state's width for the J/L/S/Z pentominoes, we can see that the gap is a lot greater than that of tetrominoes (4:2 as opposed to 3:2). This would mean that the opportunities to place the pentominoes on the vertical side would remain very much the same if not more but the opportunities to place them on the horizontal side would decrease a lot.

    You're right about how the L/J and S/Z pentominoes complement each other's respective states but they're a burden to the rest because of their imbalanced width ratios. The elegance of tetrominoes is that all the pieces, except for the I, are within the 2-3 range for width, which makes them so flexible and thus complement each other. The I is the special case used to accomodate what the other pieces cannot fix. It's width of 1 in the vertical state allows it to fit anywhere and it's height of 4 in the vertical state is more potent than any other piece.

    You're right, I actually forgot to change this line earlier when I altered the scores. If you take a look at the scores, you'll notice that the horizontal states for these are better than those of the L/J pentominoes. However, in the end, they still suffer from the horizontal to vertical ratio albeit less than the L/J.

    Hmm, I'm a little confused by what you meant. Could you perhaps draw it out?

    It's true that the vertical states are awkward and require the step pyramid structure, which is why I gave them low scores. However, the horizontal states are of more importance to this piece, certainly more than its boomerang equivalent.
     
  12. jujube

    jujube Unregistered

    well, the horizontal upright U naturally creates walls on each side, making it less receptive to horizontal placements around and across it. if you have a 3x2 gap in your stack that the U fits nicely into, so that all you're left with is a perfectly flat stack except for the little notch, then you're ok. you can place a J or L with the short side of the piece filling the notch in the stack. otherwise, you have to stack pieces vertically up the walls of the U and/or in the notch. the O tet, which creates the same walls on each side, can be surrounded on its sides and top by a J and L, and you once again have a flat area on top. the U can't be surrounded in the same fashion. the notch will grow deeper and require a long piece to fill it.

    but this isn't necessarily to say that you rarely have an area where a J or L can be placed flat (in this particular case, you'd need the short side of the J or L to fill the notch). it's a difference between wanting to put a J or L horizontal anywhere in your stack vs needing to place it in an exact location that is determined by the location of the U, and then trying to build up the stack around the U specifically so you can do it. it's hard to make a long flat area on demand in an exact location, because this is the kind of stacking that leaves little flexibility for other pieces. but to stack in a way that you can often place a J or L pentomino flat anywhere in a 12-13 wide area is not so hard with a little practice. and with that J or L horizontal anywhere in the stack, now you have a location which is receptive to many pieces. the difference is that it's a receptive area that came about naturally, and it's receptive to several pieces, not just an exact orientation of J or L.

    sorry to go into the long description of my opinion of the U (and to go off in a flat stacking tangent), but i couldn't draw out a lot of possibilities so easily. to sum it up, i believe the piece takes the flexibility out of your stacking and/or demands vertical placements around it.

    it's probably true that you'll be able to place less pieces horizontally when playing with pentominoes, because as you said there's a difference in the ratios of width vs height between tets and pents. LSL tets can create a flat area on top, while it takes LSQJ to achieve the same thing with pents. there will most likely be areas in your pent stack where you can do things like that to flatten your stack, but probably not as consistently as with tets.
     
  13. And where's the love for the R pentomino? [​IMG]
     
  14. jujube

    jujube Unregistered

    damn, i need to learn my pentomino names. i meant P earlier, not Q.

    looks like it's gonna get some love from that S in your avatar [​IMG]
     
  15. Muf

    Muf

    [​IMG]

    ... NERDS!!
     

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