Can You Always Win a Game of Tetris? 

There's a life lesson in Tetris: Your successes disappear and your failures stack up.

You didn’t take into account spins and tucks. That kind of removes the gap situations for the s and z pieces I would think

I'd like to add that with holds and a 7 bag randomiser, it's not only possible to never lose, but also pretty easy to do so. I've made some extremely trivial bots with only 1 preview before, and they pretty quickly learned how to play indefinitely (I waited until it reached 10 million lines and decided it wasn't going to die anytime soon). I wouldn't be surprised if it was possible to play without previews or holds

One thing you didn't mention - In at least some versions of the game, you can slide blocks before they are cemented in place. This means that if you get two S blocks in a row, you can let them fall without rotating them, tuck the tail of the second S under the nose of the first S, and not be forced to have an un-fillable space right away. Even so, alternating S and Z blocks would still be impossible to stack without creating some voids, and this strategy may actually not be as good as creating "lanes," so I'm not sure that it would affect the outcome in the end. However, in a randomized game, the ability to slide blocks before they stick probably makes it less likely to have voids than is depicted here.

I can't say I'm convinced that the all vertical strat is optimal, since it never considers horizontal configurations that allow for skims, nor does it allow tucks.

" Everything that can happen will happen Given enough time " You had us in the first half, not gonna lie

Interesting, I had a look at the paper since I found the explanation in the video lacking. But it seems that, regardless of the state of the game (previous blocks) before the S and Z block sequence starts, or the techniques a player can use, if the sequence goes on forever, you will lose eventually. A key argument the video is missing is the following thing mentioned in the paper: There is a maximum number of times you can place a block horizontally, since it will add more blocks to the middle columns then to an edge column, by shape. So however you place things, eventually you'll need to only place them vertically because the middle of the board has too much stuff, which leads to the problem discussed in the video.

The blocks in Tetris fall faster and faster the longer the game is played. There is a version of the game where, after you've played so long that the blocks are falling as fast as the game can make them, the falling blocks become invisible. I've seen people play past this point.

Also all modern tetris games use Super Rotating System which allow you to stack blocks in mindblowing places. Nowadays we have a lot of records where players clear 42690 lines in a row by "perfect clears" which means that after every 10th block the playfield becomes clear. There are many strategies to do that and theoretically the game can be endless, you just need to remember all PCs combinations

There are many such algorithms for "playing forever" today. One recent example is the Ultimate Simplified Jigsaw Loop: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-s7h77zb9mg8.html For a modern Tetris player, the challenge is not in playing forever per se, but in maximizing the points earned while they play.

The math has already been done on NES Tetris. Best I can remember it's game over on average at 2,000,000,000 lines. In that version there is no 7 bag system. It's 1 in 13 chance of getting the same piece as before and 2 in 13 for each of the other pieces.

I discovered this channel through your website. Thank you Brian for the great content on cs50. Can't wait to explore everything on this channel.

You didn't mention that you can slip under a gap for example the J block under the S or T block, or the L block under the Z or T block. You can also slip the I block under the S, Z or T block gap.

Nice video. Found your channel through the mega fav number playlist

You're amazing, I haven't watch but your pedagogy is out of this world. Instant sub. Ty for the great content I'll make sure to watch it. But right now I must go back to your courses, Thanks a LOT Brian Yu ! You're AMAZING !!!

I'm just about to finish CS50ai and clicked through your website to get to this channel. The funny thing is i already watched some of the videos without knowing who you were :D

When I read the thumbnail, I thought he was gonna touch on the math in tetris. I've been playing tetris for a while and I've noticed there's some interesting math in tetris that I don't quite know how to put into words. Geometry math of course. Like tspin towers are an interesting pattern and there's probably some math behind dpc Garbo talked about it back then. How broken dpc is because it's an infinite pc build and honestly it's so complicated I don't remember how it works

I have been gaming for 23 years, make games as a hobby and ranked 10th on the leaderboards on Tetris before the bots took over so I can confidently say that I can play Tetris forever if I could react fast enough. At higher levels what gets you is not what blocks you have but the time you have to move them into the correct place. The speed increases with level so once you get to a ridiculous level the blocks come down way too fast to make any decision of where to place them. ( I wrote this video mentioned most games will let you hold a piece for later.)

Your videos have been a godsend. Thank you for making these available to everybody. I really like the videos that explore different algorithms and graph theory in a illustrated way, and its helped me understand them on a deeper level. Coming from cs50x and wanting more im glad to stumble upon this channel.

I am a modern Tetris player, and I have been playing at grandmaster level for quite some time. I just saw this video, so I do apologize for not seeing this and commenting sooner. Couple things I noticed: 1 - I appreciate that you touched on 7-bag randomization which is the first way that breaks your theory. Secondly: if there were alternating S and Z pieces, a tetris player in modern would be able to "spin" one of the S or Z pieces UNDERNEATH another piece. I know this sounds really wacky, but with how the displacement of pieces work, you can spin entire pieces into places that do not appear they would work. Anyone who knows about spins would NOT have issue dealing with alternating Z and S pieces, and would end up flipping the board where they would have a double void and keep scoring doubles after a point. I would fall asleep doing this tbh. There is a point in classic, where you only have a single frame (1/60 of a second) to pull off the spin, but in modern it can be multiple seconds, or ages in a game of tetris, classic masters can still do it though, and would end up flipping the board given enough times. Yeah, it sucks, but it's far from impossible. This is also before we talk about modern's other addition not touched on: holds. You can "hold" a piece and swap it out whenever you would like, meaning you break the sequence as you see fit. I would argue in modern, you are not limited by the difficulty of the puzzle as much as the decision timer, which gets slower and slower, but time doesn't matter as much as knowing how to force pieces where to go and score higher points. sorry this was a huge post, I'm gonna go back in my hole and play more tetris now.

Very insightful! Thanks!

One common tetris strategy not mentioned in this video is the last second slide. in tetris there is a small window where you can move a piece even though it seems to be touching the surface it will rest on. You can use this to stack s or z blocks sideways rather than vertically. I'm pretty sure that using this technique effectively would make for a better strategy than the columns you mentioned.

I'm a Masters student in computer science - and I still learn something new every time I watch a video from this channel.

4:35 nice

You should show the pattern for continuing forever; it's quite satisfying : )

seeing your video first time. like it. subscribed.

Would be interesting to see the proof that you can play forever, given 7 bag, previews, and hold.

Sometimes when I think about infinite-monkey type situations, I like to try to ground my intuition with some sense of quantity. In this case, my thought is: if every atom in the known universe could somehow play a 69,600 move game of Tetris, once every planck time, for the next 100 trillion years, that would be something like 10^150 games. It's an unfathomably big number, but compared to the odds of the unbeatable Tetris game happening randomly (from the start of the game), 2*(1/7)^69600 i.e. 10^58818, it's even more unfathomably small. This doesn't negate anything in the video, it's just something to ponder. P.S., great video!

The Closed Captions on this are absolutely wild

gotta share video to friends

Thank you for this, which tools do you use to make those animations

Hey, I miss your videos. Please start uploading again.

Hey Brian, followed you here from CS50 online course.

There is something interesting and it's in the T block since if you think of the screen as a chessboard, all the other pieces except the T cover two white squares and two black squares, adding the T makes it even more difficult to efficiently find an algorithm that allows you to play well.

And now, the actually interesting question : what would be the minimum bag size that could give a sequence that would force a loss ?

You rotate the piece and fill a hole with the lower horizontal part of either the s or z block. That can then sort of 'reset' the board again.

Oh youre the dominos computer guy!! Nice video man, i subbed

Omg, I recognized this voice from the very beginning. Brian Yu)

I am not convinced. You show one logical-looking strategy and prove that that strategy doesn't work, but it doesn't prove that there isn't some kind of less obvious, but better strategy.

cool video for discussion. one thing you overlooked though is, what is the spin table are we assuming such a game has? because even with true random, modern tetris adopts a spin table which allows a bunch of different piece rotations that makes them fit. so in a game where you only get S Z patterns, in the position shown at 2:32 you 're able to force a Z rotation in the bottom line to the left by rotating counter-clockwise, which moves the gap, and then force the rotation of 2 S pieces down to the right side by rotating clockwise, which clears a line and allows you to close the following gaps. for context, spin tables are extra calculations which allows for a more forgiving set of game controls, and can vary in inplementation between different historical releases of the game.

I need more such videos😭

How can we be certain that the lanes is the most efficient strategy? I would look at the full proof but the link is broken

Modern Tetris fixes a lot of problems presented in this video and 10 Perfect Clears, something that brings you back to 0 as if you hadn't started, are doable by humans and so the game is already theoretically infinitely playable. There are setups for infinite play too for those who don't want to do PCs.

My question is, what if we don't know the sequence? Are there 2 or more sequences that preparing the board for one, will result in losing at another?

Before I watch the rest of the video, I had tried to solve this myself just yesterday, and I got no. And my sequence is alternating 41 S-pieces and 41 Z-pieces, and you are guaranteed to die after 9471 blocks. Although that solution is far from optimal, it's the first one I came up with that would kill the player eventually.

When you need an i block but doesn't show, but when you block the slot for an i block, the i block will show

is this the same for the UK version where we have Zed blocks instead of Zee blocks?

Wow. Only 1000 subs. He’s a really good RU-vidr

Willis Gibson, has become the first player to officially “beat” the original Nintendo version of the game - by breaking it.

The most important part was left out. The game speeds up the more lines you complete.

1:50 Looks like @CKTDabbler mentioned this already but you absolutely CAN tuck a next piece under an S or Z skew tetrimino. The gaps are NOT inescapable.

Nice man

there are some variants where you can't rotate the pieces and others where once your score hits a certain amount the game speeds up the drop rate, forcing you to lose

If you did it 'correctly', it would clear 4 rows at a time every time you got an "I". Once you had it cleared after one of those, it was just a matter of maintaining.

I once played a modded Tetris called stacked odds. Already knew the blocks can't be rotated, learned later the game analyzes your game state, determines an optimal piece & it's orientation, and gives you anything else, putting all odds against you. You never get the standing long block

the question is very easily answerable with various guidelines mechanics, such as the SRS rotation system, the 7-bag system, holds, and various other mechanics that allow quite easy recovery from any bad situation, even for incredibly low-skilled players. anyone past a certain level of skill *can* indeed play indefinitely. said skill level is where the player just kinda understands how the pieces fit together. for the specific purpose of a clean, flat stack, there is no such thing as a bad bag, because each piece is guaranted to arrive every 7 pieces.

I looked everywhere for the tetris trick i used in tetris on ps3 to make the biggest combo. I just remember green blocks stacked together on 3 blocks wide (starting position). Still cannot find it.

As others pointed out, you forgot spins. They've been in the game since NES tetris in 1984, almost every tetris game has them, and they solve this problem.

Just because there is room for 5 S and Z lanes, doesn't mean you have to make 5 lanes. Just make 4 lanes, and then in your alternating S and Z scenario you could easily play forever.

hey, when placing the s block dows.. you can just slide in a z block at the last moment.. it worked for the Tetris game i used to play on an old phone

Curious if there is a seed in the original Tetris that would allow such a sequence to appear? Great video though keep it up

The increase in speed through the levels also is a great factor in how a Tetris game goes I think? Also is there a difference between the let’s say Gameboy Classic Tetris and a Console Version for NES for example? Other than the colours. I mean a TV screen is bigger than a Gameboy Display…. Have only handled versions so please forgive me the maybe stupid question

3:47 Lanes are a terrible (and unnecessary) strategy as the whole goal of Tetris is to clear lines and avoid ever letting the pieces stack up too high.

🤯 thanks

How do u animate like these bro??

I've read that the the original Gameboy version had a faulty randomiser that gave too many O blocks and too few I blocks. From the endless hours that I spent playing that version, I can confirm that this is true and made it more difficult, especially on the highest level of the B game, which I strove to complete by scoring six Tetrises (four lines in one go), but to no avail despite countless attempts. Only once did I manage five Tetrises on Level 9, High 5.

At the end you mentioned the concept we refer to as 7 bag but in classic tetris it is theoretically possible to have infinite of one piece

Can't you solve the 5 lane problem by alternating one sideways block with one standing block. The problem then changes to filling in the gaps after completing a row. Not sure if this makes it infinite, but just thought I'd throw that out there.

It's a pretty simple thought experiment with a pretty simple answer. What happens if you only get z blocks? No matter how you handle it, there are spaces the piece simply cannot reach. It can never fill in the bottom row completely. In fact, if we view the entire grid as sets of 3 rows, the middle row is the only one that can ever be filled. Meaning it is guaranteed to fail at some point, and rather quickly.

I was not convinced until you said "it was proven"😆

I thought you would've used the actual Tetris music as the background music

So, you can only ever lose or quit is what I got from this.

i didnt pay attention for like a sec and my man begins talkin bout s and z lanes

Imagine if an evil villain made you play Tetris and he promises he won't kill you unless you lose.

It’s very funny to me that there is a canonical Right Way to Make Tetris

Song name?

Someone proved that an unwinnable game was possible. Tetris added some code to prevent this highly unlikely event.

are you the guy from cs50 pset videos?

The title was "Can you Always Win a Game of Tetris", and the answer @6:13 says "Yes", but no explanation was given as to how that would be done.

It's way better do lay Zs and Ss rotated so you don't get two squares on top of the gap. It makes easy to clear them afterwards. But I see that with only Zs and Ss falling down this doesn't matter much

Forever.... until you overload the CPU on the old NES that a new block cannot be selected

Put an upside down T block under the vertical S and Z blocks

For a board of width 2N+1, it would be impossible to clear a single line if only given square pieces

O block. O block. O block. O block. O block.

what about laying some of the pieces in a 3x2 fashion and others in 2x3 fashion. that means 2+3+2+3 = 10 so it fits, and wil last longer

I enjoyed this video very much, but at the very end, it is asserted that random selection without replacement can be played infinitely. While this seems intuitively true, I'd be curious to see a proof of this, which I guess is that "in the 7! possible sequences, there is no way to arrange them such that the player is forced to lose" but I can't imagine what that proof would look like. I'd be very curious. Also, this "standard" piece selection implies that it is never possible to get the same piece three times in a row, and I suspect I've played tons of variants where I've gotten the same piece three times in a row.

I want to build a JavaScript version, this provides good info

It's not just possible but quite easy to never loose at recent tetris solo games. I made thousands of lines before turning of the game.

“I really should get some sleep” Brain: HOW DOES TETRIS BLOCK SELECTION WORKRKRKRK???!!

My GenX neighbour growing up had finished arcade Tetris. He said at the end it started sending down more than one piece at a time.

The proof that the 7-bag and 14-bag variations are endless is that there are exactly 28 squares per 7-bag, and after 10 bags that’s 280 squares which is exactly enough to perfectly clear 28 lines to start the next bag with an empty board just like the start. And if you account for the bag system there are only so many ways a bag can empty which you can use to your advantage to guarantee perfect clears of 40 squares (4 lines of 10 squares lines up with 4 squares per block). So you can basically form a perfect loop every 70 blocks

Keep in mind that random generators aren't true random aswell, this might have some consequenses

The practical answer is a bit more surprising: - The speed keeps increasing beyond human capabilities, so only bots are left - There is no built-in end, the score will continue reading memory as random symbols until it crashes - It uses a PRNG which has limited randomness, therefore it can be predicted and abused Put all of these together and you get that bots can play more Tetris than Tetris can generate. That is a win.

Hmm, Tetris (at least the original version) works on a pool system. All pieces make up one pool, pieces are chosen from the pool, and every time a piece comes up, it is removed from the pool, once the pool is empty, a new pool is given. This is why you can’t get the same piece 3 times in a row.

make a video for if is it possible to consistently make Perfect Clears 100% of the time with 10 pieces.

O block mentioned

Is there a tetris game where the drop speed doesn't increase?

Ok so it’s theoretically possible to play forever. My question then would be: Is it possible to play forever without knowing the exact sequence?

2:05 they have a great time, better than all of us

ive seen a guy doing every spin possible, that guy never lost a single time