Mike Daas
Mike Daas
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The TRUE values of all chess pieces (according to maths)
These are exciting days for chess, as the FIDE Candidates Tournament 2024 is currently in full force. Have you ever wondered why the pieces in chess are valued the way they are? I sure have! So I used some maths to compute the true values of all chess pieces - let's see how close they get to what we know!
Discord server: discord.gg/frGPcD4Npf
Check out my second channel for music and gameplay videos: czcams.com/channels/dTXfBKwf2rJoVdgAKUoS_A.html
Portal 2 video essay playlist: czcams.com/play/PLFBvo5mKC3u2EUkrxq4Iyd6_avKzSc9G8.html
Please feel free to share your thoughts in the comments below.
Thumbnail made by mikatastrophe. Huge thanks to them!
Their workshop: steamcommunity.com/id/theccguy
Music: made by me.
I often upload my music on my second channel, linked above.
There's also soundcloud.com/mike-daas-1 and mikeastro.bandcamp.com/.
Chapters:
00:00 - Intro
00:48 - First attempts
04:12 - Maths ideas
06:58 - Results
09:23 - True values
11:00 - Outro
zhlédnutí: 57 677

Video

The Portal 2 tests that measure your IQ
zhlédnutí 27KPřed 7 měsíci
Scientists created an accurate measurement for fluid intelligence inside the game Portal 2. Let's explore these very special tests and see how they hold up in view of modern puzzle design standards. Discord server: discord.gg/frGPcD4Npf Check out my second channel for music and gameplay videos: czcams.com/channels/dTXfBKwf2rJoVdgAKUoS_A.html My version of the Test Battery: steamcommunity.com/sh...
The most underrated testing element in all of Portal 2
zhlédnutí 31KPřed 11 měsíci
Turrets are one of the silliest testing elements to use in Portal 2 workshop puzzles, but if used right, they can make for some truly incredible puzzles. In this video, we explore how turrets can be implemented to construct challenging puzzles and how they allow for some really amazing moves. Discord server: discord.gg/frGPcD4Npf Portal 2 video essay playlist: czcams.com/play/PLFBvo5mKC3u2EUkrx...
How can "No Elements" maps in Portal 2 be so hard?
zhlédnutí 101KPřed rokem
How can "No Elements" maps in Portal 2 be so hard?
Portal 2's paradoxical self-powering setups
zhlédnutí 164KPřed rokem
Portal 2's paradoxical self-powering setups
Why I've played Portal 2 for almost 2000 hours
zhlédnutí 5KPřed rokem
Why I've played Portal 2 for almost 2000 hours
The true potential of rotating portals
zhlédnutí 86KPřed rokem
The true potential of rotating portals
Why closed portals are sometimes better
zhlédnutí 287KPřed 2 lety
Why closed portals are sometimes better
Ghost Cubes in Portal 2
zhlédnutí 50KPřed 2 lety
Ghost Cubes in Portal 2
Portal 2's most powerful untaught mechanic
zhlédnutí 145KPřed 2 lety
Portal 2's most powerful untaught mechanic
Mikeastro plays Portal 2: ''Layers of Cognition'' by Narkodes
zhlédnutí 3,2KPřed 2 lety
Mikeastro plays Portal 2: ''Layers of Cognition'' by Narkodes
Why are most popular Portal 2 maps so bad?
zhlédnutí 318KPřed 2 lety
Why are most popular Portal 2 maps so bad?
The PUBG game of the year 2021
zhlédnutí 191Před 2 lety
The PUBG game of the year 2021
The Pink Tree - Another
zhlédnutí 312Před 2 lety
The Pink Tree - Another
The Pink Tree - Quiet Mind
zhlédnutí 212Před 2 lety
The Pink Tree - Quiet Mind
Mikeastro plays Portal 2: ''Deferral'' by Nock
zhlédnutí 620Před 2 lety
Mikeastro plays Portal 2: ''Deferral'' by Nock
Mikeastro plays Portal 2: ''Nemesis'' by SteamStream and Teo
zhlédnutí 277Před 2 lety
Mikeastro plays Portal 2: ''Nemesis'' by SteamStream and Teo
The Pink Tree - Message for the future
zhlédnutí 236Před 2 lety
The Pink Tree - Message for the future
Mikeastro plays Portal 2: ''First and Goal'' by Libbybapa
zhlédnutí 509Před 2 lety
Mikeastro plays Portal 2: ''First and Goal'' by Libbybapa
The Pink Tree - Lost for Today
zhlédnutí 104Před 2 lety
The Pink Tree - Lost for Today
The Pink Tree - Zero
zhlédnutí 157Před 2 lety
The Pink Tree - Zero
The Pink Tree - Pulse
zhlédnutí 181Před 2 lety
The Pink Tree - Pulse
The Pink Tree - Xenophobia
zhlédnutí 214Před 2 lety
The Pink Tree - Xenophobia
The Pink Tree - Perpetual Patient
zhlédnutí 109Před 2 lety
The Pink Tree - Perpetual Patient
The Pink Tree - Redo (extended version)
zhlédnutí 68Před 2 lety
The Pink Tree - Redo (extended version)
The Pink Tree - Milestones - Full Album (+bonus song)
zhlédnutí 111Před 2 lety
The Pink Tree - Milestones - Full Album ( bonus song)
Mikeastro plays Portal 2: ''Live and Let Live'' by Leo
zhlédnutí 511Před 2 lety
Mikeastro plays Portal 2: ''Live and Let Live'' by Leo
The Pink Tree - Official Album Trailer - Milestones
zhlédnutí 40Před 2 lety
The Pink Tree - Official Album Trailer - Milestones
The Pink Tree - Rose for you (extended version)
zhlédnutí 35Před 2 lety
The Pink Tree - Rose for you (extended version)
The Pink Tree - Afterglow
zhlédnutí 129Před 3 lety
The Pink Tree - Afterglow

Komentáře

  • @deni4l164
    @deni4l164 Před hodinou

    it'd be nice if there was a difficulty rating that you can vote for when you complete the map and then you could sort maps from difficulty in the workshop

  • @kingrex1931
    @kingrex1931 Před 2 dny

    The relative average values are close to what they have been calculated at for decades. The biggest change is the Bishop at 3.5 vs it's normal calculation of 3.0. The Pawn and Knight are exactly the same; the Rook and Queen are roughly the same.

  • @JanoschNr1
    @JanoschNr1 Před 7 dny

    I once played a map that was so hard I could not finish it after hours, I bet even Chell herself would have given up. Either he glitched it to get to the exist or I'm just not insane enough to get on the solution. It made no sense.

  • @r3ked272
    @r3ked272 Před 8 dny

    Comment 150

  • @one_for_one
    @one_for_one Před 9 dny

    This video inspired me to make a bunch of maps using bootstapping to program elements in the vanilla editor. If you want to check them out, or improve apon them with mod tools, my name on the workshop is the same as my comment name without the underscores

  • @saadmunir5265
    @saadmunir5265 Před 11 dny

    king has infinite value according to bobby fisher and that makes perfect sense

  • @80sGamer208
    @80sGamer208 Před 12 dny

    In EVERY game where there is community created content the populars ones suck (except geo dash)

  • @TheSixteen60
    @TheSixteen60 Před 27 dny

    Because they're not Valve employees or game devs. All they use is BEE2.

  • @dobbythefreeelf5703
    @dobbythefreeelf5703 Před měsícem

    Took five slow minutes before you just explained a mechanic that basically everyone has always used.

  • @walterfristoe4643
    @walterfristoe4643 Před měsícem

    The value of particular pieces or pawns often depends on the position.

  • @altoidsours
    @altoidsours Před měsícem

    I started Portal Revolution and it has a lot of these. I was so confused at first, because I've never played any workshop maps or anything. When I clicked on this vid I had a feeling it was gonna be about that.

  • @bubbahottep8644
    @bubbahottep8644 Před měsícem

    But the chance of a particular piece being on a particular square is not n/63. For one thing, there are four to eight times as many pawns per other piece type. For another, the pieces do not start out on random squares. Next, the pieces tend to go to certain squares by the structure and tactics of the game. And also, given a bishop of one color, the chance (even under the arbitrary and over-simplified rule you gave), the other bishop will be in one or two states: it will have a chance of 0/x of being on the same color as the other bishop, and (n-2)/[32 or 31 or 30] of being on the other color; or else, if it is a promoted pawn, it's square color is indeterminate, making calculations even less meaningful.

  • @thinboxdictator6720
    @thinboxdictator6720 Před měsícem

    this is borderline idiotic.

  • @kylefillingim6258
    @kylefillingim6258 Před měsícem

    The king may be a week piece, but it can't be captured. A game over is forced before that happens. That makes the weak king infinitely more valuable than all the other pieces.

  • @nblack2867
    @nblack2867 Před měsícem

    What about doing the same analysis you did with bishops, rooks, and queens, but with the pawn that can only move 2 squares on rank 2 if nothing is blocking it? That might affect the analysis a bit, since you are normalizing the pawn. But if the pawn's ability to move can also change over time, then you might need to look at that. That being said, great video!

  • @menjolno
    @menjolno Před měsícem

    personally: 7 bishop pair 9 queen rook anywhere between 4 and 5 miner anywhere between 3 and 4

  • @matejnovosad9152
    @matejnovosad9152 Před měsícem

    You should just download 10000 lichess games and average available squares in each position. You can only focus on endgames/openings and middle games if you like but it should be a decent estimate

  • @CliffSedge-nu5fv
    @CliffSedge-nu5fv Před měsícem

    This is pretty dumb. A computer or a human following these guidelines will lose every game.

  • @RadishAcceptable
    @RadishAcceptable Před měsícem

    You've stumbled into the same kind of thinking a computer does when calculating positions. They always try to calculate the value of their pieces as it relates to the position on the board, and what squares they control has a big effect on how the positions are valued. Your math doesn't even need to be very precise for the computer to be able to beat any human alive since they can calculate so many positions and simply choose the best move that they find. The raw crunching power will usually result in a computer outclassing the human by sheer volume of calculated potential positions. I would recommend setting the King's value to maximum, however, so that your computer doesn't try to trade its king for a rook.

  • @Ggdivhjkjl
    @Ggdivhjkjl Před měsícem

    The king's value is infinite.

  • @Euthanasia-rc1pm
    @Euthanasia-rc1pm Před měsícem

    Y is the King worth 3.75?

  • @blacklight683
    @blacklight683 Před měsícem

    0:09 huh? I mean king being the only losing condition should at least make him worth 16

  • @shawnnevalainen1337
    @shawnnevalainen1337 Před měsícem

    Really, you ought to have some series that accounts for not only the squares attacked on the next move by a piece but also squares that could be attacked in two moves or three moves. For example, a queen or rook can reach any square on an open board in two moves while a knight could take many moves to reach a given square. Bishops can only reach half the squares (but can do so in two moves). For human play, it's not really the actual values that matter but the total order on the various sums. That is, it matters whether rook and bishop are worth more or less than a queen, not whether the rook is worth 5.1 or 4.9. It would be really interesting but much more difficult to use a game database to obtain values of various factors using statistics from game results and to incorporate that into the piece value table. For example, with a standard set of piece values, having the bishop pair while the opponent doesn't is typically considered to be worth half a pawn. Could you similarly say that having an isolated pawn is worth negative .25? Are center pawns worth more than edge pawns? Is it true that three tempi are worth a pawn in the opening? Is a passed pawn inherently worth more than an unpassed pawn? What is the cost of a backward pawn? Positional factors could be assigned numerical scores by looking at performance rating, finding out how being up one pawn affects game outcomes, and then seeing how other factors affect outcomes. For example, if being up a pawn against an equal player leads to a 2% higher score over 1000 games, could we say that a feature that also leads to a 2% difference in performance is also equal to one pawn?

  • @gregwolking
    @gregwolking Před měsícem

    Excellent analysis!

  • @gibbeldon
    @gibbeldon Před měsícem

    Just pointing out some objections without providing any fix: Chess squares are not equally likely to be occupied by a piece. In the beginning four ranks are always occupied whereas the other four are always empty. Progressing from that state backranks tend to empty over time and so on. A fully occupied chess board still lets any chess piece other than the knight see their immediate neighbours. A bishop would be worth at least twice as much as a pawn in that situation. There are some more things missing that are hard to put into a calculation. The ease with which pawns are blocked from moving as compared to the other pieces, the bishops both being unique pieces, the fact that king and another minor piece aren't able to checkmate the opposing king alone whereas rook or queen can, and probably more I cannot think of right now. Still the average comes surprisingly close to what we are used to. Maybe whoever invented the point system went a similar route? Of course none of this is able to truly give us an accurate evaluation of the value of a piece in action. This is the chess players job, to correctly asses true values as the game unfolds. Pawns are worth more the further they are advanced in ranks for example, due to the potential threat of promotion. Doubled past pawns especially can be very terrifying.

  • @jakobr_
    @jakobr_ Před měsícem

    5:41 I had a bad feeling about this calculation since it seemed to take the different cases completely independently so I did it myself: 1(x) + 2(1-x)x + 3(1-x)(1-x) x + 2x - 2x^2 + 3 -6x + 3x^2 3 - 3x + x^2 1 + 1-x + 1-2x+x^2 Got the same answer. All good!

  • @JoeRoe-wp2mu
    @JoeRoe-wp2mu Před měsícem

    Something that I think should be considered is that the king isn't allowed to move to a space where it would be in check, and therefore can never control such a space. I don't know if you factored this into your calculation, but it would make the king slightly less powerful.

  • @susata5123
    @susata5123 Před měsícem

    Should we consider the amount of pieces a piece controls at the same time? A rook can control up to 4 pieces at once, unlike the knight, who's limit is 8

  • @kylerjordan9616
    @kylerjordan9616 Před měsícem

    this was the exact chess lesson i needed to improve my game because i think I understand transitioning to and from midgame significantly better now

  • @mariusvr
    @mariusvr Před měsícem

    Very interesting video and a very interesting take. Aside from the recorrent comment that your analisys didn't look into future (mainly impacting the balance between knights and bishops) and other relevant actual chess based comments, for me, one comparison that it lacked (in the video, and even more so in the comments) was against the values in which strong AI (AlphaZero or LeelaZero, for instance) evaluate them

  • @VincentHondius
    @VincentHondius Před měsícem

    Your mic has a low rumble that messes with the audio. Filter the lowest frequencies out of the signal so my subwoofer doesn't hum constantly

  • @reinerzufall1292
    @reinerzufall1292 Před měsícem

    Simple rounding error, I win

  • @SmartsellerGaming
    @SmartsellerGaming Před měsícem

    so we were quite accurate after all

  • @johnpaterson6112
    @johnpaterson6112 Před měsícem

    Anyone ignorant enough to suggest that the king has a finite value is not worth your time.

  • @adammartin2431
    @adammartin2431 Před měsícem

    Enjoyed the note for math nerds. I was thinking that, so thanks for clarifying. I think you covered it well. Sad that theres not more similar videos on your channel, all portal lol.

    • @Mikeastro
      @Mikeastro Před měsícem

      Thanks for watching! It's true, I locked myself a bit into the portal content but tried branching out a bit with this video; maybe I will make more videos in this style :]

  • @bigsmoke6414
    @bigsmoke6414 Před měsícem

    i was honestly surprised by these results. I thought that the video would be about taking a look at tons of recorded chess games and taking the controlled squares of the pieces there, i wasnt expecting this basic approximation to do so well

  • @The-Anathema
    @The-Anathema Před měsícem

    The king's value is obviously infinity since losing the king loses the game on the spot, no matter what other conditions are at play.

  • @Portal2Player
    @Portal2Player Před měsícem

    This Video is quite similar to my portal 2 journey. I have about 3.7k hours in the game and have been playing it since 2011, and a lot of thinks that happened in this video happened to me. Even getting people like LB and Nock to play my maps (they were both terrible maps, but I was really young and thought they were good) I even somehow got one of my Beemod maps In 2017 on the front page. No idea how, it was a terrible puzzle, and I remember libbybaba saying that it wasn’t a good map (I still really like his maps). And then in 2020 when we were all locked inside, I started making hammer maps, which were my first maps to get really popular. I looked back on when I released those maps and I had been cranking them out once a week! (Probably why I got bored) but now I’ve come back to Portal 2, and I hope that now after 4 years of not making anything, I can actually make a decent puzzle. Thanks for making this video!

  • @stijnvandensande3579
    @stijnvandensande3579 Před měsícem

    could you put this in an exel file so then you can put it in a graph

    • @Mikeastro
      @Mikeastro Před měsícem

      Huh, I really should have done that, shouldn't I? :/

  • @Portal2Player
    @Portal2Player Před měsícem

    The best way to describe this test is frightening

  • @ecMathGeek
    @ecMathGeek Před měsícem

    I think this method of evaluating their values ignores that control doesn't just apply to the next move, but to subsequent moves as well. A knight may only have 8 squares (at most) immediately available to it, but because of the odd nature of its movement, in just a few moves it can access the entirety of the board. While a bishop will always be limited to accessing specific squares. Similarly, it's much easier to completely block off a bishop's range of movement than it is a knight's. Also, control applies to how well a piece controls other pieces. A rook can completely block the opposing king from moving across its controlled rank and file. A rook can also protect an advancing pawn for the entirety of its journey (something a bishop and knight cannot do). A knight can produce a forking threat against multiple pieces.

  • @brianmulholland2467
    @brianmulholland2467 Před měsícem

    Nice. But I think you can do better by borrowing the concept of WAR from baseball and other sports analytics. What needs to be done is a database crawl through high level games to explore not how many squares can be moved to or threatened, but how well having particular pieces correlates with winning. As you noted, the value of a piece is likely not static throughout the game, but an excessive level of detail here defeats the purpose of the analysis, which is to create something usable. I would invite someone with access to the necessary data to try to analyze the value of pieces related to helping to create wins.

  • @BinaryDragon
    @BinaryDragon Před měsícem

    One place where this analysis, which is otherwise quite good, is deficient in my opinion, is that a piece's value is not only the number of squares it can control, but also how many squares it could control after a single move (either by the piece itself or via discovered attack after the movement of another piece).This gives the bishop, rook, and queen some extra value that the other pieces lack, and this value is extremely pronounced in games where these pieces will commonly slide in from an uncontested area of the board to give check, protect a threatened piece, or sit in front of a pawn on the way to promotion. It also helps explain why the traditional valuations of 5 and 3 respectively for rooks and bishops are more disparate than the values you were calculating - both pieces are able to control close to the same number of squares on average, but rooks can threaten basically twice as many "1-move" squares as bishops can. I wouldn't suggest that these 1-move squares should count the same as the squares being directly controlled, but rather I think a piece's value is a function of both. Making value a two-variable function also has the fun effect of creating a table that hypothetical new piece types could inhabit. For example, (using some rough, but easy to work with rounded numbers) if we say a knight controls 6 squares on average and 12 1-move squares, while a rook controls 12 squares plus an additional 30 1-move squares on average, these would sum to 18 squares controlled plus 42 1-move squares (ignoring for the moment that the sum is not the same as the union here). We could then see what value the f(18, 42) is to estimate the value of a piece that could move like either rook or knight. Of course, all of this is assuming that trying to use mobility as a metric is ideal to begin with. Given the results in the video, it's clear it's not a terrible metric, but I'd posit that the TRUE definition of relative piece value is that two sets of pieces would be equal value if games played between similarly skilled players where each player had one set of pieces resulted in neither side winning more than the other. The fact that endgame strategies dominate over piece value when there is little material on the board that you pointed out means that one couldn't simply see if a knight is worth three times the value of a pawn by measuring the average outcome of KN vs KPPP games, but you should be able to, with enough different combinations of pieces, set up a system of equations that would allow you to solve for each piece's value as a function of a pawn's. One could look at a database of chess games, index each position by the combination of pieces each player has at that point, and then measure the tendency for one side to win over the other across all games with the same index. All indices with an even (or close enough to even) win balance would thus represent equal value sets of pieces, those sets being the ones that would be used in the system of equations to solve for final value.

  • @Osiris261
    @Osiris261 Před měsícem

    value depends on the piece activity in the game.. constantly changes for each piece with every move of you and you opponent make. you can have games where a queen is worth 1 point and a pawn is worth 5.

  • @piotrkawaek6640
    @piotrkawaek6640 Před měsícem

    Very nice video! However, if you want to rly assess the strength of the piecess you should take games from database of GM players and do similar calculation (and the more frequent the position the more impact it should have on the final result). Random positions do not aproximate well the positions you can realisticly get in a chess game.

  • @B-fq7ff
    @B-fq7ff Před měsícem

    I like how you say "the queen's value will always the the sum of the rook and the bishop" and then 30 seconds later have 2.75 + 3.5 = 6.2

    • @Mikeastro
      @Mikeastro Před měsícem

      Rounding can cause such things

    • @inseptus712
      @inseptus712 Před měsícem

      ​@@MikeastroYou rounded .5 down. That's not how rounding works.

    • @Mikeastro
      @Mikeastro Před měsícem

      @@inseptus712 The actual values are 2.74 + 3.47 = 6.21; this is the top row at 11:10. It's really not that complicated

  • @DanielLCarrier
    @DanielLCarrier Před měsícem

    I was thinking you'd use some chess algorithm to calculate out how well each player is doing in a bunch of random games and look at how many of each piece they have, and then find a linear approximation to calculate about how well they'd be doing based only on number of pieces.

  • @daboffey
    @daboffey Před měsícem

    I would like to see the fact that the bishop can only reach half the board and pawns can only reach a relatively small number of squares, whereas the other pieces can reach the full board included in the analysis.

  • @thatdiamondminer2673
    @thatdiamondminer2673 Před měsícem

    Chess pieces cannot be given any "Constant Values"; as in they have variable values, the values keep changing depending on the positions that come forth on the board, in some instances two bishops can be more valuable than a rook or queen in a scenario to deliver BODEN'S checkmate pattern and same for other like the ARABIAN Mate. The piece values keep changing and sometimes a king can rise in value during endgames as for opposition and moving towards pawns and such. Chess is a really interesting game, requiring constant attention to what is happening on the board.

  • @Azure_Gust931
    @Azure_Gust931 Před měsícem

    8:56 interesting mechanic!