Corrections: * At 4:17 I claim there is no fox yet there is clearly a diagonal up-right fox in the grid! Imagine that the two tiles "of" in the bottom row are swapped * At 7:33, the percentage "1.16%" should be "0.116%". It's not 1 in 100 people who will fail 50 times in a row, it's 1 in 1000.
Here's an interesting statistic. If you got a billion people in a room all playing this game, then whenever someone won they left the room then statistically after 149 games there wpuld be one person left all by himself thinking "what am i doing wrong? This game is stupid!"
@@timefuzzball8097 A very valid concern, that reminded me of the 8th entry in the "What If" series in XKCD blog, "What would happen if everyone on earth stood as close to each other as they could and jumped, everyone landing on the ground at the same instant?" ... in the hypothetical scenario the author gathered everyone in Rhode Island, where it ended with "Within weeks, Rhode Island is a graveyard of billions." ... So ... yes ... a very valid concern ....
I tried out this game on your website, and got an amazing board layout that not only won me the game, but also... I was never, at any point, in any danger of losing it. I uncovered the tiles in the order o,o,o,f,o,f,x,f,f,x,x,x,x,f,o,o. There was no point in the game when it was even possible that clicking a tile would have made the word "fox". I wonder what the odds of that are.
I'm pretty sure you can know you've lost on Tile 6 if you draw 5 f's and then an o in that order. Tile 7 has to be an o to avoid a fox on 5-6-7. Tile 8 can be an x or an o without instant death, but using an x is more optimal to prevent an "fo" forming. Tile 9 then has to be an o to prevent a fox on 3-6-9. Tile 10 has to be an o to prevent a fox on 2-6-10 AND on 4-7-10 Tile 11 has to be an o to prevent a fox on 3-7-11 AND on 1-6-11. Tile 12 has to be an o to prevent a fox on 2-7-12. At this point, all o's have been used up (6, 7, 9, 10, 11, and 12). Tile 13 HAS to be an x because all f's and o's have been used up. This causes a fox to form on 5-9-13. And if you were wondering what would happen if Tile 8 was an o, we run out of o's on Tile 11 and Tile 12 is forced to be an x. This causes a fox to form on 4-8-12. Also, the same thing happens if you draw 5 x's and then an o.
@@JujanGames Yea, but he said it was 0.2% chance. Also thought about this, but it is much more rare. 5!11! ÷ 16! × 6/10 ≈ 0,0137%. Even if we multiply by 2 (same story but swap F's and X's), it's still almost 10 times less likely to happend than he said.
@@thehexagon_ytI mean yea, obviously this isn’t the only scenario where you would definitely know you lost. I just decided to list the simplest one mainly because I was too lazy to find the others lol
@@thehexagon_yt This also works if tile 4 is an o. In this situation you still have an f left over, but tiles 7, 9, 10, and 11 still cannot be an x. If you place an o on each of those spaces then 12 cannot be an x because of 2-7-12, 13 cannot be an x because of 5-9-13, and 15 cannot be an x because of 5-10-15, and at this point you only have 1 non x left. You can make 1 of the squares 12, 13, or 15 safe by making 7, 9, or 10 your final f instead of making it an o, but there will still be 2 squares that cannot be an x and there will only be one o remaining, so you would have lost. I believe this to be the only other way to do it. Having tile 4 be an x doesn't work because f-f-f-x f-o-o-x f-o-o-o x-x-o-x is a winning board. The odds of encountering one of these losing scenarios (including swapping F's with X's) would technically round down to 0.1%, but it's so close to 0.15% that I think this could have been a very understandable rounding error. The percentage rounded to 4 decimal places would be 0.1499%, so if his python script was showing him fewer significant figures than that, he may well have seen 1.5% and rounded up. It's also possible I'm missing something but I brainstormed basically every board that's rare enough to not push us above 0.3% and found nothing.
I kind of want to play this against someone. Take turns drawing a tile, then the first to make a fox loses. You can try setting things up so that your opponent faces worse odds than you do.
It took me 73 tries to win. Apparently that is worse than 100% of other players that played on your website (although Idk how many gave up before that). I am literally the unluckiest person to ever play this game (so far).
It's very nice to see you take interest in the math/statistics side of the game and share it with us! Also your presentation is great. The handwritten notebook on a wood table is very aesthetic, it's very reminiscent of Vihart.
Suggestion:A mode where you can choose where to place the tiles, but only before you reveal them. It would be interesting to see some strategies based on the distributions of letters on the board.
I don't think that would change anything. It would still be a random tile on every position.
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@@bencebarabas3555 it first helps you survive longer since we will not deliberate place into high-risk tile. then, you could keep track of the remain characters, so you could optimize the chance of not losing the game. for example, if you first two tiles are F O, then you could wait until the X's goes down before placing in that next tile.
@@bencebarabas3555 no, because you can do what blackjack players do when they “count cards” and figure out the best position for the letter you most likely drew
One thing that is cool about the geometric distribution is that you can also use the formula for the mean for geometric distribution (1/p) to get the what is called an expected value. The expected value is a likely outcome. In this case you are expected to win roughly on the 8th game. Of course that doesn’t always happen, and for someone extremely unlucky it is theoretically possible, but not likely to never win a game because that’s how a geometric distribution work.
For the puzzle, I figured the answer would be if you drew 5 Fs then an O. The O on tile 6 can be part of a fox four different ways, and since we're all out of Fs, the only way to block fox is with more Os. Tiles 7, 9, 10, and 11 all need to be Os. But then there's an FO- on tiles 5-9, so tile 13 must be an O. Now we're all out of Os so unfortunately the rest must be Xs. Which ends up spelling FOX at 2-7-12.
Did you explore adding an element of choice so it's not purely a game of chance? There'd clearly need to be a restriction so you can't just construct the case at 0:40 every time, but otherwise it could work the same. The obvious ones that come to mind are that you have to play adjacent to an existing tile, or that you have to play adjacent to the previously placed tile (if possible). Then it could also be a multiplayer game, where the player that makes fox loses or wins.
You could potentially do this on an infinite board, drawing from an infinite (evenly distributed) bag of tiles - allowing you to place the tiles anywhere touching another tile, but with a restriction such as "you must complete each square before placing tiles outside it (so you have to complete e.g. a 3x3 square before you could place any tiles outside that square). Your score is then the size of the square you managed to complete before catching a fox.
An interesting multiplayer variation is you take turns, you choose where to place the tile but you need to do so before seeing it. First player to complete a foxes loses
took me 15 tries (bottom 13% of people), had an attempt where i plucked five o's in a row after the first tile being an F and i still lost on tile 9 with an X.
Played it once and realized neither my intentional nor arbitrary blind choices made any difference. Is it a game? How am I winning or losing? The only agency I have is the choice to engage with the game or not. Choosing not to play wins me the sense of active participation in my own life. Choosing to play wins me the sense of passively spectating my involvement in an arbitrary system specifically designed to showcase my lack of involvement. Which is to say: the best thing about this game is that it reminds me not to waste my time. Which is useful insight to remember :)
At first I thought one could choose where to place the tile. I have to agree, this is as much a game as flipping a coin and trying to get a certain series of results in a row is.
Because this is just purely a game of luck I just made a python program to run the percentages over and over again until it won. And the first time I failed 56 times and the next time I failed 48 times. Talk about bad luck, ignore the fact I won in 4 tries the third time.
i really like the way you visualized information in this video! feels refreshing compared to everyone using manim (which makes sense, it's an amazing project, but gets bland)
I found this concept to be very fascinating, so I mapped out all possible ways to lose, also wrote some terrible python code to simulate a game, and theoretically have accurate results for simulating 1 million games! The first thing I did was write down all possible ways to lose. I did this first starting at 1, then changed it to starting at 0 to make my python code easier (indexes start at 0 lol) There's 4 main directions that fox can be made; horizontally (8), vertically (8), and 2 diagonals (4 each). This results in 24 different ways. Then because we're also counting reverse, this gets doubled to 48. So that means there's 48 places on the board that fox can be made. I agree that there's 2,018,016 possible boards. That's 16! / (5!*6!*5!) (!=factorial if any non-math people are reading this :D) What I don't understand yet is how you calculated the number of winning boards (or losing boards). That doesn't matter for my python code, though, because all I need are the ways fox can be made, then check those positions in a shuffled list of 5 f's, 6 o's, and 5 x's. All that's left is to shuffle the list and run the fox check until no fox's are made, record the number of attempts and repeat a million times! The results: a beautiful exponential curve of y=146438e^(-0.136x) with an R^2 of 1 (only the 2nd time I've seen R^2 equal 1) The more interesting results: winning on the first attempt has a chance of 12.6512%, which is what you said in the video. I mainly wanted to do all this to try to find an algorithm to test for fox, which I succeeded in doing, so then I just had it repeat a million times to see what would happen lol. If you'd like to see any of my work, I'd be happy to send it to you! I had fun with this puzzle, and your videos on it are great!
I you get the board state FFFF FO Or XXXX XO You are guaranteed to lose. Even though you haven't lost yet, you will. Idk if that accounts for the full 0.2% chance though.
Also, the more tiles you place down, the easier it is to overlook a fox, for example at 4:16, there is a fox at places 14, 11 and 8. But anyhow, I will continue watching this journey.
You wanna make this game harder? Make the 16th tile a blank aka a joker that counts as all 3 letters. So "blank - o - x" is a loss (blank=f), but "blank - o - f" is also a loss (blank=x this time). This makes it diabolically harder to win, since you pretty much need the blank to hit a corner surrounded by 2 x an both sides...
I'm so impy with this video, you analysed and answered a lot of questions I hadn't even thought to consider (knowing you've lost so early in the game is wild lol) Absolutely incredible job, bravo! 😁
5:05 The Guaranteed loss happens if you get 5 Fs to begin the puzzle, with O as the 6th tile in Row 2 Column 2. The O now blocks off the four remaining spots surrounding it as possible places for X The game stays alive with another O at r2c3, but that blocks the final space in row 3 from being able to be an X. Now, all of row 3 MUST be an O in each space to avoid the loss, which works if you have an X at R2C4. However, now you've spent all of your Fs and Os, meaning X is the only option, and you lose with the first placement of an X in row 4.
The website's broke for me :/ It does not increase the number of attenpts & sometimes says that I won without even attempting despite the truth being otherwise
Just wanna point out that at 7:30, the odds for 50 seem to be off by a digit? You'd expect the odds of more than 50 attempts the square root of the odds of 100 or more attempts (or, more generally, for n and 2n attempts, respectively), but that would be roughly 0.116%. Double checking the numbers, (1-0.1265)^50 is roughly 0.001156 = 0.1156%. And another stat that would have been interesting is the probabilities of "knowing you've lost" on a certain square, except you're given that you actually make it to this square - so P(reach square x)/P(know you've lost on square x).
Thanks so much for pointing that out, I've pinned a corrections post to correct the two issues people have pointed out so far. And you're right, the conditional probabilities would be very interesting!!
this would be interesting to try as a 2 player game, where each player flips a tile then gets to place it anywhere on the board, and whoever spells fox loses
5:07 FFFF FO works. You used up all Fs here, so at this point there is 5 Os and 5 Xs left. In order to prevent fox as much as possible, we place an O after each FO, as the only other letter that's left is X which would make FOX: FFFF FOO_ _OO This blocks FOX with any combination around the initially placed O. In this configuration, we can see that the entire 3rd row needs to be Os now due to some of the other Os that we needed to place: FFFF FOOX OOOO I also placed an X in the spot that's guranteed save now. We placed 6 Os now, so there is none left. However, the leftmost column will have FOX when we place an X. So the best we can do is lose on turn 13 and the final board in this case will only contain a single FOX: FFFF FOOX OOOO XXXX Of course, swapping F with X in the starting position also works, as those states are essentially equivalent.
Wow. I just played the game no and won on my first attempt. I think this is something ill enjoy playing a lot, I love games like this where you can forsee your loss and where you could win too, it makes it more engaging honestly.
Adds 1 rule to make it fair rather then luck/statistics, The first letter revealed must always occupy the 1 square and all subsequent letters must be within a 2 square range (such that from the refrence square Fox could be arranged) range from the previously played tile (this means that after turn one squares 2,3,5,6,9 and 11 are valid for the 2nd letter to be played )
Excellent video! Remarkable how many interesting sub-questions u were able to come up with. Especially considering this "game" is not even really a proper game. Good job :D
I love the thought experiment here and how it encourages discussions about statistics, but I really don't think it counts as a game. There's never any decision points, no strategy, and the whole thing could just run by itself.
You could play this as a 2-player game! Each person takes a turn putting a tile on the board wherever they want. First player to find the fox wins/loses.
5:12 I think it’s you get all the Fs or Xs and an O because at that point you need to pull O, X/F, O, O, O, O to make it 5 more moves and you’d still lose at the 13th because you’d need to pull an F/X or an O from a pile that only contains an X/F. Do note that the order I put the X and F in does matter for each pair
Won on my 15th try, with a game where there were two Os in the central positions of the top row, two Os in the central positions of the left column, and two Os in the central positions of the right column. Probably the nicest-looking guarantee of a win.
I would think this comes down to the number of layouts that include the word fox versus those that don't and that is the chances of not having fox on the board. However, I believe the biggest factor is the middle 4 squares. O's in these spots are likely bad news for overall chances, especially 2 O's. O's in corners are great and you want pairs or better of O's on the edges or around corners. A great look would be 4 O's along one edge. I would guess a very common trait for winning boards would be no or a single O in the middle and one or more group(s) of 2 or more O's in a row along an edge or around a corner.
Tried the game, quite polar outcomes! First attempt: f, o, x immediately lol. Second attempt: oofx oofo o and at that point with all o's gone I knew I'd won.
Damn, I really feel bad for you. I've now played it twice online. The first time I played it a few days ago I got it in 3 attempts and decided to play it just now after finishing the video and got it on the second attempt. You might wanna consider that it's not purely random for you since you're doing it irl with tiles. Maybe you need a better system to shuffle them. Like maybe put them all in a bag or something shuffle really well and then pull them out one by one. If you want them all to be on camera for transparency sake maybe try shuffling in the bag dumping the bag on the table, flip all the ones that are upside up and then shuffle them again with your hands and closed eyes.
Surprisingly, I managed to avoid the fox in just 1 attempt. The site does indeed indicate I scored better than 87% of people, so it looks like the site has achieved a large enough sample size to display the 12.65% win chance.
I would be interested to see how the probability of winning changes as the number of O's increases, but not interested enough to write that code myself.
It would be interesting to see how this changes on different board sizes (or even shapes). Also what distribution of tiles gives you the lowest chance of finding a fox. An alternative to this game would be to have a grid of pre-laid face down tiles, and you get to flip N of them in an attempt to find a fox.
4:25 - I'd argue your bigger issue is the diagonal FOX, but your point still stands (if you swap the F & O on the bottom line, your next move will always cause you to lose) Edit: Tried it online, success on attempt 1, never in doubt OOFO OFXO XXFX XFFO Attempt 2, hugs & kisses XOXO XFXO XFFO OFOF Attempt 3, finally lost, quickly OFOX Took 10 attempts to get back to winning ways. I'm done updating now
FFFF FO You have used all the Fs. So every remaining tile is O or X. 7, 9, 10, and 11 have to be O to avoid a fox across tile 6. Then tile 12 has to be an O to avoid a fox at 2-7-12. Then tile 13 has to be an O to avoid a fox at 5-9-13. Even if you get through all that, every remaining tile is an X, so you lose on tile 15 with a fox at 5-10-15. You also have the equivalent solution where you swap all Fs and Xs in the explanation above.
@@chompyzilla For some reason I thought the guaranteed loss was those four tiles in the top-left corner and was losing my mind over why I couldn't get it to work
Is the guarenteed failure at the sixth tile something like FFFF FO? Fs and Xs being interchangeable of course. Been trying to construct a winning board from that position, and it does seem impossible.
Yep. From that position an X in square 7, 9, 10, or 11 would make "FOX". We're out of Fs, so we'd need Os in all those positions. But with those Os placed, we now also can't have Xs in squares 12, 13 or 15, and we only have one O left.
@@AJCham (Just illustrating what you said) 1° F F F F F O _ _ _ _ _ _ _ _ _ _ Only positions 7, 9, 10 and 11 would make FOX with X. So we need Os: 2° F F F F F O O _ O O O _ _ _ _ _ Now positions 12, 13 and 15 would make FOX with X, we would need 3 more Os, but there's only one available... 3° F F F F F O O _ O O O 'O' 'O' _ 'O' _ Game Over
I just played 2 games of fox. First game I got fox in 3 tiles (first possible fox). And incredibly enough I won the game in my second attempt. What are the odds..?
I would forget what I tried before and keep using the same formulas and getting the same losing answer until I got frustrated and gave up, which is why I can’t code despite attending coding classes on the college level.
2:12 what about making "F.O.X." tile, it is any letter that would screw you more in any given situation, you put it at the end of FO it's X, you put it between an F and X it's O, so on and so on.... (configuartion would be 5 F's, 5 O's, 5 X's and 1 F.O.X.)
Two attempts! Three O's along the top, then three F's below them, with two X's on the side. Good start, but then all the remaining X's were on the next row!
i know that the known win at tiles 6 is 6 o's but theres no way for the known loss to have the same odds as the known win, because 6o's requires 6 spedific tiles in a row, where there would be duplicates for any possible combination, (i.e if the answer would be f f f f f o, that o could be any of the 6 o's) where with the 6 o's it has to be those exact tiles
I guess intuitively it makes sense that having more O’s would be the hardest. Obviously it’s preferable to have F’s and X’s touching together, so having 1 more of them increases the chances of that happening. Currently playing right now for funsies: I had one attempt where I lost on the very last tile, and then the next attempt I spelled fox with my first 3 tiles lol finally won on my 11th try. That was fun 😊
after a horrible first attempt where my first 3 tiles were fox, and a slightly better 2nd attempt where tiles 5 6 and 7 were fox, i managed to beat the game in attempt 3
This is an interesting thing to discuss, but I can't help but wonder if it could be made into more of a game by introducing an element of player choice. Right now it's effectively equivalent to being given a random board state, and hoping it's a winning one. Just a roll of the dice. (btw, I got it in 7 attempts)
Yeah, at present there is no skill involved, just luck. But obviously if you had full control of where you put the tiles, you'd just put all the Os in the first six spaces, and always win. Perhaps have a rule that each new tile has to be adjacent to a previously placed tile. Though I suspect there might still be a strategy to never lose in that case too.
Corrections:
* At 4:17 I claim there is no fox yet there is clearly a diagonal up-right fox in the grid! Imagine that the two tiles "of" in the bottom row are swapped
* At 7:33, the percentage "1.16%" should be "0.116%". It's not 1 in 100 people who will fail 50 times in a row, it's 1 in 1000.
I KNEW IT!
Here's an interesting statistic. If you got a billion people in a room all playing this game, then whenever someone won they left the room then statistically after 149 games there wpuld be one person left all by himself thinking "what am i doing wrong? This game is stupid!"
Id be more concerned about finding an exit lmao. Imagine being stranded in the middle of that room, where 1 billion people could fit.
He was left there for months until he starved.
On the table was "xof"
@@not_umbre Well at least it wasn't "POE" scrawled over and over again with an increasing level of misanthropic insanity.
@@timefuzzball8097 A very valid concern, that reminded me of the 8th entry in the "What If" series in XKCD blog, "What would happen if everyone on earth stood as close to each other as they could and jumped, everyone landing on the ground at the same instant?" ... in the hypothetical scenario the author gathered everyone in Rhode Island, where it ended with "Within weeks, Rhode Island is a graveyard of billions." ... So ... yes ... a very valid concern ....
We need to do this during a live stream or something
I tried out this game on your website, and got an amazing board layout that not only won me the game, but also... I was never, at any point, in any danger of losing it. I uncovered the tiles in the order o,o,o,f,o,f,x,f,f,x,x,x,x,f,o,o. There was no point in the game when it was even possible that clicking a tile would have made the word "fox". I wonder what the odds of that are.
it's even more OP when you get
o o o o
at the start
I just got o,f,o,o,o,o,f,x,o in my first go and thought I had it in the bag, then got an x in 10th
There's more O's @@silsquare
i lost on the final tile on my first attempt
On my first try just now i got O, F, O, O, O, X, F, F, O, F, X, X, X, O, X, F
I have photographic proof of me losing on my first 3 tiles on attempt 1 of Don't Find The Fox
that happened to me three times during my 15 attempts x_x
yeah but you also won on your first attempt of Find The Fox in 3 Tiles, which is a more difficult game. Awesome job!
That just happened to me too!
I have photographic proof of doing this two times in a row, first 2 tries.
Same happened to me. F O X in that order. I laughed.
I'm pretty sure you can know you've lost on Tile 6 if you draw 5 f's and then an o in that order.
Tile 7 has to be an o to avoid a fox on 5-6-7.
Tile 8 can be an x or an o without instant death, but using an x is more optimal to prevent an "fo" forming.
Tile 9 then has to be an o to prevent a fox on 3-6-9.
Tile 10 has to be an o to prevent a fox on 2-6-10 AND on 4-7-10
Tile 11 has to be an o to prevent a fox on 3-7-11 AND on 1-6-11.
Tile 12 has to be an o to prevent a fox on 2-7-12.
At this point, all o's have been used up (6, 7, 9, 10, 11, and 12).
Tile 13 HAS to be an x because all f's and o's have been used up. This causes a fox to form on 5-9-13.
And if you were wondering what would happen if Tile 8 was an o, we run out of o's on Tile 11 and Tile 12 is forced to be an x. This causes a fox to form on 4-8-12.
Also, the same thing happens if you draw 5 x's and then an o.
@@JujanGames Yea, but he said it was 0.2% chance. Also thought about this, but it is much more rare. 5!11! ÷ 16! × 6/10 ≈ 0,0137%. Even if we multiply by 2 (same story but swap F's and X's), it's still almost 10 times less likely to happend than he said.
@@thehexagon_ytI mean yea, obviously this isn’t the only scenario where you would definitely know you lost. I just decided to list the simplest one mainly because I was too lazy to find the others lol
@@JujanGames tbh I also have no idea either what are the others
@@thehexagon_yt This also works if tile 4 is an o. In this situation you still have an f left over, but tiles 7, 9, 10, and 11 still cannot be an x. If you place an o on each of those spaces then 12 cannot be an x because of 2-7-12, 13 cannot be an x because of 5-9-13, and 15 cannot be an x because of 5-10-15, and at this point you only have 1 non x left. You can make 1 of the squares 12, 13, or 15 safe by making 7, 9, or 10 your final f instead of making it an o, but there will still be 2 squares that cannot be an x and there will only be one o remaining, so you would have lost. I believe this to be the only other way to do it. Having tile 4 be an x doesn't work because f-f-f-x f-o-o-x f-o-o-o x-x-o-x is a winning board. The odds of encountering one of these losing scenarios (including swapping F's with X's) would technically round down to 0.1%, but it's so close to 0.15% that I think this could have been a very understandable rounding error. The percentage rounded to 4 decimal places would be 0.1499%, so if his python script was showing him fewer significant figures than that, he may well have seen 1.5% and rounded up. It's also possible I'm missing something but I brainstormed basically every board that's rare enough to not push us above 0.3% and found nothing.
@@seminolo17 Oh yea that definitely works too. After FFFO FO you have only 1260 boards you can make, and each of them has at least one fox.
I kind of want to play this against someone. Take turns drawing a tile, then the first to make a fox loses. You can try setting things up so that your opponent faces worse odds than you do.
that's what I thought this was at the beginning of the video!
It took me 73 tries to win. Apparently that is worse than 100% of other players that played on your website (although Idk how many gave up before that). I am literally the unluckiest person to ever play this game (so far).
"terrible python code", ah yes, a man of culture
a real stand-up guy
alex "parker" cheddar
Parkers code
ah yes, spaghetti code 🍝
Non-binary code
It's very nice to see you take interest in the math/statistics side of the game and share it with us! Also your presentation is great. The handwritten notebook on a wood table is very aesthetic, it's very reminiscent of Vihart.
4:20, there is an diagonal fox
Yeah you're right
Suggestion:A mode where you can choose where to place the tiles, but only before you reveal them. It would be interesting to see some strategies based on the distributions of letters on the board.
That seems like a very fun idea actually
I don't think that would change anything. It would still be a random tile on every position.
@@bencebarabas3555 it first helps you survive longer since we will not deliberate place into high-risk tile. then, you could keep track of the remain characters, so you could optimize the chance of not losing the game.
for example, if you first two tiles are F O, then you could wait until the X's goes down before placing in that next tile.
@@bencebarabas3555 no, because you can do what blackjack players do when they “count cards” and figure out the best position for the letter you most likely drew
Would be a good game for card counters.
One thing that is cool about the geometric distribution is that you can also use the formula for the mean for geometric distribution (1/p) to get the what is called an expected value. The expected value is a likely outcome. In this case you are expected to win roughly on the 8th game. Of course that doesn’t always happen, and for someone extremely unlucky it is theoretically possible, but not likely to never win a game because that’s how a geometric distribution work.
For the puzzle, I figured the answer would be if you drew 5 Fs then an O.
The O on tile 6 can be part of a fox four different ways, and since we're all out of Fs, the only way to block fox is with more Os.
Tiles 7, 9, 10, and 11 all need to be Os.
But then there's an FO- on tiles 5-9, so tile 13 must be an O.
Now we're all out of Os so unfortunately the rest must be Xs.
Which ends up spelling FOX at 2-7-12.
the X/F symmetry also applies here, so XXXXXO would also work as the solution
I may have lost this game, but you’ve lost THE game.
oh my god i hate you
AAArg, I've got to remember to do this to other people.
That was good run
Did you explore adding an element of choice so it's not purely a game of chance? There'd clearly need to be a restriction so you can't just construct the case at 0:40 every time, but otherwise it could work the same. The obvious ones that come to mind are that you have to play adjacent to an existing tile, or that you have to play adjacent to the previously placed tile (if possible). Then it could also be a multiplayer game, where the player that makes fox loses or wins.
You could potentially do this on an infinite board, drawing from an infinite (evenly distributed) bag of tiles - allowing you to place the tiles anywhere touching another tile, but with a restriction such as "you must complete each square before placing tiles outside it (so you have to complete e.g. a 3x3 square before you could place any tiles outside that square). Your score is then the size of the square you managed to complete before catching a fox.
An interesting multiplayer variation is you take turns, you choose where to place the tile but you need to do so before seeing it.
First player to complete a foxes loses
what mathematicians call a game always disappoints me, and I never stop falling for it. "fool me 58000 times, what am I doing with my life."
took me 15 tries (bottom 13% of people), had an attempt where i plucked five o's in a row after the first tile being an F and i still lost on tile 9 with an X.
Nooo I just won 3 times in a row 😭
I won on my first time😂😂
Took me 21 tries (bottom 6% of people) :l
Played it once and realized neither my intentional nor arbitrary blind choices made any difference. Is it a game? How am I winning or losing?
The only agency I have is the choice to engage with the game or not.
Choosing not to play wins me the sense of active participation in my own life.
Choosing to play wins me the sense of passively spectating my involvement in an arbitrary system specifically designed to showcase my lack of involvement.
Which is to say: the best thing about this game is that it reminds me not to waste my time. Which is useful insight to remember :)
we live in a society
At first I thought one could choose where to place the tile. I have to agree, this is as much a game as flipping a coin and trying to get a certain series of results in a row is.
Because this is just purely a game of luck I just made a python program to run the percentages over and over again until it won. And the first time I failed 56 times and the next time I failed 48 times. Talk about bad luck, ignore the fact I won in 4 tries the third time.
i really like the way you visualized information in this video! feels refreshing compared to everyone using manim (which makes sense, it's an amazing project, but gets bland)
So basically, this game is the same as rolling a d8 and winning when you roll an 8
Close enough.
Ty for shoutout lol. I did this for fun not knowing that it was that hard to get that many attempts.
Is it really a game if you're just... pulling a random tile and placing it in order, with zero decisions to make?
I found this concept to be very fascinating, so I mapped out all possible ways to lose, also wrote some terrible python code to simulate a game, and theoretically have accurate results for simulating 1 million games!
The first thing I did was write down all possible ways to lose. I did this first starting at 1, then changed it to starting at 0 to make my python code easier (indexes start at 0 lol)
There's 4 main directions that fox can be made; horizontally (8), vertically (8), and 2 diagonals (4 each). This results in 24 different ways. Then because we're also counting reverse, this gets doubled to 48. So that means there's 48 places on the board that fox can be made.
I agree that there's 2,018,016 possible boards. That's 16! / (5!*6!*5!) (!=factorial if any non-math people are reading this :D)
What I don't understand yet is how you calculated the number of winning boards (or losing boards).
That doesn't matter for my python code, though, because all I need are the ways fox can be made, then check those positions in a shuffled list of 5 f's, 6 o's, and 5 x's. All that's left is to shuffle the list and run the fox check until no fox's are made, record the number of attempts and repeat a million times!
The results: a beautiful exponential curve of y=146438e^(-0.136x) with an R^2 of 1 (only the 2nd time I've seen R^2 equal 1)
The more interesting results: winning on the first attempt has a chance of 12.6512%, which is what you said in the video.
I mainly wanted to do all this to try to find an algorithm to test for fox, which I succeeded in doing, so then I just had it repeat a million times to see what would happen lol.
If you'd like to see any of my work, I'd be happy to send it to you! I had fun with this puzzle, and your videos on it are great!
I you get the board state
FFFF
FO
Or
XXXX
XO
You are guaranteed to lose. Even though you haven't lost yet, you will.
Idk if that accounts for the full 0.2% chance though.
Great video before my probability exam.
FOFX
OXOX
FOFO
FXOX
It's like a combination of Mine Sweeper and Chess.
Also, the more tiles you place down, the easier it is to overlook a fox, for example at 4:16, there is a fox at places 14, 11 and 8.
But anyhow, I will continue watching this journey.
Oops!
If tiles 13 and 14 were swapped, that fox wouldn't be there.....
You wanna make this game harder? Make the 16th tile a blank aka a joker that counts as all 3 letters.
So "blank - o - x" is a loss (blank=f), but "blank - o - f" is also a loss (blank=x this time).
This makes it diabolically harder to win, since you pretty much need the blank to hit a corner surrounded by 2 x an both sides...
But why would you ever want to not find a fox? We're amazing.
Geek out much? Still, THIS IS AMAZING!!!!
If you were to name the game, I don’t think it should be “fox”, I think it should be called “oxf”
Ofx
"do not find the fox" is already descriptive enough
I'm so impy with this video, you analysed and answered a lot of questions I hadn't even thought to consider (knowing you've lost so early in the game is wild lol)
Absolutely incredible job, bravo! 😁
I manage to get F O X in order as the first 3 tiles on my first try. Not the point of the game, but that seems highly improbable.
4:13 what do you mean you haven’t made a fox yet?
I noticed that too. 😂
Square 14, square 11 and square 8.
5:05 The Guaranteed loss happens if you get 5 Fs to begin the puzzle, with O as the 6th tile in Row 2 Column 2.
The O now blocks off the four remaining spots surrounding it as possible places for X
The game stays alive with another O at r2c3, but that blocks the final space in row 3 from being able to be an X.
Now, all of row 3 MUST be an O in each space to avoid the loss, which works if you have an X at R2C4.
However, now you've spent all of your Fs and Os, meaning X is the only option, and you lose with the first placement of an X in row 4.
So basically a quirky inverse bingo? this would be a very engaging replacement in a nursing home
Answer 2 questions 1. What is the chances of winning where there are 4 Os in the diagonal 2. What notebook do you use to play
The website's broke for me :/
It does not increase the number of attenpts & sometimes says that I won without even attempting despite the truth being otherwise
Nice video, pretty nice diagrams and stuff
2:10 love how 12% is almost half of 100%
Just wanna point out that at 7:30, the odds for 50 seem to be off by a digit? You'd expect the odds of more than 50 attempts the square root of the odds of 100 or more attempts (or, more generally, for n and 2n attempts, respectively), but that would be roughly 0.116%.
Double checking the numbers, (1-0.1265)^50 is roughly 0.001156 = 0.1156%.
And another stat that would have been interesting is the probabilities of "knowing you've lost" on a certain square, except you're given that you actually make it to this square - so P(reach square x)/P(know you've lost on square x).
Thanks so much for pointing that out, I've pinned a corrections post to correct the two issues people have pointed out so far.
And you're right, the conditional probabilities would be very interesting!!
Excellently made video! Keep it up👍
Watched the video, and then went on the site and won first try! Thanks for the cool content, keep it up!
this would be interesting to try as a 2 player game, where each player flips a tile then gets to place it anywhere on the board, and whoever spells fox loses
im deadass buying that cow word search book, gonna kill hours on it
5:07
FFFF
FO
works. You used up all Fs here, so at this point there is 5 Os and 5 Xs left. In order to prevent fox as much as possible, we place an O after each FO, as the only other letter that's left is X which would make FOX:
FFFF
FOO_
_OO
This blocks FOX with any combination around the initially placed O. In this configuration, we can see that the entire 3rd row needs to be Os now due to some of the other Os that we needed to place:
FFFF
FOOX
OOOO
I also placed an X in the spot that's guranteed save now. We placed 6 Os now, so there is none left. However, the leftmost column will have FOX when we place an X. So the best we can do is lose on turn 13 and the final board in this case will only contain a single FOX:
FFFF
FOOX
OOOO
XXXX
Of course, swapping F with X in the starting position also works, as those states are essentially equivalent.
Wow. I just played the game no and won on my first attempt. I think this is something ill enjoy playing a lot, I love games like this where you can forsee your loss and where you could win too, it makes it more engaging honestly.
Adds 1 rule to make it fair rather then luck/statistics,
The first letter revealed must always occupy the 1 square and all subsequent letters must be within a 2 square range (such that from the refrence square Fox could be arranged) range from the previously played tile (this means that after turn one squares 2,3,5,6,9 and 11 are valid for the 2nd letter to be played )
Could also be fun as a 2 player game
Excellent video! Remarkable how many interesting sub-questions u were able to come up with. Especially considering this "game" is not even really a proper game. Good job :D
Took me two attempts to win on ur website -- what a lucky start into the day :))
I love the thought experiment here and how it encourages discussions about statistics, but I really don't think it counts as a game. There's never any decision points, no strategy, and the whole thing could just run by itself.
The real question here: do I get a fox plushie if I win the game
You could play this as a 2-player game! Each person takes a turn putting a tile on the board wherever they want. First player to find the fox wins/loses.
45 attempts, my god
5:12 I think it’s you get all the Fs or Xs and an O because at that point you need to pull O, X/F, O, O, O, O to make it 5 more moves and you’d still lose at the 13th because you’d need to pull an F/X or an O from a pile that only contains an X/F.
Do note that the order I put the X and F in does matter for each pair
Woooah I like your markers, they look so vibrant
They're acrylic paint markers!
Won on my 15th try, with a game where there were two Os in the central positions of the top row, two Os in the central positions of the left column, and two Os in the central positions of the right column. Probably the nicest-looking guarantee of a win.
I would think this comes down to the number of layouts that include the word fox versus those that don't and that is the chances of not having fox on the board. However, I believe the biggest factor is the middle 4 squares. O's in these spots are likely bad news for overall chances, especially 2 O's. O's in corners are great and you want pairs or better of O's on the edges or around corners. A great look would be 4 O's along one edge. I would guess a very common trait for winning boards would be no or a single O in the middle and one or more group(s) of 2 or more O's in a row along an edge or around a corner.
This is the definition of "powerless knowledge", this doesn't give you any sort of power or advantage whatsoever, it's just... knowledge.
Tried the game, quite polar outcomes! First attempt: f, o, x immediately lol. Second attempt: oofx oofo o and at that point with all o's gone I knew I'd won.
That's a cool pen. I like how the ink looks on the paper. What's the pen?
Damn, I really feel bad for you. I've now played it twice online. The first time I played it a few days ago I got it in 3 attempts and decided to play it just now after finishing the video and got it on the second attempt. You might wanna consider that it's not purely random for you since you're doing it irl with tiles. Maybe you need a better system to shuffle them. Like maybe put them all in a bag or something shuffle really well and then pull them out one by one. If you want them all to be on camera for transparency sake maybe try shuffling in the bag dumping the bag on the table, flip all the ones that are upside up and then shuffle them again with your hands and closed eyes.
Solving this without code would be a pretty good combinatorics problem. I don’t think I’m good enough to solve it but people definitely could
Surprisingly, I managed to avoid the fox in just 1 attempt. The site does indeed indicate I scored better than 87% of people, so it looks like the site has achieved a large enough sample size to display the 12.65% win chance.
I would be interested to see how the probability of winning changes as the number of O's increases, but not interested enough to write that code myself.
It would be interesting to see how this changes on different board sizes (or even shapes). Also what distribution of tiles gives you the lowest chance of finding a fox.
An alternative to this game would be to have a grid of pre-laid face down tiles, and you get to flip N of them in an attempt to find a fox.
4:25 - I'd argue your bigger issue is the diagonal FOX, but your point still stands (if you swap the F & O on the bottom line, your next move will always cause you to lose)
Edit: Tried it online, success on attempt 1, never in doubt
OOFO
OFXO
XXFX
XFFO
Attempt 2, hugs & kisses
XOXO
XFXO
XFFO
OFOF
Attempt 3, finally lost, quickly
OFOX
Took 10 attempts to get back to winning ways. I'm done updating now
Won on the 4th try and realized I won on square 11. Now I wish I paid a bit more attention to see if I could have figured that out earlier
Got it on the 25th attempt. Still puzzling over the 6th tile guaranteed loss conundrum.
FFFF
FO
You have used all the Fs. So every remaining tile is O or X. 7, 9, 10, and 11 have to be O to avoid a fox across tile 6. Then tile 12 has to be an O to avoid a fox at 2-7-12. Then tile 13 has to be an O to avoid a fox at 5-9-13. Even if you get through all that, every remaining tile is an X, so you lose on tile 15 with a fox at 5-10-15.
You also have the equivalent solution where you swap all Fs and Xs in the explanation above.
@@chompyzilla For some reason I thought the guaranteed loss was those four tiles in the top-left corner and was losing my mind over why I couldn't get it to work
Is the guarenteed failure at the sixth tile something like FFFF FO? Fs and Xs being interchangeable of course. Been trying to construct a winning board from that position, and it does seem impossible.
Yep. From that position an X in square 7, 9, 10, or 11 would make "FOX". We're out of Fs, so we'd need Os in all those positions. But with those Os placed, we now also can't have Xs in squares 12, 13 or 15, and we only have one O left.
@@AJCham
(Just illustrating what you said)
1°
F F F F
F O _ _
_ _ _ _
_ _ _ _
Only positions 7, 9, 10 and 11 would make FOX with X. So we need Os:
2°
F F F F
F O O _
O O O _
_ _ _ _
Now positions 12, 13 and 15 would make FOX with X, we would need 3 more Os, but there's only one available...
3°
F F F F
F O O _
O O O 'O'
'O' _ 'O' _
Game Over
what
but i want to find the fox... i like foxes
I went to the website. I avoided the fox on my 24th try
96.1% people won before me!
I did the one where you choose where it goes let’s just say it took me 110 attempts lol
It took me 48 attempts from your website, it seems to be having an encasement of sorts can provide safety
Coming here after being part of the 12.65% that won first try :D
I did the game and it took me 3 tries
I love your little diagrams they are so satisfying
Just went to the website. Took me 18 tries
I just played 2 games of fox.
First game I got fox in 3 tiles (first possible fox).
And incredibly enough I won the game in my second attempt.
What are the odds..?
I went to your website to play. Don't know how I did it, but I won on the first attempt!
I have photographic evidence of getting a win on game 1 and I am baffled. It was a weirdly cool problem though
I don't give a fox
I would forget what I tried before and keep using the same formulas and getting the same losing answer until I got frustrated and gave up, which is why I can’t code despite attending coding classes on the college level.
2:12 what about making "F.O.X." tile, it is any letter that would screw you more in any given situation, you put it at the end of FO it's X, you put it between an F and X it's O, so on and so on.... (configuartion would be 5 F's, 5 O's, 5 X's and 1 F.O.X.)
In 27 tries I lost it 4 times on the last tile. How unlucky am I?
It took me 52 attempts.
Two attempts! Three O's along the top, then three F's below them, with two X's on the side. Good start, but then all the remaining X's were on the next row!
I just beat the game. Knew I was gonna win on tile 13. Less than a 2% chance, I'll take it. :)
i know that the known win at tiles 6 is 6 o's but theres no way for the known loss to have the same odds as the known win, because 6o's requires 6 spedific tiles in a row, where there would be duplicates for any possible combination, (i.e if the answer would be f f f f f o, that o could be any of the 6 o's) where with the 6 o's it has to be those exact tiles
have you done any math on if you can decide where on the board the pieces can go?
My only question is if I'm allowed to place the tiles anywhere in the grid and not have to go one at a time.
New Tic Tac Toe is looking pretty strange. What’s this version called, Foxes and Boxes?
I guess intuitively it makes sense that having more O’s would be the hardest. Obviously it’s preferable to have F’s and X’s touching together, so having 1 more of them increases the chances of that happening.
Currently playing right now for funsies: I had one attempt where I lost on the very last tile, and then the next attempt I spelled fox with my first 3 tiles lol finally won on my 11th try. That was fun 😊
after a horrible first attempt where my first 3 tiles were fox, and a slightly better 2nd attempt where tiles 5 6 and 7 were fox, i managed to beat the game in attempt 3
This is an interesting thing to discuss, but I can't help but wonder if it could be made into more of a game by introducing an element of player choice. Right now it's effectively equivalent to being given a random board state, and hoping it's a winning one. Just a roll of the dice.
(btw, I got it in 7 attempts)
Yeah, at present there is no skill involved, just luck. But obviously if you had full control of where you put the tiles, you'd just put all the Os in the first six spaces, and always win. Perhaps have a rule that each new tile has to be adjacent to a previously placed tile. Though I suspect there might still be a strategy to never lose in that case too.
Fun fact: If you fail 41 times in a row, tne in game board starts to display the attempts counter off the book.
ok i spentt all my unluck in failing 49 times in a row
So what is the expected value of the number of attempts you need to make in order to win the game at least once?
Answer: about 8, since probability of winning is about 1/8. Expected value of attempts before 1st win = 1/p = 8 approx.