How to 'always' win at Battleship? 

Me calculating the entire probability map of a 10x10 grid while my friend is wondering why I took an entire hour to fire one shot:

I think calculating the probability maps for each shot will take longer than actual naval conflicts

Another way to win is to move your ships around after each move and always claim the shot was a miss

An important caveat is that, if your strategy is known, your opponent can be adversarial about their ship positions. So if your strategy isn't random enough, your strategy might only be as good as the worst possible score rather than the average.

Fun fact. In Russia, there's a different variant of the ruleset. The only but major differences are: 1. After you hit (wound or destroy a ship), you can fire again immediately 2. There are no 5-cell ships, but instead each player has 4x 1-cell ships, totalling up to 4x1, 3x2, 2x3, 1x4 3. Ships cannot occupy adjacent cells, _even diagonally_ This changes the game pattern drastically and adds a good level of mindgames during the deployment phase.

A still better strategy is not to shoot where the ship most likely is, but to shoot whichever square gives you the most *information* about where the ships are. Once you have 100% information, then you can take out the ships.

This video forgets a crucial part of the game: The part where you initially hide your ships. Where are the best and worst places to put the boats at? If you can work out the last place your opponent would think to guess, then you could have a huge advantage by sticking a boat there.

The best strategy for battleships is to *not draw any ships on your side of the board* . That way, wherever your opponents shoots, he always misses. When you win the game, you simply screw up your paper so the opponent never knows. Except this one time, in the late 1980s. We were at school, it was a 'wet lunch' so everyone was inside doing various things. Battleships was a popular way to pass the time (many people spent longer drawing elaborate warships than actually playing). and a lot of kids were crowded around this particular boy and girl playing each other in an apparently long lasting game of over-the-table battleships. The boy thought he was unbeatable. He had drawn a grid to put ships on, but not actually drawn any warships. He was playing on a blank grid so could not lose. Except this time, his opponent was unbeatable too. The girl had drawn all sorts of things on her page, fish, seagulls, rainbows, stars, clouds..... but no ships. Obviously all the people around the table knew what was going on, but the players were oblivious - until the end of lunch bell rang and both players gave up and showed the other their 'fleet'..... Never heard the word 'miss' said so many times in one game......

you don't need to hunt ships that you hit. you may instead count all possibilities for what you may have hit and where to continue, and either hit another square where you are likely to find something, or hunt the ship by choosing the spot where you are the most likely to continue sinking the ship. that may slightly lower the average time to sink the whole fleet.

The problem with this strategy is assuming your opponent will place randomly. An opponent who knows about this may choose to place their ships around the edge. Unless they know that you know that they know, in which case they will cluster in the middle. Best to build up an immunity to iocaine powder beforehand, just to be safe.

One important caveat about the "hit and hunt" strategy: ships can be placed next to each other (this is different from the version more common in Eastern Europe). If the opponent has done this, your hunt may take longer than expected. You could easily have a string of 5 hits and sink nothing. I'm not saying that hunting around a bit is a bad idea, but for completeness you may wish to account for this possibility when adding your probabilities.

Your really underrated I thought I was watching someone with around 100000+ subs

I discovered you could stack all the ships on top of one another. The beauty is two-fold: 1) It's much harder to find the 5 spots. 2) After the sink the top ship they don't fire again at the same spots to sink the one beneath it... I'd be incredibly honest and admit a HIT if they did.

I shoot in the 4 long pattern first - that gives a 50% chance of a destroyer hit, and 75% for the sub and cruiser. The 4 long pattern can be converted to the 2 long checkerboard after all found ships are sunk. Being aware of what patterns can be converted helps a lot.

Ok but this assumes a perfectly random placement of each ship

We played a version where you didn't announce when your opponent had sunk a ship. This led to sneaky tactics like placing the cruiser and submarine end to end, and your enemy would stop shooting after 5 hits thinking it was the carrier, when really you still had the tail end of the submarine alive XDXDXD Placing ships in a zig zag meant that they had no idea what was still alive to adjust their probability maps.

The rules that I learned were a bit different. Each turn you had to announce 3 shots, and your opponent would only tell you the result of all three shots together, without saying which shot touched what. And the winner was not the one who sunk all the ships of the opponent, but the one who could locate all the ships of the opponent. A bit like mastermind.

I'm proud to say that I thought of the first three strategies all on my own while playing battleship. Unfortunately, I must be very unlucky, my sister always manages to beat me through random chance before I beat her.

I always just do the pattern where you search for any length-3 ships, and you have a 66% chance of hitting the little length-2 guy. Also there are times where I don't finish off ships after the first hit because you can waste shots finding direction, but would be clear exactly what direction it is if the grid is a little more filled out.

Even if you don't calculate the exact probabilities every time, you can eyeball it all pretty quickly, which intuitively makes sense as well. Chances are higher in big open areas.

In my school we used to play with 1 4 squares long ship, 2 3 squares longs, 3 2 and 4 ships with only one square Now this is where my top strat comes in to play, put all bigger ships around the edge of the map, but then scatter the smallest four all over the middle Won every time someone didn't know how to counter it (we usually also applied a rule of "followup strike" meaning if you hit you could do another strike allowing you to take out entire ships in one turn)

I wrote this game and used a similar scoring strategy. My score was based on the largest ship available, not the sum of the best shot over all ships remaining. The result is almost always a set of squares with the same high score, so the algorithm picks one of those randomly to shoot. But, humans can beat it because humans don't place ships evenly spaced. Also, the computer player needs a strategy for placing ships. My game uses random placement, which humans can hit fairly easily. The game side needs good ship placement and good shooting algorithm to beat a human.

If "no touch" rule is apllied, it changes probabilty a lot.

I played one game of battleship with my son, he tells me as we are playing that he has a winning strat. The next day I'm recommend this video. Thanks for spying on every conversation I have with my children.

my favorite strategy at this game is either : put ur ships in all corners or just stack'em as one big pile, just note that stacking them can confuse ur enemy at first because, when they shoot around they might find that one of ur boat have a "+"shape instead of a "-", but once they realise u just glued them all, u basically lost. (also try playing shipwrecker with the wind waker noises, it makes it more fun, if u know what i mean)

The true optimal strategy would assume your opponent has knowledge of the probability map during the placement phase. In this case you would use a weighted probability matrix where the weight is equivalent to the inverse of that squares pre-game probability value.

It's only works if your enemy is picking the place at random the enemy could know what you're thinking and places it on the last square you're gonna pick using this strategy, and your opponent will probably also use that strategy so you could be the first one losing

As a shorter heuristic, (1) Map out the projected shots for finding the 3-length boats. (2) Start shooting at the projected locations near the center. (3) Don't aim for locations nearby your other shots (3+ away from other shots). (4) Once (3) can no longer easily be done, start expanding outwards towards the board edges and in between shots, always filling in the projected locations.

So glad I just found this channel, you got so much highly underrated high quality content.

In my country the smallest ship is just one square in size, not 1x2. And it's prohibited to place ships right to each other or connect in any other way (i.e. a 2x1 ship occupies 3x4 area - the ship itself and "borders").

Neat. I once played a game of Battleship with my brother, and that mad lad placed all his ships horizontally in the bottom rows!

Very nice, i cannot wait to play this game and forget immediately lol

I always found it strange that you start with 5 ships, but you only get to shoot once per turn. I wonder how the strategy would change if you were allowed to shoot as many times as you have ships available (so 5 shots if you have all 5 ships, 4 shots if you have 4 ships, 3 shots if you have 3 ships, and so on).

in poland you have 1 4 grid long ship, 2 3 grid long ships, 3 2grid long ships and 4 1grid long ships. so you cant just follow the checkerboard, or you would miss all the single grid "yachts" HOWEVER ships cannot touch at all, even on diagonal, so if you sink a ship you can just dot all the squares around it as empty

Love this! Once in a while I ask myself this question and this sounds like a good answer. Enjoyed the vid a lot.

What accent is this?

I really thought this video had 580 000 views and not 580, i was surprised by the quality

Great video! Will think of this

Beautifully done video, very succinct ending. I think you could have easily done an 'example' game as well for demonstration purposes but I can't honestly criticize this methodology. Well done.

3:11 small optimization is that you only need to update the squares around the missed shot and you can cache the probabilities of squares that arent affected

What if, when you shoot around a hit square, you also apply the probability map, but not yet updated, and shoot the adjacent square with the highest probability?

This is hella cool and earned my sub

Awesome video!

There's also a SALVO version included in the rulebook. You get to call out one shot for each ship you have remaining, and then the opponent tells you which shots hit after you call all of them. How does this change the formula, if you have to call 5 shots without knowing which one was a hit?

It would be interesting to know mathematically what the most effective ship placement is, if your opponent is using this strategy

Really great video keep up the HQ content

Nice. I have been using a similar strategy, but here you analyze the position better. 👍

Wow... battleship in Brazil have completely different types of ships. For instance, the submarine is just one square, and there is the seaplane, which are 3 squares in diagonal, forming a "V" shape. Also, our grid is 15x15.

Fascinating. Now please may we have a video about the best way to deploy your fleet?

underrated, you deserve more subs

Thanks for your guides

It's refreshing to see this. Search and destroy is nice, but 4/5 of the time you don't find a DD. What happens to your approach if you wait until you find 2 or more ships to start destroying? Destroying ships represent wasted shots if you eventually find most ships, as you're more likely to know the found ship's alignment.

Which arrangements survive the longest against the final strategy? And which strategy is the most efficient at against it?

The "heat map" idea is genius!

So I'm curious if weighting the smaller ships probability maps heavier on the last method would make it any faster? Cause other techniques are faster once you've already sunk the smallest ships and I'm wondering if the same thing applies.

The task of calculating and/or updating that probability heat map is very likely to be too expensive in terms of computation resources. The interesting part is to find reasonable simplifications that can speed up the process at the cost of precision, for example allow overlapping and touching ships.

If you know your opponent will always use that strategy, what is the best placement to counter it?

That is a very cool video! Though i want to share one thing In my country we play battleships differently We still have 2 opposing players, each one has a 10x10 grid And there are changes Each player places the following ships on the grid: 4 one-tile ships 3 two-tile ships 2 three-tile ships And 1 four-tile ship The ships cannot touch each other and cannot touch diagonally and by that i mean by their corners Also the large ships can be adjusted freely and that means your eg. Four-tile ship can be a 4x1 line or a 2x2 square or even a (eg.) A1,B1,B2,C2 ship etc. So yeah these are the rules and if you play wisely it’s also pretty easy to exploit and „always” win I just thought it’s very interesting that basically the same game actually differs so much depending how’d you learnt to play, and hopefully you’d like to try this version too ;) Have a good one everybody!

Here in poland when I was a kid my mom taught me these rules: - there is one 4 square ship, two 3 squared ships, three 2 squared ships and four 1 squared ships. - each ships are called x-masted ships, where x is number of squares that the ship ocupies, so i.e a ship that ocupies 3 squares is called three-masted ship. - here is the most important change: the ships can bend. so four-masted ship can make an L shape, a square or just be straight. - the ships can't touch even if they are diagonal. so after the ship is sunk, you can instantly eliminate all squares around the ship.

yeah but wouldn't this mean it becomes optimal to place ship in spots with the least overlapping possible ship placements? (which means it becomes optimal to check those spots first). Although there is also something to be said about placing ships on the edge reducing the odds of missing a shot when checking for the orientation of your ship. This makes me feel like an optimal strategy would something like placing size 5 and 4 ships on the edges and side 3 and 2 ships at locations that aren't too central but not directly on the edges. can't prove it mathematically this is my intuition =p (and there'd probably be a meta where you can sometimes place ships in the most obvious spots but only a small percentage of the time because doing it too much would give the strategy presented in the video too much power).

Nice. In Poland, however, we have battleships with 10 ships. 1 with length 4, 2 with length 3, 3 with length 2 and 4 with length 1. That means that no matter how good your strategy is, everything comes to the luck of how quick you will be able to destroy all length 1 ships. :(

I am feeling quite proud that 6 or 7 year old me had figured out at least a little bit of this strategy and would likely account for why I always seemed to win.

That was awesome.

did you take into account that you can trick your oponent by placing two ships in contact? for example, set the cruiser horizontally and the submarine, vertically, just left to the cruiser. your strategy only deals with where to shot but not how to hide your own ships.

And ships should never touch with each other.

A fun variant is to roll a d4 at the beginning of each turn to dictate how many shots you get. Each volley is shot in its entirety before Hits and Misses are announced.

I play with: one ship of 4 cubes, two ships of 3, 3 of 2 and 4 of 1. But is the same thing. Good video.

Forgot to mention that ships must have 1 tile gap between them.

Strange rules. Usually it contains 4, 3, 2, and 1 squares ships 🚢. Never heard about 5 square ships in my life

Saw this and had flashbacks to when i was 12 - used to win every game of battleships on binweevils with a slightly rudimentary version of this strat. 20 games a week, I WAS UNSTOPPABLE!

I would occasionally put all my bigger ships in one corner or along one edge, leaving the destroyer in open water. Drove them crazy... :)

nice. here i am, thinking, oh, such a trivial game, i already know all that, and you managed to show me a new trick (approximate probability map)

Hm, weird rules. in Ukraine we use 1: four-squared, 2: three-squared, 3: two-squared, 4: one-squared, placed only in straight direction and you can't place then close to each other, at least one square must be between ships... So we have realy different strategies :)

opponent: "d4" me: "miss" opponent: "dang, your turn" me: "one sec"

I had always thought this was pretty simple. This formalizes it a bit more, but once you figure out the psychology you take to place vessels, and that it's worthless to clump shots too much... you can just start a walking pattern to figure out if you are anywhere nearby.

I have a really specific strategy for a specific opponent. When my brother and played when I was younger, I always made my ships in the shape of a J. Of course, he figured this out pretty quick. At some point I switched to always placing along the edge, and somehow he never realized the change. There were a solid few months were my placement strategy gave me a big enough headstart that I could beat him.

i like playing the faster burst ship mode. you target a point and say either (x) or (+). they tell you how many hits were in that cross or plus but NOT the squares hit and missed. if you lose a ship, you lose one edge of your burst. there is also scatter where you have one guess on your turn for each live ship remaining but that gets complicated really fast.

I usually rely on mind games. I know some people in my life are more likely to cluster them, some are more likely to put at least one touching a corner. But this will be great for the windwaker minigame

We had a little bit different rules and ships but my strategy was something like strategy 3 but backwards (search for the biggest first - and hope to find small ones)

Thank you for the tip, I start calculating the probability map for 3 hours and my opponent resigned

Thought the video would go into whether it's worth it or not to out ships on edge of the board, which used to be my strategy most of times

The psychological aspect can also be considered when you start needing to bring it out of the purely mathematical stage, I wonder how you would quantify the frequency of putting a ship in a corner/ along a wall. Cool Video!

I remember two versions that I played before. The first was dubbed "volley rules" (there might be a more proper name, but IDK). In that rule set, you each fire 5 shots a turn. You say each shot one at a time, and the opponent will say either hit or miss for each. After you do 5 shots, the opponent will call out 5 shots. This results in far quicker games, obviously. The second was one that I thought was a little weird. It went normally, until you either just miss a opponent's ship, or you hit a ship. If you hit, you get to fire a second shot. If you miss by a square (as if your called shot hits right next to a ship), the opponent gets to fire two shots in a return action.

I love this would you consider doing something like this for another game?

I did something similar to this growing up but instead of a checker pattern i made a "x" first then a "+" it wasn't as good as this video but i also noticed that people avoided placing their ships in some areas. Using that bit of psychology, i was able to win most games.

To simplify the last approach, always choose a point in the middle of the largest open area.

There was a commodore 64 battleship type game with bigger board. Each player got 20 shots with full fleet and number of shots was based on the ships at your disposal. So 2 square destroyer gives only 1 shot. First turn was all about finding biggest ships and second turn was making sure every found target was sunk if possible. Oh and not all ships were straight lines.

I'm not from Chad to be able to recalculate the probability map after every shot:) But when playing this game at school I fugured that a viable strategy would be to hunt the biggest ships first, since this reqires minimal amount of cells to be checked and maximal amount of crossed out cells as a result. Plus yes, as someone mentioned, in Russia you get an extra shot if you hit a target, so finding something quick improves your chances even more.

Just easy counter strategy: put all big ships in one line on the border of map and put smallest ship randomly. For this you will have around 10+...50+ shoots advantage. When other player will have to make insane calculations hunts, etc.

I tried your strategy. My nephew got very upset when I told him I need an hour for my next move. I'm Currently picking game markers out of the cat bowl. I really can't say that your strategy is all that great when you consider the bigger picture.

I usually quarter the board on the diagonals then fire in 4's, then 3's, then 2's. It's usually the most effective strategy.

something I always do, is that after you sunk a ship you can cross out the squares around the ship, because you are not allowed to overlap ships or place them next to each other.

Love it!

I played a version where each ship had different abilities, so the Aircraft carrier could send out 2 jets and then the jets could scout and shoot but only shoot once per game, they would also have different ways of searching with x and + patterns. The battleship shot a tomahawk missile which chunked out 9 squares and then you couldn't use it again. The submarine was the most powerful ship by being able to shoot 2 torpedoes which would keep going till contact or had reached the other side of the row or column, then after that it could scan and tell you if a ship was in the area or not, wouldn't give you exact coords. Then there was the light missile cruiser which could shoot 2 shots that would blow up three squares in a row or column. then there was the anti-aircraft missile which you could use to shoot jets with. so you had to both balance resources and find and destroy ships and then also not be wasteful with your moves. There was also a couple of different game mode such as classic, you have 1 turn, then its your opp's. then there was one where you could have as many turns as you had ships left so if you had all 5 you would take 5 shots, then the one my dad and I played which was target plus 1, if you hit you got another shot.

My fave strategy is to hide ships in the corners and at sides. Many players know about probability in the middle higher, so they will start from there. And if you must keep 1 cell distance between ships, even if some ships a killed, the enemy gets less data about denied squares. It works against humans just once. But for one game it makes miracles.

Reminds me of back when id play this in my Nintendo DS. I can still hear the angry captain yelling "Argh, you sunk my BATTLESHIP!"

actually the 2 tile ship is the Patrol Boat in some/most depictions of the game while the Destroyer is one of the 3 tile ships instead of the Cruiser

My strategy: 1) Think of the board as checkered, and only target one color of the grid (unless of course you hit something) 2) Hunt for the carrier and/or battleship first. They're easiest to find because they're so big. Minimize wasted shots for when you need to backtrack on searching an area. 3) Once you find the carrier (or whatever else you stumble upon), use that information to infer where the other ships might be. Sometimes people bunch up all their ships in one area. Sometimes they spread them evenly. Sometimes they bunch up 4 and put their destroyer far away.

Without knowing the math, I was following this approach when I was 7. My preferred strategy is to have the player near something reflective so I can increase my statistical insight into where to place my next shot.

Whats expected number of shots given that opponent also knows you update shots based on probability maps and hence places adversarially, hence updating your probability map etc. In the limit where you get to an equilibrium