Odds of never missing in a game of Battleship

Quote: Nareed

The problem, as usual, is the honesty of the players. I did know people who'd cheat at Battleship, Mastermind and Go Fish.

[goad]Did they believe in God?[/goad]

I guess the rules you remember are likely dependent upon where/how you learned the game. My older brother and I were taught Battleship by our father, and we used quadrille paper ("graph" paper with 1/4" blocks). Each player drew two game box outlines and positioned our "ships" in one of them. The other box was for marking where we fired shots at the other player's ships.

In our game, I think there were five ships, with lengths ranging from one to five blocks. Each player had as many shots on a turn as he had un-hit blocks on his own ships, so the first player's initial volley was 15 shots. We marked the shots we took on the "opponent" game box, numbering them with the round number -- 1s for the first volley, 2s for the second, etc. After the first player fired a volley, the other player reported how many hits there were on each of his ships, then he fired his volley.

Under those rules, you could track were your full volley was aimed and which ships were hit, but you didn't know which shots hit which ship. You had to analyze the hits from each volley to try to figure out where the opponent's ships were positioned.

I remember my younger brother having a toy-store version of the game with pegs or markers or something. I don't remember the rules of that game, but I probably knew them back then. Later, I saw ads for an electronic version of the game, but I never saw it outside of a box. Maybe that was during the era when one of my kids might have played.

I do remember we laughed at the picture on the outside of the box for one of those games. It showed two boys playing the game, with one of them calling out the location of a shot. The other boy responded, "It's a hit!" (This seems to support the idea of immediate feedback, unlike the game my father taught us.) The amusing thing was you could see the board with the ship locations, and the co-ordinates for that shot did not hit any ship. Whoever did the cover graphics apparently did not understand the game!

Strategy aside, cant you determine the odds of 17 straight hit as if you were betting a 17 out of 17 pick in keno with it having 100 numbers? Sure playing the game is different, but were talking about 17 random picks hitting.

You also have to figure out every possible combo of layout the ships could be in. If you pick A1. you MUST chose B1 or A2. You cant keep both as a miss. Here is an easier way. If I set my ships, what are the odds my opponent set them exactly the same?

There's Battleships the Movie coming out soon. Sigh.

The standard version I played was with 1 battleship (4 squares long) 2 Cruisers (3 squares), 3 Destroyers (2 squares) and 4 Submarines (1 square each). Turns were strictly you go/I go (Ugo-Igo).

I know of one variant where each ship had at least one gun placement and you got as many shots as gun placements, much as Doc describes.

Another was that all shots were fired in Salvo's of three, which had to be in a line. Again you'd be told number of hits and if you sank anything.

All ships had to have a clear space all the way around them (no touching, even diagonally)... this will reduce your number of shots and chances of hitting a perfect score of all hits no missed.

Battleships : Galaxies has also been released as a major revamping of the game. It has some of the hidden features of the original, but much more tactical in nature from what I've heard.

Quote: Ibeatyouraces

Strategy aside, cant you determine the odds of 17 straight hit as if you were betting a 17 out of 17 pick in keno with it having 100 numbers? Sure playing the game is different, but were talking about 17 random picks hitting.

This is what Face and DJTeddyBear calculated earlier. About 1 in 6.65 quintillion.

Quote: Ibeatyouraces

If you pick A1. you MUST chose B1 or A2. You cant keep both as a miss.

Again, it depends upon which rules for Battleship you are following. In the version I was taught by my father back in the early '50s, as described above, the smallest ship only covered one box. It would be possible to have that ship in position A1 and nothing in B1 or A2. If the rules you are considering only have ships larger than that, then I agree completely.

I think your "easier way" might be close. However (per the rules of my father's version of the game) I could have my 2-block ship end-to-end with my 3-block ship in the same position as your 5-block ship, or my 1-block and 3-block ships touching and in the same position as your 4-block ship. Thus, there are ways to cover the exact same coordinates without having the exact same ship layout. This might not work with other versions of the game -- I don't remember the ship sizes in those games.

Quote: CrystalMath

This is what Face and DJTeddyBear calculated earlier. About 1 in 6.65 quintillion.

And if this were a casino bet, they would probably pay 100,000 for 1!

The two versions I remember (I think both are in the original rules) are:
(a) Players alternate taking one shot at a time;
(b) "Salvo Battleship" - each player takes a number of shots equal to the number of ships the other player has remaining; each hit must have its ship identified (e.g. "B-6 was a hit on my submarine").

Thinking about this some more.

If you just consider all of the ways that each boat can be placed on the board independently, which would include overlapping boats, we can overestimate the number of unique boat placement patterns:

boat	size	unique placements
aircraft carrier	5	120
battleship	4	140
submarine	3	160
destroyer	3	160
patrol boat	2	180

The total number of possible placements (including overlapping boats for ease of calculation) = 120*140*160*160*180 / 2 = 38,707,200,000. I'm dividing by two because we don't care if the submarine and the destroyer are swapped.

I have also already determined that once you place the aircraft carrier, there are, on average, 120 places to put the battleship. So this reduces the total possibilities to an upper limit of 33,177,600,000 (120*120*160*160*180 / 2).

Without additional strategy, such as selecting spots adjacent to hits, the worst possible odds of hitting all 17 with 17 picks is 1 in 33,177,600,000. I think there's a chance that using perfect strategy could get the odds better than the powerball.