"I claim this corner of the world for Britain!" - What game are Alex and Brooke playing?

Question

^{An entry in Fortnightly Topic Challenge #45: Flags}

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Alex and Brooke are playing a game. I've transcribed their conversation below. Can you make sense of it?

Alex: I claim this corner of the world for Britain!

Brooke: Haha! You've missed your chance. I declare Japan the center of the world!

Alex: Ho ho, but you know what happens when you're in the center? I can flank you! Or my allies can. Jamaica, go 'round Japan. We'll squish 'em between.

Brooke: ... Jamaica? Why are you helping Britain? Nevermind. I got Bangladesh on my side! We'll claim some untrammeled corner of the world for us.

Alex: You don't see it, do you? You've already lost. Now, I'm calling in some friends closer to home. Scotland, go to my south! Let’s colonize the last corner of this world.

Brooke: You really don't know your geography, do you? Scotland is part of Great Britain, and the planet is round, and... oh, no. I see what you meant. I'll wave the white flag.

QUESTION: Make sense of their game to tell me – what game are Alex and Brooke playing here? Please include an explanatory diagram (or diagrams!) in your solution.

_{Inspired by this much superior puzzle}

Answer 1

You are playing:

Tic-tac-toe, or noughts and crosses as our British friends call it! All of the countries named have a flag with either a cross (Britain, Jamaica, Scotland) or a circle in the middle (Bangladesh, Japan). Here is the gameplay:

First move:

"I claim this corner of the world for Britain!" - It has to be an upper corner, as we will see in a second.

Second move:

"I declare Japan the center of the world!"

Third move:

"Jamaica, go 'round Japan. We'll squish 'em between." - This indicates that we take the opposite corner from Britain.

Fourth move:

"Bangladesh on my side! We'll claim some untrammeled corner of the world for us." - Nought takes the upper right corner. It has to be the upper right corner, since the next move needs Scotland to go south of England.

Final move:

"Scotland, go to my south! Let’s colonize the last corner of this world." - At this point, crosses block the noughts possible diagonal, and give themselves two possible winning plays that cannot both be blocked. Win for the Commonwealth!

Clever observation from Braegh:

Crosses are played by aleX, while noughts are played by brOOke!

Answer 2

Wrap-up: The Making Of “I claim this corner of the world for Britain!” - What game are Alex and Brooke playing?

This is not a solution to the puzzle, but provides notes from its poser. This type of answer has been approved by the community.

Caution: This post may contain spoilers.

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Inspiration

I wanted to make an entry into the FTC. I've made flags puzzles before, but those were both connect-walls for an earlier FTC. And I didn't have any fun ideas to make another connect-wall. While browsing around Puzzling at random, I stumbled into Stiv's excellent puzzle that disguised a game using cards. Now I had an idea - disguise a game using flags!

Creative steps

So now I had to find a game to disguise with flags. I made myself a list:

• Must be simple (I didn't want a complicated puzzle)
• Must have tokens/parts/players with distinctive characteristics which can be mimicked by flags
• Must have a quick winning strategy (I didn't want a long puzzle)
• I have to be familiar with it

Now I went browsing through the tags on Puzzling for ideas. (The plan after this was to look through Wikipedia's list of lists of games; luckily I didn't have to go that far) Immediately, tic-tac-toe stood out. Going through my list:

• Simple? Check
• Tokens? Crosses and circles, those are on flags. Check
• Quick winning strategy? I knew about the corner trap. Check
• Familiar to me? I played far too much of this as a wee one. Check

Now I had a solid idea. I would use flags with Xs and Os on them to play out the corner-trap strategy in tic-tac-toe.

Logistical steps

Like any good internet denizen, I did my research. More exactly I typed "flags with crosses" and "flags with circles" into Google. There are surprisingly few, but I found enough to pull off 5 turns of the game. When writing the banter and story flowed nicely.

I worried that "corner" was overused - but I couldn't figure out another way to specify corner locations! I also wanted to precisely specify which corners, but the eventual product was ambiguous with a possible reflection over the vertical midline.

Then there was the double-checking. I checked that all of the countries mentioned did indeed have flags with Xs or Os. (I checked this maybe 5 times, which in hindsight is a bit much, but it was a very important part of the puzzle). When checking I realized that the flag I had as "England" was actually the flag of Great Britain... chalk that up to me being an ignorant, uncultured American.

Right up until posting I kept making tiny adjustments to the banter. Changing the names to "AleX" and "BrOOke" was a last-minute hint and also my way of making this not just another Alice and Bob puzzle.

Takeaway

This was my first attempt at a story puzzle. I'm shocked at its reception. I wish I could leave you with the magic formula for puzzle popularity, but I don't really have one besides "make interesting puzzles which are answered quick and then HNQ'd". Which is, y'know, hard.

I do have some advice, though. If you want to make a story puzzle, short and simple is more satisfying to solve than long and complicated. Stuff as many hints as you can into the text. Keep in mind that what's blindingly obvious to you could be what a solver needs to grasp onto as a starting point. And finally, good luck.

Answer 3

While Jeremy Dover's answer fits better,

If they're playing Scrabble, each country can be played off of the previous one.