007 Strategy

Remembered that 007 game I used to play a lot in primary school (I think that's the right translation?).

Out of curiosity I wanted to see how could I strategy analyze it.

Written 12/07/2025.

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Base rules

The game is similar to rock paper scissors: 2 players, you say 0-0-7 and on 7 you both reveal a hand gesture to denote your move.

You have 3 moves available to you:

• Shoot (finger guns at opponent),
• Reload (finger guns pointing up),
• Shield (arms crossed).

You each start with 0 bullet (which we kept track of by memory). Reloading gives you 1 bullet, shooting costs 1 bullet.

If you shoot at shield, nothing happen and you wasted your bullet; shoot at reload and you win; shoot at shoot and it's a tie.

Issues

There are 2 issues with this rule set, one very minor and one major:

• As you start with 0 bullet, there's nothing to shield against on turn 1, so reload is the only real turn 1 move.
• You can just spam shield and the game never ends.

The first is minor and easily fixed: just have everyone start with 1 bullet (we did not figure this out in primary school).

The second tho is a much bigger issue, and shield spam was indeed what we did most of the time.

Fixing shield spam

I have 3 ways in mind to fix the shield issue, some of which I remember we tried back then:

• Have a limited number of shields per game (like 1).
• Can't shield on consecutive turns (I think we did that one but I'm not sure).
• Add a 4th move: Bazooka (mime holding a bazooka), costs 3 bullets, is like shoot except it wins against shield (we did this one).

And now that I look back at it, I wonder how these variants affect the strategy.

Strategy on single shield and bullet

I don't fully have the game theory knowledge but I got some maths background so let's try our best and see what we can find.

The first step is always to start with a simpler example and work from there. Let's try the following:

• Limit the number of bullets held to 1 to make the state space finite.
• Only have 1 shield per player per game (without shield the game is trivially a tie).

This makes 16 possible game states: for each of the 2 players you can have a bullet or not, and you can have your shield or not.

As the game is symmetrical, let's say we are P1, so we can represent the game states with this table that we will fill out:

P1		P2
		Shield		No shield
		Bullet	No bullet	Bullet	No bullet
Shield	Bullet	Start	?	?	?
	No bullet	?	?	?	?
No shield	Bullet	?	?	?	?
	No bullet	?	?	?	?

Let's make some easy remarks on how the game progresses:

• If you have no bullet and no shield, you can only reload (and thus lose if your opponent has a bullet).
• If nobody has a bullet, both should reload as shielding would only waste it.
• If both players lost their shield, whoever has a bullet win. If both or neither player has one, then it's a tie:
  • If both have a bullet, if both reload then we end at the same position, and if only one reload then they lose.
  • If neither have a bullet, then they both have to reload, and we end at the situation above.
• If someone shoots, either a shield is spent or the game is over, which removes 3 possible states from the game.

This lets us start filling the table like this:

P1		P2
		Shield		No shield
		Bullet	No bullet	Bullet	No bullet
Shield	Bullet	Start	N/A	?	Win
	No bullet	N/A	N/A	?	Reload
No shield	Bullet	?	?	Tie	Win
	No bullet	Loss	Reload	Loss	Tie

So it's the shield's presence that gives some complexity. From these above remarks we can also get the following on the starting position:

• If both shoot it's obviously a tie.
• If both shield then we end at the no shield situation, and since both player start with a bullet that's also a tie.
• If both reload the game has not moved from the starting position (as here you can only hold 1 bullet).

That makes the interesting positions the ones where only one player shields on turn 1. For simplicity let's say P2 shields turn one:

• P1 shoots, they're now 0 bullet 1 shield vs P2's 1 bullet 0 shield.
• P1 reloads, they're now 1 bullet 1 shield vs P2's 1 bullet 0 shield.

This leaves only 2 game states left to study (as it's symmetrical), which are the 2 results from the 2 branches above.

No bullet

The easiest of the 2 options as you have 1 less move available. In both cases P2 can now only shoot or reload, so let's be exhaustive this time:

• P1 shields:
  • P2 shoots, it's now 0 bullets and 0 shields accross the board, it's a tie.
  • P2 reloads, it's 0 bullet 0 shield vs 1 bullet 0 shield, so P1 loses.
• P1 reloads:
  • P2 shoots, P1 loses.
  • P2 reloads, it's now both 1 bullet but P1 has a shield, that's also our other big case.

So in this situation, P1 can never win if they shield, and P2 can never lose by shooting. Tho we still need to evaluate that last case to see what it entails.

Yes bullet

This time P1 can also shoot, and shielding leads to a different situation as they still have a bullet.
P1 reloading leads to the same outcomes as above so we won't repeat it.

• P1 shoots:
  • P2 shoots, it's a tie.
  • P2 reloads, P1 wins.
• P1 shields:
  • P2 shoots, all shields are out but P1 still has a bullet, so P1 wins.
  • P2 reloads, both players have 1 bullet and no shield, it's a tie.

Here, as long as P1 does not reload then they can't lose, and if they reload then they either lose or we loop to the same position, so they should never reload.

From there, whether P1 wins or it's a tie is basically a coinflip, as P2 shooting ties if P1 shoots and loses for them is P1 shields, and vice versa for P2 reloading.

This lets us conclude that on the previous big situation (0 bullet 1 shield vs 1 bullet 0 shield), both players reloading leads to coinflip on P1 winning or a tie.
This makes it the only option on that big situation that advantages P1, but if they attempt it while P2 takes the safe option of shooting then they lose.

Wrapping up

So we see that if P2 shields, if P1 shoots then it's a guaranteed tie or P2 win, and if P1 reloads it's a guaranteed tie or P1 win.

Based on the fact that both players reloading essentialy means "move to same shield but both bullets", we can complete the table like this:

P1		P2
		Shield		No shield
		Bullet	No bullet	Bullet	No bullet
Shield	Bullet	Start	N/A	Win/Tie	Win
	No bullet	N/A	N/A	Loss/Tie	Win/Tie
No shield	Bullet	Loss/Tie	Win/Tie	Tie	Win
	No bullet	Loss	Loss/Tie	Loss	Tie

This lets us do a little conclusion with the possibilities of turn 1:

You	Opponent
	Shoot	Reload	Shield
Shoot	Tie	Win	Loss/Tie
Reload	Loss	Restart	Win/Tie
Shield	Win/Tie	Loss/Tie	Tie

I don't really know what to analyze more on that, so I guess it's time to ramp up the complexity.

2 bullets 1 shield

I think the next one to consider is the ability to hold 2 bullets. Unfortunately I'm out of brain juice so that's all for today.

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