Calculating the Number of Unique Decisions Made Each Game of Global 40

[Make_It_Round]

I’m interested in trying to find out how many decisions players are forced to make in each game of Global 40 from a game theory perspective.

If a game has too many choices in it, players feel overwhelmed and tired.

If a game has too few choices in it, players feel underwhelmed and bored.

I think Global 40 gets the number of choices about right, in that it’s a game with a meaningful number of choices in it that keeps players stimulated enough, without alienating them.

So let’s think about Italy’s first turn, perhaps the simplest case.

10 IPCs to spend = 10 main alternatives

1. fighter
2. destroyer, save 2 IPCs
3. transport & infantry
4. tank & artillery
5. sub & artillery
6. tank & mech inf
7. sub & mech inf
8. 2 infantry & artillery (my personal preference)
9. 2 infantry & mech inf
10. save IPCs for future purchases

I’m assuming that there’s no research dice being purchased, or any allied industrial raids that have been performed so far in the game; that even more AAA are not perceived as being good purchases; and that if the Italian player decides to spend her money, she will spend as much of it as possible. Even with those parameters in place, the first purchasing decision(s) of the game generate a pretty impressive menu of choices. The number of permutations will increase with each additional IPC added to Italy’s income, which usually increases for the first few turns at least.

If we look at positive choices (choosing ‘to’ do something) as opposed to negative choices (choosing ‘not to’), then usually I choose 3 things to purchase for Italy (i.e., 2 infantry & artillery).

Combat Movement

Some of this depends on what the UK does, and what Germany doesn’t do, but in general there are some standard options:

1. Southern France
2. Gibraltar
3. Greece
4. Tunisia
5. Alexandria
6. Syria
7. Trans-Jordan
8. Egypt
9. Anglo-Egypt Sudan
10. Cyprus
11. Malta
12. French fleet in SZ 93
13. British fleet
14. crazy DoW on USSR (actually relies on an earlier political decision)
15. crazy Dow on neutrals (actually relies on an earlier political decision)

And of course the list goes on, to include aerial interventions in the North Atlantic, to invasions of British Somaliland, and any combinations of the above list in Chinese menu format. Overall, Italy will usually end up making 4 or 5 attacks out of a list of about 20 possibilities.

During combat, Italy may need to make some important choices as regards the order of losses, and whether or not retreats are required. Because Italy seems to need to make more of these kinds of choices than other nations, let’s expect that they’ll make about 3 of these in the course of conducting combat.

Let’s also allow approximately 4 or 5 meaningful non-combat choices, including where planes are landed.

Choices of placement are limited to one of the two factories, or both. So there’s a maximum of 2 positive choices that can be made here.

Thus, the Italian player will typically make approximately 17 positive choices in I1 (and several dozen negative choices).

Assuming that the number of choices are generally increased by territory and unit gains, and generally reduced by losses of the same type, and that the average game of Global 40 lasts 10 rounds, an average game for an Italian player might include upwards of 200 positive choices (and several hundred negative choices).

I’m speculating slightly here, but it looks to me like playing Italy (one of the most maligned nations to play on its own) compares rather favorably with the complexity and satisfaction of choices involved in a challenging and lengthy game of chess.

Just curious: what do people think are the lower and upper thresholds of the numbers of unique decisions that an average adult would tolerate / find interesting? Would you play a game that only offered you 20 unique decisions? How about 5? Or 100,000?

[MrMalachiCrunch]

It depends on what you mean by a choice.  The choice of a particular battle could be a binary Yes/No.  But that really is a summation of many choices.  How many units to use in a given battle?  There might be 20 viable battles with a range of potential outcomes from low success/high payout to high success/low payout to other permutations of which you can accomplish say 5.

How did you come to the ‘knowledge’ that there was 20 viable battles?  Experience and weighing the odds.  So how many battles could you engage in?  Perhaps 100s if you look at all the legal possible moves including using 1 infantry against a force of 5 infantry on a valueless territory or attacking a battleship with a transport which is a legal move with no chance of success.  That is a choice, a bloody silly one so it wouldn’t make the list of 20, but a choice.

Combinatorial explosion comes to mind quickly.

[Gargantua]

I think it’s important to note that the -option- is not the -choice-.

For example, you only make one decision from the above 10 options.  IE you had a choice and chose (1).

That said, because of dice, and opposing strategy, your choices are somewhat controlled.  Thus calculating the number of -choices- a player makes is impossible, as for example, someone like myself, chooses to remove the ability of my opponent to -choose- as part of the overall plan.  Impossible to account for or against.

You should also account for the fact, that some countries, like Russia/America don’t get to make many choices, until war has begun.  Purchasing being 1, moving the other.

[Make_It_Round]

@Gargantua:

I think it’s important to note that the -option- is not the -choice-.

For example, you only make one decision from the above 10 options.  IE you had a choice and chose (1).

That said, because of dice, and opposing strategy, your choices are somewhat controlled.  Thus calculating the number of -choices- a player makes is impossible, as for example, someone like myself, chooses to remove the ability of my opponent to -choose- as part of the overall plan.  Impossible to account for or against.

You should also account for the fact, that some countries, like Russia/America don’t get to make many choices, until war has begun.  Purchasing being 1, moving the other.

Fair points Garg.

I agree that the best players of A&A try to reduce the number of viable choices their opponants have (taking out enemy transports is the move of choice in this regard); and in so doing, they definitely reduce the amount of fun others can have. Cost of doing business!

My question is: how few viable choices can be left to a player before the game becomes not worth playing for them, i.e. not fun anymore?

If I am left with three attack options for example, but all of these are suicidal, and I have no hope of surviving their combined attack on my defence next turn, then I might concede the game. The apparent ‘choice’ I have in this case is no real choice at all, and it is of little interest for either me or my opponant to see the dismal proceedings through to their bitter end. This is presumably because the victor will have too many viable options which allow victory, to the point where the game is no longer challenging to her.

I think it is possible, however tedious, to count the number of meaningful choices that players have in any given game, and to guess at one’s enjoyment threshold in terms of these. It would just require a lot of careful analysis, which is not why every person chooses to play A&A… I bring it up here simply to raise awareness of the issue, and to lay some conceptual groundwork for future possible game theorizing on this basis.

[Gargantua]

The trick is in how you present the choice…

Do you want to wear red socks?  Or blue socks? :)

[mastermind93]

@Make_It_Round:

I agree that the best players of A&A try to reduce the number of viable choices their opponants have (taking out enemy transports is the move of choice in this regard); and in so doing, they definitely reduce the amount of fun others can have. Cost of doing business!

My question is: how few viable choices can be left to a player before the game becomes not worth playing for them, i.e. not fun anymore?

When I play with friends, we rarely finish a game. We also play for capitals/ world-domination, so there’s always a point at which it no longer is fun for the apparent loser of the game. If there is a general consensus that one side is going to lose and wants to surrender, I -ahem- the other side lets them do so honorably, rather than dragging it out.

[Canuck12]

@Make_It_Round:

I think it is possible, however tedious, to count the number of meaningful choices that players have in any given game, and to guess at one’s enjoyment threshold in terms of these.

It is utterly impossible to count the number of meaningful choices that players have in any given game because each “meaningful choice” is a product of the other “meaningful choices” that were made previously. Furthermore, each “meaningful choice” is then subject to all of the possible dice outcomes, and thus multiplied by all of those possibilities and then multiplied by all of the “meaningful choices” offered by the various non-combat possibilities as they are determined by the dice outcomes. As you can see we get into these massive factorial situations where we are multiplying massive exponentials by even more massive exponentials until what is essentially infinity.

To make a comparison: In chess there are only 20 possible moves to make on the first turn. (16 pawn moves and 4 knight moves) The opponent is faced with the same. So the possible combinations for the opening 2 moves (1 each) in chess is 400. None of which are absolutely stupid. there are 8,902 possible moves by 2 each and by move 7 there are almost eleven MILLION possible positions. That’s without dice, with only 2 players, with a much much much more limited scope for unit movement, no scope for adding units and far far fewer spaces.

Now you asked about the “meaningful choices”. Some work has been done in this regard in chess and it seems that in the average game of about 30 moves (moving a single piece at at time. There are over 4.5 MILLION games outcomes in smart competitive situations. Now, multiply that by the factor of dice, multiple movement of units, game spaces, purchases and the fact that most AA games will see over 100 times that 60 units move factor and you have an utterly infinite combination of outcomes.

Which is part of the reason it is so much more entertaining than chess.

…or maybe just because we get to play with little tanks and planes.