## Sid Meier Keynote and my thoughts on game odds.

## Interesting talk from Sid Meier - I'm still watching, but this is a note for later.

At around 20 mins in, Sid introduces a conundrum regarding player combat and the discrepancy in player perception of odds.

The example given is of the player accepting that they may occasionally lose a 2:1 battle (approximately 1 in every 3 games) - but has difficulty reconciling the idea that they lost a 20:10 game "I have 10 more!"

Sid points out that this their assumption mathematically unsound and continues to speculate on the psychology of gamers (while the audience chuckle derisively in the background).

This scenario makes perfect sense to me, however. I understand the basic mathematics of 20:10 == 2:1 (obviously). However I propose that the two may not be that similar, especially in terms of combat (and other somewhat complex, or emergent) systems. Instead it should be looked at in terms of combinatorics, possibly considering the average individual's combat capacity, rather than the sum.

See, the reason the player has difficulty with this is that every single player they have in advantage, should also have a (randomish) high chance of fighting well above their capacity. Ie. just as the disadvantaged player in a 2:1 battle has a chance of winning, every additional unit on the field in a match of equal ratio should have a chance of beating at least 2 (or more) opponents.

What seems logical for a player is the idea that in (say) a 20:10 match, they should be able to be down to their last player with their opponent absolutely slaughtering them, for example 1:9 and there will still be a chance - albeit a small one - of pulling out a victory. Perhaps the remaining opponents have already been weakened by other (now dead) allies? Perhaps the survivor has learnt a few things watching their mates getting killed? There are any number of justifiable (though mathematically 'illogical') reasons to assume this is okay.

I feel this is because rudimentary statistics like those used on horse races are inherently unsatisfactory for modelling higher-level processes like fighting, survival, etc.

## So what?

I'm going to give this a little more thought, as it could easily be modeled with an iterative function:

```
```function calculateTeamOddsScalar( teamObject, teamAverageStrength, opponentAverageStrength ) {
var total = 1;
for (var i=0; i<teamObject.totalUnits; i++) {
// results of a simplified combat, > 0 for our winning amount, < 0 for our losing amount
var diff = random(teamAverageStrength) - random(opponentAverageStrength);
total += diff;
}
return total;
}

```
I would, however like to find a more elegant mathematical solution.
```

## No really, so what?

The numbers will more accurately reflect the type of odds we expect in real life, rather than the pure mathematical approach. We're constantly skirting the odds and statistics are useful for certain types of analysis - however they are limited by their simplicity in common game engines.

Remember that odds make sense generally over very large sample sets, not necessarily on a short time scale. The fact that I have a higher chance of dieing in a car-crash than an aeroplane crash doesn't in any way reduce my chances of being in an aeroplane crash. These statistics are only useful when looking at humanity as a whole. And really only good for proving inane points, or seeming like a smartass.

## Conclusion

I'm clever and this is a good idea so poo poo to you you.

Or I'm potentially a complete moron stating the entirely obvious.

I'd give you the odds that each of those statements are true,

but they'd be meaningless.

GDC 2010: Sid Meier Keynote - "Everything You Know is Wrong" - YouTube