- Thread starter keithburgun
- Start date

Does the goal type contribute to interestingness of decisions in a game?

Score games have no such foregone conclusions. No matter how poorly or how well the player has done so far, they will still be able to do better or do worse, and thus influence the score they get at the end of the match. If you are in a foregone conclusion in a win/loss game, it doesn't matter if you start to do worse or better, since the outcome is already determined. Even in the case of merely being

But on a more fundamental level, I think that it's slightly mistaken to think in terms of interesting

One important thing for learning is feedback, and score is much more effective as end-of-match feedback than a win/loss, simply because it conveys more useful information. So even beyond the obvious impacts on the interestingness of decisions, score systems will lead to games that are more fun than win/loss systems, because better feedback means more learning.

Score games have no such foregone conclusions. No matter how poorly or how well the player has done so far, they will still be able to do better or do worse, and thus influence the score they get at the end of the match.

Or maybe a problem that it's impossible to set things up like that? Perfect difficulty can't ever be achieved? Mechanics can't be paced like that without them getting too swingy and output randomnessy towards the end? I'm currently mulling over endgame pacing in my WIP game so that's a live issue for me! (Switching to a score goal is out of the question for this game btw.)

Score games can still have have forgone conclusions, they're just easier for the designer to avoid since they have more outcome resolution.

I qualified that statement with "well-structured" because it's actually pretty easy to avoid foregone conclusions if you don't care about structure. As @richy alluded to, one way to avoid foregone conclusions is just to make the game very swingy, so that at any moment the player could randomly get screwed over or receive a large power boost. Many roguelikes and roguelites are like this.

As to your question, @richy , about whether it's possible to create a win/loss game that avoids foregone conclusions while also having good structure, I'm highly doubtful, mostly because the foregone conclusion problem is actualy a special case of a more general problem that follows directly from the properties of win/loss games. This more general problems is that as the chance of victory gets further from 50% (in either direction), the chance that new actions will change the outcome of the match gets lower. A foregone conclusions is merely the most extreme example of this problem, but the same problem persists (to a lesser degree, of course) when the chance isn't quite 100% or 0%, but instead only 99% or 1%, and it even persists to a small degree at 75% or 25%. The only way to avoid the problem entirely would be to always have the winrate stay at 50% until right near the end of the match, but if the winchance stays at 50% then clearly nothing you are doing actually matters to the outcome of the match, so it wouldn't really be what we would call a "strategy game".

Last edited:

E.g It seems more likely to me that score-based goals could lead to foregone conclusions than binary goals. In a win/loss game we can make it so players have the ability to close out wins quickly. Similarly losses can be made to happen quickly once inevitable. Surely it's a score goal which runs the risk of forcing the player to chug all the way to the required score?

I've thought for several days about this next thing you said and finally think it's very insightful but draws a questionable conclusion:

"The only way to avoid the problem entirely would be to always have the winrate stay at 50% until right near the end of the match, but if the winchance stays at 50% then clearly nothing you are doing actually matters to the outcome of the match."

This seems good, and I think viewing win/loss strategy matches as steady marches from an initial 50% chance through 60%, 70%, 80%, 90%, and finally 100% victory at the end, may be a mistake. IMO the meaning of gameplay (like life??? ) is at a maximum when fully ambiguous, and as you said, we should want players to always be thinking and learning and playing moves conjecturally. A game which keeps the player fully uncertain about whether they'll win or lose for as long as possible seems ideal. The opposite to "nothing you are doing actually matters" - arguably it matters the maximum amount!

You said a similar thing yourself in the same paragraph:

"This more general problems is that as the chance of victory gets further from 50% (in either direction), the chance that new actions will change the outcome of the match gets lower."

For me I do agree the second point seems like something needing attention when designing mechanics. Clearly when randomness is involved we can expect players to find themselves at (say) mid-match in better-than-normal and worse-than-normal positions, so handling that is a practical design problem.

I don't have answers, but I'm looking for them atm by assuming it'll be a good thing (as per above) to try and make it so win chance remains fairly steady through the match until the point when, over the information horizon, we glimpse that a win or a loss is quite close and perhaps nearly inevitable. Players playing above their skill level will start with a low win chance, and should find their frequent losses coming quite quickly and their occasional wins taking a relatively long time. Players below their skill level will be starting with a high win chance and should find the reverse - many quickish wins and few lengthier losses. And we would 'tune' the mechanics to work best for players on an appropriate skill level where their win chance starts, and mostly remains, at 50%. (Perhaps a new perspective on the good old "what is the

The problem is how to make all this happen! As I said, the discussion is really stimulating even if I'm not ready to get on board the score-goal bandwagon! I'm interested in any other thoughts you have on the subject, especially if what I said above is utter nonsense (please say why!)

In a win/loss game we can make it so players have the ability to close out wins quickly. Similarly losses can be made to happen quickly once inevitable. Surely it's a score goal which runs the risk of forcing the player to chug all the way to the required score?

I agree that there are often ways to improve win/loss games so that they are less suceptible to foregone conclusions, but I'm skeptical about how far this process can be taken. I'd love to be proven wrong, though. I think that having structure makes it harder to avoid foregone conclusions. Let me give an example to demonstrate what I mean:

Imagine that there is a game that lasts 100 turns, and you win if you have 500 gold at the end, and lose otherwise. This game might have a foregone conclusion if the player does very poorly for the early game and still has 0 gold at the end of 50 turns, and so to eliminate that situation we might add a rule that says "At turn X, you lose if you don't have more than 5*(X-10) gold", so in other words you lose if you still have 0 gold at turn 10, or only 5 gold at turn 11, 10 gold at turn 12, 200 gold at turn 50, etc. This effectively eliminates a lot of foregone conclusion situations, BUT it only works under the assumption that how well the player is doing is roughly proportional to the amount of gold they have. If the game has structure and allows multiple strategies, one of the strategies might involve heavy investment in the early game in something other than gold, and then spending the late game cashing in on the investment to create a lot of gold. So the player could have 0 gold at turn 50 but actually be in a very good spot.

More generally, to the degree that a game has multiple viable long-term strategies (which is a feature of games with good structure), it will be hard to find a single variable/resource that describes how well the player is doing, and therefore it will be hard to avoid foregone conclusions by changing the win/loss conditions. You could maybe try to define a loss condition in terms of multiple variables in order to account for multiple strategies, but that would quickly become pretty hard for the player to comprehend.

With regard to your other point, I don't think I was contradicting myself. When I said "if the winchance stays at 50% then clearly nothing you are doing actually matters to the outcome of the match" I didn't mean that nothing mattered because it was

It's easy to get caught in the trap of thinking of winchance as a resource or something, where you can be a better position even if you have less it under some circumstances, but winchance is actually something fundamentally different. A resource (or other variable in the gamestate) can only ever be a heuristic measurement of performance, and thus it is fallible, but the winchance is never fallible. If you have a higher winchance you are doing better at the game, and if you are doing better at the game you have a higher winchance, by definition.

I bring this up because I think you were making this mistake, of thinking of winchance as being like a resource, when you made this point:

The way I look at it, a player who spends most of a match with win and loss evenly poised like that is definitely doing at least one thing that matters a lot, namely not losing.

And I think this is important because it means that this:

t'll be a good thing (as per above) to try and make it so win chance remains fairly steady through the match until the point when, over the information horizon, we glimpse that a win or a loss is quite close and perhaps nearly inevitable.

Excuse me for barging in at this late stage; a very engaging discussion so far!

Hopenager: a thoroughly argued point, and I absolutely agree on your distinction between win-chance and resources, in that the maximisation of the former is always good, whereas that is not necessarily true of the latter. However, the win-chance staying at 50% does not indicate a poor player performance.

What really matters for evaluating the player’s performance over Δt (a given change in time) is not the resulting win-chance, nor is it even Δ(win-chance). The true measure of player performance is the likelihood of doing at least as well - or conversely, at least as badly - as they actually did, with regard to Δ(win-chance).

To put that into English, if the player’s win-chance changes by +2% over a given turn, that in itself is meaningless - what matters is the how likely it was to do at least that well. If the chance of achieving +2% or better was one in ten, then the player has performed very well. If the odds were even, they’ve done on par. If the odds were against them that they’d get +2% or*less*, then the player has performed poorly.

Therefore, that win-chance remained at 50% throughout much of the match does not necessarily indicate poor play. If the chance of maintaining win-chance had stayed around one in two throughout the match, then this would have been on-par play.

The question for the designer is where they would like win-chance to sit and how they would like it to evolve. Having win-chance above or below 50% means the system is partially solved, to the extent that win-chance deviates from 50%. Therefore, given that strategy games should be maximally ambiguous, in a well-designed strategy game, win-chance should tend towards 50%.

P.S. This principle is most obviously true in multiplayer games. In a well-matched and well-played game of chess, for example, we would hope both players to be fighting tooth and nail almost to the last turn, each with as close to even chances of winning as the other for as long as possible. This principle, may, however, seem counter-intuitive in single-player games, where we would naturally expect good play to result in a high win-chance. I still think this principle applies, though - single-player games, just as multi-player games, should make good play result in*higher* win-chances, but not *high* win-chances. The designer has to balance the imperative to provide feedback (ie. reward and punish) with the imperative to keep win-chance close to 50%.

When I said "if the winchance stays at 50% then clearly nothing you are doing actually matters to the outcome of the match" I didn't mean that nothing mattered because it was *at* 50%, but because it *stayed* at 50%. The number 50 isn't important to my point here, it's just the staying at a constant value that matters; actions at 40% that kept you at 40% would also not matter. This is because the winchance is the ultimate metric as far measuring how well the player is doing at the game, it captures everything that is important about the player's performance in a win/loss game (as EV of score does in a score game). The player's goal is to win, and to do that they try to increase their winchance, and so "doing well" is just another way of saying "increasing the winchance".

What really matters for evaluating the player’s performance over Δt (a given change in time) is not the resulting win-chance, nor is it even Δ(win-chance). The true measure of player performance is the likelihood of doing at least as well - or conversely, at least as badly - as they actually did, with regard to Δ(win-chance).

To put that into English, if the player’s win-chance changes by +2% over a given turn, that in itself is meaningless - what matters is the how likely it was to do at least that well. If the chance of achieving +2% or better was one in ten, then the player has performed very well. If the odds were even, they’ve done on par. If the odds were against them that they’d get +2% or

Therefore, that win-chance remained at 50% throughout much of the match does not necessarily indicate poor play. If the chance of maintaining win-chance had stayed around one in two throughout the match, then this would have been on-par play.

The question for the designer is where they would like win-chance to sit and how they would like it to evolve. Having win-chance above or below 50% means the system is partially solved, to the extent that win-chance deviates from 50%. Therefore, given that strategy games should be maximally ambiguous, in a well-designed strategy game, win-chance should tend towards 50%.

P.S. This principle is most obviously true in multiplayer games. In a well-matched and well-played game of chess, for example, we would hope both players to be fighting tooth and nail almost to the last turn, each with as close to even chances of winning as the other for as long as possible. This principle, may, however, seem counter-intuitive in single-player games, where we would naturally expect good play to result in a high win-chance. I still think this principle applies, though - single-player games, just as multi-player games, should make good play result in

Last edited:

if the winchance stays at 50% then clearly nothing you are doing actually matters to the outcome of the match

In this diagram orange rectangles represent player decision points, blue ovals represent random events, and the black triangles represent game-over states. The numbers in the middle of each node represent the win-rate (or, equivalently, the EV) of the node. The percentages on the edges between nodes represent the chance of that edge being taken.

Clearly the choice between the two blue ovals matters to the outcome of the match, the bottom one leads to a win 50% of the time rather than merely 25% of the time. But if the player is perfect and picks the bottom oval 100% of the time, then their win-rate at the orange rectangle is also 50%. So despite having made a meaningful decision at the orange rectangle, their win-rate remains unchanged.

Other examples could be constructed, including ones with imperfect players who do not make moves with 100% certainty.

Last edited:

Clearly the choice between the two blue ovals matters to the outcome of the match, the bottom one leads to a win 50% of the time rather than merely 25% of the time. But if the player is perfect and picks the bottom oval 100% of the time, then their win-rate at the orange rectangle is also 50%. So despite having made a meaningful decision at the orange rectangle, their win-rate remains unchanged.

What really matters for evaluating the player’s performance over Δt (a given change in time) is not the resulting win-chance, nor is it even Δ(win-chance). The true measure of player performance is the likelihood of doing at least as well - or conversely, at least as badly - as they actually did, with regard to Δ(win-chance).

If the odds were against them that they’d get +2% or *less*, then the player has performed poorly.

Therefore, there are constraints on the types of winrate-possibility-scenarios that can exist. For instance "Imagine that you have a 60% winchance, and there is a 90% chance that next turn you will have a 99% winchance, and a 10% chance that next turn you will have an 20% winchance" is actually a mathematically incoherent scenario, because the winrate can be calculated as 0.9*0.99+0.1*0.2 = 0.911, and therefore it can't be 60%.

For the same reason, it's impossible for the the odds to be against getting +2% or less, and it's even impossible for the odds of getting +2% to be even. The average Δ(win-chance) over all possible scenarios at a particular point in the future must be 0% (this follows from the property that I described above), so if we assume that there was a 50% of getting +2%, then that can be "balanced out" by there being a 50% chance of getting -2%. BUT if there is a 50% chance of getting +2%

I still think this principle applies, though - single-player games, just as multi-player games, should make good play result in *higher* win-chances, but not *high* win-chances.

Of course, my recommendation would be to ditch win/loss design entirely and instead move to score-based games. In a score game, the player is maximizing the expected value of their score (or EV(score)) instead of their winchance. Increasing the EV does not inherently move the game away from ambiguity, but in a win/loss game, increasing the winchance above 50% does.

...it's impossible for the the odds to be against getting +2% or less, and it's even impossible for the odds of getting +2% to be even. The average Δ(win-chance) over all possible scenarios at a particular point in the future must be 0% (this follows from the property that I described above), so if we assume that there was a 50% of getting +2%, then that can be "balanced out" by there being a 50% chance of getting -2%. BUT if there is a 50% chance of getting +2% *or lower*, that can't be balanced out, because any negative Δ(win-chance) possibilities we used to balance it out would be *lower than* +2%, and therefore it would increase the chance of getting +2% or lower above 50%, and this is a contradiction.

But the winchance must collapse to either 0% or 100% by the end of the match, and so it isn't possible to spend the *whole* match close to 50%. Even if the majority of the match takes place rather close to 50%, it will have to stray far from 50% near the end. And if a game naturally stays close to 50% for all but the late-game, the late-game would be much more consequential than the early-game. A player who cares about learning to play better would thus feel as though everything before the late-game was mostly a waste of time that they merely have to suffer through to get to the end, because the late-game is where stuff really starts to matter. If you don't want the player to have that feeling, if you want the whole game to be roughly consistently consequential, the player's ability to change the winchance should be about constant.

...if a game naturally stays close to 50% for all but the late-game, the late-game would be much more consequential than the early-game.

This latter example is a case where good play at a very consequential part of the game keeps WC constant. Therefore that WC stays close to 50% for all but the late-game does not imply that most, or any, of the game is inconsequential. Therefore such a game can be full of feedback.

Having discussed Hopenager’s point I would like to add something to a point of my own from my last post.

Having win-chance above or below 50% means the system is partially solved, to the extent that win-chance deviates from 50%. Therefore, given that strategy games should be maximally ambiguous, in a well-designed strategy game, win-chance should tend towards 50%.

No, because the winchance at the orange rectangle is only 50% once the player has *already committed* to choosing the lower of the two circles. If they haven't yet decided which to pick then the winchance in the orange rectangle would be less than 50%, and thus the decision to go for the lower of the two circles would increase their winchance.

Last edited:

However this does not imply that it is impossible for ΔWC > 0 to be against the odds.

For a part of the game to be consequential, I assume we mean that decisions have a considerable likelihood of significantly impacting WC, which is to say that on any given turn, ΔWC has a* considerable likelihood* of becoming one of *a wide range *of values

This latter example is a case where good play at a very consequential part of the game keeps WC constant. Therefore that WC stays close to 50% for all but the late-game does not imply that most, or any, of the game is inconsequential.

You can only sensibly calculate win-rate if you have a probability distribution for the player's decisions.

but you can also construct examples where the player has a non-zero chance of picking each available option but where at least one of the options still leaves their win-rate unchanged and at least two of the options differ from each other in win-rate.

Eg. If all options are equally likely; two options represent 50% WC, one option 75%, and one option 25%. WC is currently at 50%, and the player could choose an option that puts them again at 50%.

This tends to reflect the most gripping game structures. For example, in professional CS:GO, assuming a balanced match-up, the game tends to reside at WC=50%, until suddenly one side is outnumbered, then that numerical advantage usually leads to a swift victory. In some worse-paced games, like Red Orchestra, a team can be the clear winner for most of the match and still have to work for another five or ten minutes. That’s just labour, not decision-making, and is not ideal for strategy games.

My solution to this problem is simply to move away from win/loss games and use score-systems instead, in which the player tries to maximize EV(score), instead of WC. Score systems avoid the tension because there is no need for EV to stay near any particular value, i.e. score systems have no analogue to the problem that win/loss systems have of needing to stay near 50% winchance for maximum feedback efficiency.

If I'm understanding you correctly, @BiggJobag , you are proposing a different solution to this tension: the game starts at 50%, and then should consist of ΔWC distributions that have a likelyhood of 0 change and a small likelyhoods of very high changes, e.g. a distribution with a 90% chance of 0% change, 5% chance of +50%, and 5% chance of -50%. Such distributions ARE consequential, but mean that the game doesn't spend much (if any) time far away from 50%.

I don't think this is a good idea. A distribution like that would correspond to a situation where the player takes an action that probably won't do anything important, but will occasionally be hugely impactful (e.g. moving around a corner in CS:GO; most of the time there's nothing there and so nothing happens, but on occassion you'll find an enemy and one you the two of you dies). A game that consists almost entirely of situations like that certainly doesn't seem ideal; most of the player's time is wasted on actions that end up not mattering in the end (even though they had a chance of mattering before they were made). Why not, in a game using distributions like that, change the distributions so that they don't have they don't have any chance of landing on 0%? e.g. instead of using the distribution (5% : -50%, 90% : 0%, 5% : 50%), use (50% : -50%, 50% : 50%). This would reduce the length of the game radically, but all that would be removed are the time-wasting parts, the parts that would have left the winchance unchanged.

in professional CS:GO, assuming a balanced match-up, the game tends to reside at WC=50%, until suddenly one side is outnumbered, then that numerical advantage usually leads to a swift victory.

I think that WC staying near 50% is good for making the game feel tense and on-edge, which is a large part of the appeal of execution games and makes the game more exciting to watch, so it's definitely a good idea for CS:GO. But I don't think that tenseness is an inherently good thing in strategy games, and we certainly shouldn't sacrifice other things that are important to strategy games (like, in my opinion, the ability for the winchance to smoothly change over time) for the sake of a feeling of tension.

In some worse-paced games, like Red Orchestra, a team can be the clear winner for most of the match and still have to work for another five or ten minutes. That’s just labour, not decision-making, and is not ideal for strategy games.

...varying at all from 50% is not a foregone conclusion, a foregone conclusion is only when the winchance gets very close to 100% or 0%. A situation where the winchance isn't 50%, but also isn't a foregone conclusion, (e.g. when the winchance is 75%) won't feel like "We all know player A is going to win, we just have to play for 10 more minutes to actually get to the 'Player A wins!' screen", it will feel like "Player A has a significant advantage, but Player B could still pull back and win".

At WC = 0 or 1, there are no decisions. Nothing the player does can change WC (otherwise WC couldn’t be 0 or 1).

At WC = 50%, there are plenty of decisions, assuming the system is a well-designed strategy game.

At WC = 1% or 99%, there are very few decisions. This is because, in the case of WC=1%, there’s no use taking the safer option when only the risky option can save you; and at WC=99%, there’s no point taking the risky option when the safer option will leave you almost certain to win.

What these particular cases are demonstrating is that as WC falls from 50%, riskier options become more attractive and safer options less attractive, and as WC rises above 50%, the reverse. Of course, any decision can be balanced so that it is most ambiguous at any WC, but to me, it makes the most sense to balance decisions to be maximally ambiguous at 50%, given that at the start of the match, the odds should be even (as Keith has argued). And obviously, where the decision is best balanced, WC should tend to reside...

This point to me seems to be arguing that deviating from WC=50% is not necessarily bad for strategy games

the foregone conclusion problem is actualy a special case of a more general problem that follows directly from the properties of win/loss games. This more general problems is that as the chance of victory gets further from 50% (in either direction), the chance that new actions will change the outcome of the match gets lower. A foregone conclusions is merely the most extreme example of this problem, but the same problem persists (to a lesser degree, of course) when the chance isn't quite 100% or 0%, but instead only 99% or 1%, and it even persists to a small degree at 75% or 25%.

We could say something like on turn 0 the win chance is 50%, but only because the player has chosen a difficulty where they know from experience they win about 50% of the time. But we're not saying it because we have a position evaluator which tells us it's 50%. After a few moves we might broadly see that the player didn't do anything wildly good/bad or have any luck that was wildly good/bad, so we might guess still somewhere in the 40-60% range, but really how can we know if the game is unsolved? If it is solved, why are we discussing how to make such a game?!

Maybe we should aim for something like the empirically known win% at the start, 50% or whatever, which rapidly becomes indeterminate and remains so for most of the match duration (Schrodinger's match), followed by a relatively short period when the win% becomes clear and the win or loss follows.

OK I know we might say