**SOMETIMES, CHOICES ARE REBALANCED WHEN WIN-CHANCE CHANGES.**

Let’s analyse what it means for choices to be rebalanced when win-chance changes. This means that the rate of change of the expected change in win-chance, or, to misuse a term, expected value (EV) of a given option in a choice, with respect to win-chance; is non-zero. To put it symbolically:

Given that EV is equal to expected benefit, EB, minus expected cost, EC; and d(a-b) / dx = (da - db) / dx; our formula becomes the suddenly much more helpful

This is clearly the case, to take a simple example, if there is some action which, when taken, has a fixed cost with respect to win-chance, but a declining benefit. Imagine, for example, a racing game with a special ability to fire booster rockets, giving you a temporary speed boost, but which have a 1 in 10 chance to set your car on fire, ending your race. If you are already in the lead, then there’s no point taking the risk for the relatively small benefit of the speed boost; while if you’re far behind, there’s no point

*not*taking the risk, since you have nothing to lose. Only somewhere in the middle is the choice balanced to be maximally ambiguous. This is win-chance rebalancing.

It seems obvious to me that this problem is a highly pervasive one which designers should be bearing in mind when designing binary strategy games. Anywhere where an option’s EV could be affected by WC, which is pretty well everywhere, this problem will loom. Now, three solutions I can offer (besides scrapping a binary goal):

**ENSURE THAT THE EV’S OF EACH OPTION IN ALL CHOICES ARE PROPORTIONAL WITH REGARD TO WIN-CHANCE**, i.e. that, for all choices, even as win-chance changes, the relative EV of each option within the choice remains in the same proportion. No one option becomes relatively better or worse, compared to the alternatives, as win-chance changes. This you might do with proportional or exponential rewards, for example, earning more money in a city-builder allows you to build more new buildings, for the same proportion of your wealth, than if you had earned less money. However, this would tend to lead to positive feedback loops which are disliked by some designers, and would be a gargantuan effort to balance. I personally don't necessarily mind positive feedback loops, so I'd be on board for this method, provided it was practical.

**PRESENT DIFFERENT CHOICES AT DIFFERENT WIN-CHANCES**, or have many choices such that there is ambiguous decision-making balanced for any given win-chance. One might complain that if there are qualitatively different decisions being made at different win-chances, the player’s learning will be disrupted, according to a similar line of thought that explains why systemic complexity is evil. And again, there is the practical concern of the amount of balancing work required to design such a system. I personally would steer away from this method for those reasons, but if those obstacles were overcome it certainly solves the problem of win-chance rebalancing.

**ADOPT A "KNIFE-EDGE" MATCH STRUCTURE**, whereby win-chance tends to remain around ½ (given ½ is the ideal win-chance for a match to start at), and when win-chance deviates from ½, there tends to be either a swift return to even odds or a swift resolution. (This is the solution we spent a lot of time discussing in the other thread.) By this “solution”, the problem is dodged rather than solved, since, with most of the match spent at one win-chance, the fact that decisions will be unambiguous at other win-chances is of little concern. I like this solution, despite it not truly being a solution at all - it gets rid of the problem and does so without the extra balancing work required by the other two solutions.

Please let me know what you think of this, if you disagree in part or in entirety, or if you have anything to add.