Unwinnable

A no-win situation, also called a “lose-lose situation”, is one where a person has choices, but no choice leads to a net gain. For example, if an executioner offers the condemned the choice of death by being hanged, shot, or poisoned, all choices lead to death; the condemned is in a no-win situation. This bleak situation gives the chooser no room: whichever choice is made the person making it will lose their life. Less drastic situations may also be considered no-win situations - if one has a choice for lunch between a ham sandwich and a roast beef sandwich, but is a vegetarian or has a wheat allergy, that might also be considered a no-win situation.

In game theory, a "no-win" situation is one in which no player benefits from any outcome. This may be because of any or all of the following:

Carl von Clausewitz's advice (never to launch a war that one has not already won) characterizes war as a no-win situation. A similar example is the Pyrrhic victory, in which a military victory is so costly that the winning side actually ends up worse off than before it started. Looking at the victory as a part of a larger situation, the situation could either be no-win, or more of a win for the other side than the one that won the "victory", or victory at such cost that the gains are outweighed by the cost and are no longer a source of joy.

For example, the "victorious" side may have accomplished their objective, but the objective may have been worthless, or they may lose a strategic advantage in manpower or positioning. (One example is Great Britain in WWII, where Britain was one of the victorious powers, but found itself so exhausted in the process as to no longer be able to maintain its great power status in a world now dominated by the United States and the Soviet Union.) A related concept is sometimes described as winning the battle but losing the war, where a lesser (sub-) objective is won but the true objective beyond it is not well pursued and is lost.

In past Europe, those accused of being witches were sometimes bound and then thrown or dunked in water to test their innocence. A witch would float (by calling upon the Devil to save her from drowning), and then be executed; but a woman not a witch would drown (proving her innocence but causing her death).

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Wikipedia