Resigning
In principle, a game of Hex ends when one player achieves a solid chain of adjacent pieces connecting their two edges. In practice, the game usually ends when one player achieves a virtual connection between their two edges and the opponent (1) has noticed the virtual connection, and (2) is reasonably sure that the winning player has also noticed the virtual connection and knows how to defend it. At this point, it is customary for the losing player to resign.
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Resigning vs. forfeitting and abandoning
Resigning is different from forfeiting. To forfeit a game means to lose it by default, for example because the player ran out of time (if there is a time limit), didn't show up, refused to play, walked away during the game, or broke the rules in some other way.
It is also different from abandoning a game, which happens when both players collectively agree to end the game prematurely, with no penalty for either player.
One could say that forfeiting is a form of rule breaking, and abandoning is a form of setting the rules aside, whereas resigning is a normal way of ending a game of Hex within its rules.
When to resign
Resigning too late
It is often difficult for less advanced players (and even for advanced players) to analyze a complicated virtual connection. In this case, the losing player may continue playing, even though the winning player already knows that they will win. There is nothing wrong with this. No player is ever forced to resign, and any player who believes that they are winning should be prepared to prove it.
However, if both players are at a similar level of proficiency, it is not good style for the losing player to continue playing much past the point where it is obvious to both players how the game will end.
Resigning too early
If the losing player is more experienced than the winning player, it sometimes happens that the losing player can see that they are losing long before the winning player becomes aware of it. In that case, it is not advisable to resign too early, since there is still a chance that the winning player will make a mistake and lose the game. If there is any doubt that the winning player knows what they are doing, it is a good idea — and never an insult — to make them prove their win. In fact, it can be frustrating for a player if the opponent resigns and the player does not know why.
It also sometimes happens that a player resigns because they think they are losing, when in fact they could have won but failed to see the winning move. This is also frustrating for the opponent, who probably had a cunning plan they never got to execute. This is another reason not to resign too early.
The best time to resign?
So if one should neither resign too early nor too late, then what is a good time to resign? As mentioned before, the best time to resign is when the losing player is reasonably sure that both players know how the game will end. When exactly this point is reached depends on the skill of the players. When in doubt, it is certainly acceptable to continue playing until one player has a virtual connection consisting of simple templates such as bridges and ziggurats, and it is conventional to resign at that point.