The Rule and the Scoring
When you call trump, you have the option to go alone. Your partner sits the hand out (their cards stay face down), and you play against both opponents with five cards against their combined ten. If you win all five tricks, you score four points instead of three. If you win three or four tricks, you still score one point. If you win fewer than three, you are euchred for two points, the same as any other failed call.
The headline is the march bonus: four points for a loner march versus three for a partnership march. One extra point is the entire reward for taking on a much harder task. That seems small, and it is. The math only works when the loner march is highly likely.
The Math
Compare two outcomes. With partner, a march scores three points. A loner march scores four. The difference is one point. To justify going alone, the increased likelihood of failure has to be small enough that the expected value comes out ahead.
If your hand sweeps with partner 90% of the time and sweeps alone 70% of the time, the math says do not go alone: the expected value of partnership play (2.7) beats the expected value of going alone (2.8 minus the much higher chance of getting only one point or being euchred). Real hands are messier, but the principle is clear. Going alone is only correct when you can win all five tricks alone with very high probability.
The other way to think about it: going alone makes sense when your partner contributes nothing. If your hand is so strong that partner's expected contribution is zero or close to it, you may as well take the bonus point.
Lock Hands
The clearest go-alone hands are lock hands: ones where you cannot lose five tricks regardless of how the cards are distributed. The textbook lock hand is both bowers plus the ace of trump plus two cards that can take tricks at the end. Both bowers guarantee two tricks. The ace of trump usually guarantees a third (it takes any trick led that contains no higher trump, and the only higher trumps are already in your hand). After three rounds of trump have pulled out the opponents' trump, your two remaining cards win whatever is left.
Both bowers plus the ace of trump plus the King of trump plus any side card is also a lock against most distributions. The only risk is your side card being trumped on the fifth trick after opponents kept a trump back. Against careful defenders that can happen, but it is rare.
Both bowers plus the ace and King of trump and the Queen of trump is essentially unloseable. You have the top five trump, and you simply lead them out.
Near-Lock Hands
Below the lock hands are near-locks: hands that march alone most of the time but have a realistic loss path.
Both bowers plus the ace of trump plus two off-suit aces is a strong loner candidate. The off-suit aces will likely take their tricks because each opponent only has five cards, and the probability that the missing suit is held short by both opponents combined is reasonable. The risk is that one opponent voids a suit early and trumps your ace.
The right bower plus the ace of trump plus two more trump plus an off-suit ace is borderline. The left bower is the worry: an opponent could hold it, and if they do, they take a trick. This hand depends on the location of the left bower.
The right bower plus the left bower plus two off-suit aces plus a King is a coin flip on the King. Three trump tricks plus two ace tricks would do it, but the King of trump is missing, so an opponent's third trump beats you if your fifth lead is in the suit they voided.
Position and Up-Card Effects
Going alone as the dealer after picking up the up-card is the strongest position. You see one card more than any other player (the up-card itself plus its color implications), and the pickup increases your effective hand size by one. Many strong loner hands only become strong because the dealer picks up a bower or an ace.
Going alone in third seat against an unknown table is the next strongest, because everyone in front of you has passed. Two passes in a row mean those players probably do not hold a bower of the proposed trump suit. That increases the chance your bowers do not have to fight any opposing high trump.
Going alone in first seat is the riskiest. You have no information from the other players' passes, because nobody has had a chance to pass yet. The probability of a missing bower or ace landing in opponents' hands is at its baseline.
Score Situation
The score on the board changes the value of going alone. When your team is at six points, going alone for four is a likely game winner. When your team is at two points, going alone for four versus three is barely worth the increased euchre risk that going alone carries (defense against a loner can sometimes succeed where defense against partnership play would not, because you have no partner to cover a slip).
When your team is at nine points, going alone is pointless. You only need one point to win. Take the partnership call.
When your opponents are at nine points and you must win the hand to survive, going alone is sometimes correct on hands you would otherwise pass on, because you cannot let them win even a single trick that would let them take the hand. This is a desperation move, not a standard play.
Playing Against a Loner
When an opponent goes alone, your job is no longer to euchre them (they will be running cards you cannot beat) and is instead to stop the march. Stopping a march is worth one point in differential, because they score one for three tricks versus four for a sweep.
Hold onto any high trump and any high side cards. Do not waste your King of trump on a trick the loner is already winning. Try to keep at least one card in each suit if you can, so you can follow suit on the fifth trick if it is led off-suit. The single trick you save is worth one point of swing.
If you hold a bower against a loner, lead it early. The loner has at most two bowers; if you hold one, leading it forces them to expend a higher card. Saving your bower for later usually means it gets stranded.
Common Mistakes
The most common mistake is going alone with both bowers and a 9 of trump and two low side cards. Both bowers look great, but you have no card after the bowers to control the hand. A defender with even one high trump will take a trick.
The second is going alone in first seat with a near-lock hand. The same hand in third seat is much stronger because of the information from first and second seat passes.
The third is going alone when your partner has been consistently scoring with you. Taking your partner out of a hand they would have helped you win is a one-point gain at best and a missed point at worst.
See Also
For the basics of calling trump (the decision before you decide whether to go alone), see how to call trump in euchre. For the underlying scoring, see the euchre rules.