One-handed solving

The same cube with one hand: the rules, turning, choosing algorithms and adapting your method.
One-handed solving is its own WCA event: the 3x3 solved with a single hand. The puzzle and the stages of your method stay the same. What changes is how each turn is made, which algorithms are worth knowing, and how you plan the cross and the pairs so the hand rarely has to let go of the cube.

The rules

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    During the solve only one hand may operate the cube (WCA Regulation C1b), and once you have turned with one hand you may not use the other (C1c).
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    Inspection is not part of the solve: you may hold and study the cube with both hands (C1b+).
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    You may hold the cube against the table to help turn it (C1b4).
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    You need not use the same hand in every attempt (C1b++), and a pop or a lockup is fixed with the solving hand only (C1b2).
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    Everything else, starting and stopping the timer included, follows the ordinary speedsolving procedure (C1).

Which hand

Either hand is legal, and you may change between attempts. One-handed algorithms, ours included, are written in R and U for the left hand: Michael Atkinson and Chris Hardwick's classic one-handed tips teach the left hand's move combinations as R and U turns, and the right hand's as their mirror images in L and U. If you solve with the right hand, mirror each algorithm left to right: R becomes L', U becomes U', and every other turn becomes its mirror image.

Turning with one hand

Their standard grip holds the cube with the thumb on the front centre and the middle finger on the back centre, leaving the index and ring fingers free to turn: with the left hand, the ring finger flicks R and the index finger pulls U'. They recommend practising every turn from that grip, chaining turns made by different fingers into quick combinations, and a loose cube, since the hand tires over a solve. Holding the cube against the table is legal and helps with turns the fingers find hard, the middle slice above all. Every regrip (letting go to hold the cube another way) costs more than it does with two hands, so a good one-handed algorithm keeps the hand where it is.
Rotations are allowed, and the one-handed sheets use them: several of their algorithms begin with y or z so that the hand turns R and U rather than another face.

Choosing algorithms

A good two-handed algorithm is not always good for one-handed solving. Turn on One-handed picks (in Settings, or on any set's page) and every card, sheet and drill shows each case's one-handed pick instead of its first algorithm: the algorithm a one-handed sheet suggests, where such a sheet exists (for OLL and PLL, the CubeSkills sheets by Feliks Zemdegs and Andy Klise), otherwise the case's algorithm in the best of these classes, by the faces it turns:
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    R and U only
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    R, U and M
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    R, U and M with F or D
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    R, U and M with F and D
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    needs L, B, S or E
Within a class, fewer rotations come first, then the source's own ranking. The classes describe which faces an algorithm turns, not how it feels in your hand: try the alternatives on each case page and press Use this on your favourite.
Ua with R and U only, (R U' R U) R U (R U' R' U') R2: the sheet's choice in place of the two-handed algorithm's M turns.
start
R
U'
R
U
R
U
R
U'
R'
U'
R2
Open the case
H without the middle slice, R2 U2' R U2' R2 U2' R2 U2' R U2' R2: half turns of R and U.
start
R2
U2
R
U2
R2
U2
R2
U2
R
U2
R2
Open the case
Ja from the sheet, (R' U L' U2) (R U' R' U2' R) L U', turns L, which the classes rank last: a sheet's choice comes before the classes.
start
R'
U
L'
U2
R
U'
R'
U2
R
L
U'
Open the case

Adapting your method

Most top one-handed solvers use CFOP; ZZ and Roux are the usual alternatives. Each has a one-handed page here with the same stages and its sets under the one-handed picks.
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    CFOP: plan the cross so the pairs can be solved with R and U turns where possible, since a rotation or an F turn costs more with one hand. Learn the one-handed OLL and PLL in each sheet's order.
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    ZZ: after EOLine the first two layers need only R, U and L turns and no rotations, and the last layer starts with its edges oriented, so OCLL and PLL, COLL or ZBLL finish it.
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    Roux: the blocks are built with R, U, r and M turns, CMLL keeps them, and the last edges use M and U, where holding the cube against the table helps turn M.

Practice

Start with the last-layer cases you meet in every solve, then drill them on the Solve desk with One-handed picks on so the desk shows the algorithms you are learning. J Perm's one-handed guide puts a practised one-handed average at just under double the same solver's two-handed average: a rough guide, not a target.
Atkinson and Hardwick add three habits. Use the slower turning to look further ahead: in the intuitive steps, weigh every option, as in a fewest-moves solve. Turn smoothly rather than as fast as you can, because a lockup costs effort the hand cannot spare. And practise every algorithm you know with one hand: those learnt as two-handed finger tricks are the first to go under pressure.
One-handed solving: the whole walkthrough
The rules
Which hand
Turning with one hand
Choosing algorithms
Adapting your method
Practice
All systems