Is an online I Ching reading as valid as tossing coins yourself?

Yes, as far as chance is concerned: a well-built online caster produces every line with exactly the same probabilities as three fair coins, and nobody — not you, not the website — chooses the result. What an online reading cannot give you is the physical ritual of tossing coins, and some people find that ritual helps them concentrate. That part you can bring to a screen as well, if you choose.

What "valid" depends on

Whether a casting method is "valid" depends on what you think makes a reading meaningful. There are three common views:

• Randomness. The cast is valuable because it is out of your control: it confronts you with a situation you did not pick. On this view, any fair random process is as good as any other.
• The moment. Jung's idea of synchronicity holds that the cast reflects the moment of asking. On this view, too, what matters is that the result falls when you ask, not what device produces it (see Jung, synchronicity and the I Ching).
• Sincerity and attention. The tradition stresses the asker's state of mind: one clear question, asked once. The fourth hexagram warns 初筮告，再三瀆，瀆則不告 — the first cast informs; asking again and again is disrespectful. This depends on you, not on the coins.

On none of these views does the material of the coins carry the meaning.

The tradition already changed its tools

It helps to remember that the three-coin method is itself a shortcut. The oldest described method uses fifty yarrow stalks, as set out in the Great Commentary: 大衍之數五十，其用四十有九, "the number of the great expansion is fifty; of these, forty-nine are used". Sorting the stalks for one hexagram takes a long while; tossing coins takes a couple of minutes. Coins became the everyday method for most readers centuries ago, and a second tradition, Plum Blossom numerology, dispenses with both and derives the hexagram from numbers such as the date and hour.

So the question "is a faster method still legitimate?" has been answered many times in Chinese practice, mostly with a yes, though always with some voices preferring the slower way. Zhu Xi, for example, wrote out a careful ritual for consulting the yarrow (筮儀).

The probabilities: coins, yarrow and digital

Each line of a hexagram is one of four values: 6 (old yin, changing), 7 (young yang), 8 (young yin) or 9 (old yang, changing). Different methods give these values with different odds.

Three coins. Each coin counts 3 for the plain side and 2 for the inscribed side, so three coins add up to 6, 7, 8 or 9. With fair coins:

• 6 (old yin): 1 in 8
• 7 (young yang): 3 in 8
• 8 (young yin): 3 in 8
• 9 (old yang): 1 in 8

Yarrow stalks. The stalk procedure is lopsided in an interesting way:

• 6 (old yin): 1 in 16
• 7 (young yang): 5 in 16
• 8 (young yin): 7 in 16
• 9 (old yang): 3 in 16

Both methods give a quarter chance that a line is changing, and both give yin and yang equally often. The difference is which lines change: with yarrow, an old yang line is three times as likely as an old yin line, so yang lines are more "restless" and yin lines more stable. With coins, the two are equally likely. Some readers who care about this use a method that copies the yarrow odds with marbles or extra coins; most are content with three coins. The details are in the three-coin method and the yarrow-stalk method.

A digital caster can follow either distribution. What matters is that it says which one it uses, and that its randomness is good.

Since a changing line has a one-in-four chance with both methods, the chance of a cast with no changing lines is (3/4)⁶, about 18% — roughly one cast in five or six, whichever method you use. That is worth knowing if you feel your "still" hexagrams come up too often or too rarely; see no changing lines.

How our caster works

Our I Ching caster follows the three-coin method exactly:

• Eighteen virtual coins. A cast is six throws of three coins, the first throw being the bottom line, just as by hand.
• Each coin is a fair bit from a cryptographic random source. The server draws them with the platform's cryptographically secure random number generator, the same kind of source used for security keys, so each coin is heads or tails with equal probability and the line values come out at exactly 1/8, 3/8, 3/8 and 1/8.
• The result is fixed before you see it. The toss happens on the server when you press the button. If you choose Toss the coins, the 3D coins on screen replay that stored result throw by throw; Instant skips the animation. The animation is for your attention, not a source of chance — nothing about how you click or how long you wait changes the coins.
• No one picks the hexagram. There is no weighting toward "nice" or "dramatic" hexagrams, and the question you type does not influence the toss; the area of life you choose only affects how the reading is presented.

The reading then shows the primary hexagram, the changed hexagram if any lines are moving, and related figures such as the nuclear hexagram, with the Chinese text and James Legge's 1882 translation.

Physical coins: the real advantages

Tossing coins yourself has genuine benefits, and they are worth keeping if they help you:

• Slowness. Six throws by hand, written down one at a time, make you stay with the question.
• Touch and ritual. Holding the coins, clearing a space, perhaps lighting incense — these mark the reading off from the rest of the day.
• Independence. You need no device and no connection.

Real coins are very nearly but not perfectly fair; research on coin tossing has found small biases. For a reading this hardly matters. See what coins to use and which side of the coin is yang if you cast by hand.

Our caster does not currently take hand-tossed results as input, so if you cast with your own coins, write down the six lines and look the hexagram up in the hexagram library.

Putting it into practice

Choose the method that helps you ask well, then stop thinking about the method. If you use a screen, give the moment some of the weight of a ritual: close other tabs, write your question down, take a breath before pressing the button, and cast once. If you use coins, keep a notebook beside them. Either way, it is the clarity of the question and the honesty of the reading that make the cast worth having.