Start with these ideas
- Name the missing tiles and preserve an alternative.
- Compare the possible reward with the actual payment risk.
- A dead required tile can end one route without ending every route.
Start with what the hand already offers
Suppose your thirteen tiles contain Red–Red–Red, Green–Green, White–White, 1–2–3 Characters and 4–5–6 Dots. Drawing Green completes Little Three Dragons: Red and Green triplets, White pair and two Chows. That is a concrete one-tile route; merely having one of each dragon is not.
Drawing White works too: White becomes the second triplet and Green the pair. Keep both routes in mind. Chasing Big Three Dragons from this hand also requires rebuilding the remaining set-and-pair allocation, not simply adding another dragon tile.
Little Three Dragons supplies 5 faan in our house rules, including the two dragon Pungs; do not add those Pungs again. Concealment and self-draw can add ordinary bonuses up to the cap. Check the pattern page before assuming another table counts the same way.
Stop when the route loses its supply
A thirteen-orphans attempt missing White Dragon cannot complete if all four Whites are already in public discards and melds and none is still available to claim. That is a hard impossibility for this route. It does not mean every other way to win is impossible.
Count your own copies too. If you hold two Greens and the other two are public, you cannot make a Green triplet by drawing another. A discard already on the table cannot be claimed later after the response window has passed.
In the example above, if both remaining Greens are already unavailable, the Green-triplet route is dead but drawing White can still complete Little Three Dragons with Greens as the pair. If both remaining Whites are also unavailable, neither one-tile route works. Reassess the whole hand instead of waiting for a fifth copy.
A claim changes what remains possible
A claimed Chow prevents All Pungs. A declared off-suit meld prevents a Full Flush in your chosen suit. Any declared meld prevents our Nine Gates and Thirteen Orphans. These are structural consequences, not a judgement that every claim is bad.
A legal 3-faan All Pungs route may be preferable to a remote 8-faan limit. Compare how many tiles must change, the visible supply, remaining wall and the current match score. There is no universal turn-number deadline that makes the decision for you.
For a flush decision, suppose you have 1–2–3, 4–5–6 and 7–8–9 Characters, a Red Dragon pair and 4–5 Characters. Drawing 3 or 6 Characters completes a Half Flush. Full Flush requires replacing the Dragon pair as well. If a Dragon Pung is already exposed, it cannot be discarded away to turn this into Full Flush.
Compare the reward with the actual loss
Under our house payment formula, discarding into 3 faan loses 24 points; into 8 faan loses 768. These are payment amounts, not probabilities. A large possible reward does not prove that a slow chase has positive expected value.
For practice, write down one target and one fallback before playing. Revisit them after each claim or a critical tile appearing publicly. Judge the decision by information available then, not by the eventual lucky outcome.
Check your understanding
All four copies of a tile your Thirteen Orphans needs are public, and no claim is still available. What follows?
Choose a statement to see the explanation.
A few things to know
When is a big hand worth pursuing?
Start with a concrete route: identify the missing types, available copies and sets or pair still needed. A nearly complete Little Three Dragons hand is different from holding one of each dragon. Also weigh exposed-set restrictions, the minimum and the cost of continuing.
Can I turn an exposed Half Flush into Full Flush?
Only if every declared meld is already in the intended suit and you can remove all honours from the remaining concealed tiles. An exposed honour Pung or Kong makes Full Flush impossible; declared sets cannot be taken back.
Should I keep chasing once the required tile is exhausted?
No fifth copy exists. If all four copies are accounted for and no current claim can supply it, that route is blocked. Check whether another tile can complete the same pattern or whether a lower-faan plan remains legal.