Mahjong is a game of incomplete information and probability. You cannot see your opponents' hands, and you cannot predict what the wall will give you. But probability gives you a framework for making better decisions under uncertainty. You do not need to do mental arithmetic every turn — you need to understand a few key concepts that change how you think about your draws, your waits, and your discards.
1. The Deck: 108 Tiles Total
Blood Battle Mahjong uses tiles from three suits: Wan, Tiao, and Tong. Each suit has ranks 1–9. Each rank appears four times in the deck. Total: 3 suits × 9 ranks × 4 copies = 108 tiles.
| Suit | Ranks | Copies per Rank | Total |
|---|---|---|---|
| Wan | 1–9 | 4 | 36 |
| Tiao | 1–9 | 4 | 36 |
| Tong | 1–9 | 4 | 36 |
| Total | 27 distinct tiles | 4 each | 108 |
After dealing (13 tiles × 4 players = 52 tiles), roughly 56 tiles remain in the wall. This is your draw pool for the entire round.
2. Outs: How Many Tiles Can Help You?
In poker terms, an "out" is a tile that improves your hand. In mahjong, we count outs to measure how fast we can expect to advance toward tenpai. Every tile that reduces your shanten count is an out.
Example: you hold a two-sided wait tile (4-5-wan). Your outs are 3-wan and 6-wan — any of them completes the sequence. In a fresh deck, that is 4 copies of 3-wan + 4 copies of 6-wan = 8 outs. With 56 tiles in the wall and 8 of them completing your set: roughly 1 in 7 draws helps you.
3. Probability of Drawing a Specific Tile
How likely are you to draw a specific tile in the next N draws? Formula: P(at least one in N draws) ≈ 1 − ((remaining wall − outs) / remaining wall)^N
Simpler practical rules:
| Outs Available | Draws to ~50% chance | Draws to ~90% chance |
|---|---|---|
| 8 outs | ~5 draws | ~15 draws |
| 4 outs | ~10 draws | ~30 draws |
| 2 outs | ~19 draws | ~50+ draws (unlikely) |
| 1 out | ~38 draws | Essentially impossible |
This table reveals something important: with only 1 out (e.g., single tile wait when opponents have discarded 3 copies), you are unlikely to draw it in a typical round of 15–20 draws per player. Multiple outs = multiple chances = faster progress.
4. Why Wide Waits Win More Often
A two-sided wait (8 outs) is not just "twice as likely" to complete as a single-tile wait (3 outs) — it is dramatically more likely per draw, and more likely to win before the wall runs out. Each draw from the wall is an independent trial. More outs = more trials that can succeed = faster wins.
Over a long session, a player who consistently enters tenpai with 6–8 outs will win significantly more rounds than a player who consistently waits on 2–3 outs, even if both players build hands of equal quality.
5. Counting Dead Tiles in Practice
"Dead tiles" are tiles where most or all copies are visible in discard pools. You do not need to track all 108 tiles — just the ones relevant to your hand:
- Identify your winning tile(s) — the tiles that complete your hand.
- Look at every discard pool. Count visible copies of your winning tile(s).
- Subtract from 4 per tile type. That is your remaining outs.
6. Probability and the Void Suit Decision
Choosing a void suit involves probability too. The suit with fewest tiles is easiest to void, but consider: how many of those tiles are likely to appear as draws?
If you must void Wan and you hold 3 Wan tiles, you need to discard 3 tiles. But how many more Wan tiles will you draw from the wall? On average, 1/3 of remaining wall tiles are any given suit. Expect to draw roughly 5–8 more Wan tiles during a round (if you do not void quickly). The faster you establish your void, the fewer surprise void-suit draws you must immediately discard.
This is why early void clearing pays: every turn you delay, there is a ~33% chance your next draw adds to your void pile rather than your hand.
7. Expected Draws to Tenpai
If you are 2 shanten from tenpai (need 2 improvements to reach tenpai) with 10 outs at each step:
- First improvement: ~4–5 draws to achieve with 10 outs.
- Second improvement: another ~4–5 draws.
- Total: roughly 8–10 draws to reach tenpai from 2 shanten with good outs.
A typical round lasts about 15–20 draws per player. 2 shanten with good outs = you will usually reach tenpai. 3+ shanten with poor outs = you may not reach tenpai at all. This is why simplifying your hand goal when you have high shanten is important — more focused goals mean more outs per step.
8. Practical Takeaways
- Always prefer waits with more outs. Two-sided (8 outs) beats single (3 outs).
- Count visible copies of your winning tiles before finalizing your tenpai wait.
- If your winning tile has only 1 copy remaining, switch waits if possible.
- Expect 1/3 of your draws to be your void suit — clear it fast to stop this waste.
- From 2 shanten with good outs, you will usually reach tenpai. From 3+ shanten, consider simplifying.