Dragon Tower strategy: the maths of the climb
How Dragon Tower pays
Row r gets its own HMAC-SHA256 block with cursor r, and the first safe floats of that block pick the egg positions without replacement, exactly as Mines does within one row. Everything is fixed before the first tile opens. After climbing r rows the payout is floor(0.99 × (tiles ÷ safe)^r × 10,000) ÷ 10,000.
What difficulty does
| Difficulty | Tiles | Eggs | Survive a row | Rows to reach 2× | Survive that far | Pays | Top (row 9) pays | Reach the top, one in |
|---|---|---|---|---|---|---|---|---|
| easy | 4 | 3 | 75.0% | 3 | 42.2% | 2.3466× | 13.19× | 1 in 13 |
| medium | 3 | 2 | 66.7% | 2 | 44.4% | 2.2275× | 38.06× | 1 in 38 |
| hard | 2 | 1 | 50.0% | 2 | 25.0% | 3.9600× | 506.88× | 1 in 512 |
| expert | 3 | 1 | 33.3% | 1 | 33.3% | 2.9699× | 19,486.17× | 1 in 19,683 |
| master | 4 | 1 | 25.0% | 1 | 25.0% | 3.9600× | 259,522.56× | 1 in 262,144 |
| Row | easy pays | medium pays | hard pays | expert pays | master pays | easy reach | medium reach | hard reach | expert reach | master reach |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1.32× | 1.48× | 1.98× | 2.97× | 3.96× | 75.0% | 66.7% | 50.0% | 33.3% | 25.0% |
| 2 | 1.76× | 2.23× | 3.96× | 8.91× | 15.84× | 56.3% | 44.4% | 25.0% | 11.1% | 6.3% |
| 3 | 2.35× | 3.34× | 7.92× | 26.73× | 63.36× | 42.2% | 29.6% | 12.5% | 3.7% | 1.6% |
| 4 | 3.13× | 5.01× | 15.84× | 80.19× | 253.44× | 31.6% | 19.8% | 6.3% | 1.2% | 0.4% |
| 5 | 4.17× | 7.52× | 31.68× | 240.57× | 1,014× | 23.7% | 13.2% | 3.1% | 0.4% | 0.0977% |
| 6 | 5.56× | 11.28× | 63.36× | 721.71× | 4,055× | 17.8% | 8.8% | 1.6% | 0.1% | 0.0244% |
| 7 | 7.42× | 16.92× | 126.72× | 2,165× | 16,220× | 13.3% | 5.9% | 0.8% | 0.0457% | 0.0061% |
| 8 | 9.89× | 25.37× | 253.44× | 6,495× | 64,881× | 10.0% | 3.9% | 0.4% | 0.0152% | 0.0015% |
| 9 | 13.19× | 38.06× | 506.88× | 19,486× | 259,523× | 7.5% | 2.6% | 0.2% | 0.0051% | 0.0004% |
What cashing out early and staking plans do
“Climb three on easy and cash out” is a 42.2% bet paying 2.3466×. “One row on hard” is a 50% bet paying 1.98×: a coin flip that pays 1.98×, which is Dice at 50%. Both return 99%. Pairing either with martingale reproduces the Dice wall. Doubling covers 6 losses from a 1,000 bankroll at a 10 base, and at a 42.2% win rate a run of 7 losses appears in 85% of 200-climb sessions. (Because the payout is 2.35×, a double more than recovers a loss; the exact recovery factor is 1.74×, which stretches the wall out but does not remove it.)
The simulator treats each climb as a binary bet: martingale on three rows of easy, martingale on one row of hard, and flat betting three rows of easy. All three print a realised return on turnover near −1%; the ruin rates differ because the shapes differ.
Stopping after a near-miss, switching difficulty mid-session and picking the same tile position every row are the other ideas. Each row's eggs come from a fresh HMAC block and are drawn uniformly, so position, history and difficulty history carry no information about the next row.
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Questions
- Which Dragon Tower difficulty is best?
- None in expectation: after any number of rows on any difficulty, survival times payout is 0.99. Easy survives each row 75% of the time and tops out at 13.19×; master survives each row 25% of the time and tops out at 259,523×, reached 1 in 262,144 climbs. The difficulty sets how spiky the outcome is, not what it is worth.
- What are the odds of reaching the top of the tower?
- 7.51% on easy (1 in 13), 2.60% on medium, 0.20% on hard, 0.0051% on expert and 0.00038% on master (1 in 262,144). Each is the per-row survival raised to the ninth power, because every row is an independent draw from its own HMAC block.
- Is it better to cash out early?
- Cashing out after r rows is a bet that wins with probability (safe ÷ tiles)^r and pays 0.99 ÷ that. Every r has the same 99% expectation. Three rows on easy is a 42.2% bet paying 2.3466×; one row on hard is a 50% bet paying 1.98×. Earlier is safer per climb and pays less, and the average is untouched.
Keep going
Last reviewed 2026-09-27