WHITEOUT SURVIVAL ・ STRATEGY ANALYSIS, PROVEN IN NUMBERS
Should you move on after the grand prize unlocks at three lines? What do you do with a bad board? If you spend, what do you buy first? Most players decide these by feel. Here are the nine decisions this event puts in front of you, each settled with the probabilities the game itself publishes.
The conclusion first. In this event you always clear the board.
Once a board starts, draw until all ten lines are complete. Do not stop when the grand prize unlocks at three lines. Do not stop because the board's rewards are poor. That is nearly the whole game.
Three more things.
There is almost nothing to decide, and that is the character of this event. The parts driven by luck — board rank, which rewards land — are out of your hands. The parts you control are the four above. The rest of this article shows why each one holds.
Run your own numbers →Answer49.04 — and half the time it takes all 50.
Lighting all 25 squares completes all ten lines, so the question is: drawing from 1–50 without replacement, how many draws until you have pulled all 25 board numbers? There is an exact answer.
The general form is n(N+1)/(n+1). The distribution is the interesting part.
| Lanterns | Chance of finishing by then |
|---|---|
| 45 or fewer | 2.5% |
| 48 or fewer | 24.5% |
| 49 or fewer | 50.0% |
| Takes all 50 | 50.0% |
Half of all rounds consume the full 50. The chance that the very last number drawn is on your board is exactly one half. So the cost of a round barely moves. The feeling that "lanterns are draining fast today" is probably an illusion — what actually varies is the board rank and which rewards land.
The breakdown matters just as much.
| Line | Lanterns to here | Step |
|---|---|---|
| 1st | 30.0 | 30.0 |
| 2nd | 35.5 | 5.5 |
| 3rd | 38.8 | 3.3 |
| 5th | 43.2 | 2.0 |
| 8th | 47.1 | 0.7 |
| 9th & 10th | 49.0 | always together |
About 30 lanterns for the first line, about 19 for the remaining nine. The first line alone eats 60% of the cost. A number already drawn never comes back that round, so hits get easier as you go. The ninth and tenth lines always complete on the same draw, because the last square finishes the one remaining row and the one remaining column at once.
AnswerNo. Your next board's promotion odds go from 20% to 6%.
At three lines the grand prize unlocks and you may jump to the next round manually. On a Regular board that prize is 7 Fire Crystals, 6 gear chests and 120 coins. The temptation is real.
But board rank is decided by a promotion roll that accumulates 2% per line completed.
Chance the next board is Bian. One in five.
One in seventeen.
Then the first-line hill stacks on top. Reset and you pay roughly 30 lanterns again for line one. Stay on the board and the remaining seven lines cost about 10.
Per lantern, continuing returns 21.6 coins against 6.4 for resetting. More than a threefold gap.
This is the part that slips the mind. Every line you complete advances two separate counters, on top of the reward printed on the board.
One is cumulative lines. 5 lines gives 5 lanterns, 10 gives 500 coins, and it continues at 30, 60, 100, 200, 350, 500, 650, 800 and 1000. Altogether 580 lanterns and 19,000 coins.
The other is lines that day, for the daily missions. 10, 40 and 65 lines pay 250 coins each, up to 1,000 a day.
Divide that total by the lines you run and you get the hidden income per line: about 28 coins over a 52-round event.
That bonus is identical on every line, regardless of what the board shows. That independence is what settles the next question.
AnswerThere is exactly one exception, and it comes up once in 5,000 rounds.
Start with board quality. All ten rewards are visible from the start: five down the right (one per row) and five along the bottom (one per column). Their coin total is distributed like this.
A fifteenfold spread from worst to best. A bad board really does cut your income roughly in half. The feeling is correct.
It still does not change what you do. The bonus from the previous section and the 20%-versus-6% promotion both arrive independently of what the board holds. And at zero lines the skip button does nothing — it needs three lines — so rerolling a fresh board is not even on the table.
What about collecting the coin lines early? On average 4.5 of the ten rewards are coins, and which three lines complete first is random.
| First three lines are all coin rewards | 9.1% |
| Coins fully collected, nothing left in the other seven | 1.5% |
The 9.1% case usually just means you banked them early and coins remain on the board. Truly running dry is 1.5%.
Here the one exception appears: how many lanterns the three lines took. Reaching three lines early means fewer squares are lit, so finishing costs more than average.
| Three lines at | Frequency | Squares lit | Left to finish |
|---|---|---|---|
| 28 lanterns | 0.6% | 17.4 | 20.6 |
| 30 lanterns | 1.6% | 17.9 | 18.7 |
| 34 lanterns | 7.1% | 18.7 | 15.0 |
| 38 lanterns | 17.5% | 19.5 | 11.3 |
| 42 lanterns | 19.3% | 20.3 | 7.8 |
| 46 lanterns | 4.2% | 21.2 | 4.5 |
Three lines at 30 lanterns leaves 18.7 to finish — nearly double the average. Here stopping is genuinely worth weighing.
But the break-even sits at fewer than 25 coins left across the remaining seven rewards. The smallest coin reward is 35, so that means literally no coins left. Multiply it out: three lines by 30 lanterns (1.6%) and no coins remaining (1.5%) gives 0.02% — once in 5,000 rounds.
Whether that is worth memorising is debatable, but the structure behind it — finishing early costs you — is worth knowing.
AnswerThree times and six times the coins. But the 19% of boards at the top carry 45% of all income.
One full-cleared round, ten lines plus the grand prize.
| Rank | Line rewards | Grand prize | Total | vs Regular |
|---|---|---|---|---|
| Regular | 272.3 | 120 | 392.3 | 1.00× |
| Bian | 810.0 | 360 | 1,170.0 | 2.98× |
| Sen | 1,710.0 | 720 | 2,430.0 | 6.20× |
Per lantern the gap widens, because Regular and Bian pools hand lanterns back.
| Rank | Lanterns returned | Net spend | Coins per lantern | vs Regular |
|---|---|---|---|---|
| Regular | 2.90 | 46.14 | 8.50 | 1.00× |
| Bian | 5.80 | 43.24 | 27.06 | 3.18× |
| Sen | 0 | 49.04 | 49.55 | 5.83× |
Sen returns no lanterns at all, which trims its multiple from 6.20 down to 5.83.
The steady-state contribution shows the real shape.
| Rank | Frequency | Share of total income |
|---|---|---|
| Regular | 80.9% | 55.0% |
| Bian | 16.2% | 32.8% |
| Sen | 2.9% | 12.3% |
Bian shows up 16% of the time and earns 33% of the coins. Sen is 2.9% and 12%. Together, 19% of boards carry 45% of the income. The 20%-versus-6% from section 2 is the price of admission to that 45%.
AnswerThe 800 JPY pass. At 4.30 JPY per lantern it is more than twice as cheap as anything else.
| Source | Lanterns | Price | Per lantern |
|---|---|---|---|
| Pass (Moonlit Blessing) | 186 | 800 | 4.30 |
| Pack 1 | 15 | 150 | 10.00 |
| Pack 2 | 30 | 320 | 10.67 |
| Everlasting Moon (one-time) | 300 | 3,200 | 10.67 |
| Pack 3 | 50 | 800 | 16.00 |
| Pack 4 | 90 | 1,600 | 17.78 |
| Pack 5 | 160 | 3,200 | 20.00 |
| Pack 6 | 360 | 8,000 | 22.22 |
The pass doubles the daily grant from 18 to 36 lanterns: 60 immediately plus 126 over seven days, 186 in total. Its break-even price works out to about 3,200 JPY. It sells for a quarter of that. If you intend to spend a single yen, this is the first thing you buy.
Packs unlock one per day, strictly in order 1→6; you cannot see the next until you buy the current one. Unit price rises monotonically with pack number, so filling the cheapest slot across every day before moving up is optimal. Everlasting Moon is a one-time purchase outside that daily sequence, which puts the order at: pass → packs 1 and 2 across all seven days → Everlasting Moon → pack 3 and up.
AnswerEvery day. The same lanterns swing 4,852 coins.
Daily missions reset each day, so the same total pays differently depending on how many days you spread it over. With 52 rounds' worth of lanterns, the daily-mission coins come out as:
| Pattern | Daily-mission coins |
|---|---|
| All in one day | 1,000 |
| Across four days | 3,646 |
| Across seven days | 5,852 |
A 4,852-coin gap — more than a tenth of a 45,000 goal.
The best split also depends on the total. With only 21 rounds available, concentrating into five days (2,672) beats spreading over seven (1,873), because five days clears the 40-line tier each time.
By efficiency, the 250 coins for one round a day is the richest tier of all. Securing at least one round on each of the seven days is the first move.
Answer22,490 JPY. It carries a permanent +2% attack buff.
The headline item is the 45,000-coin City Decor. It is not cosmetic: it grants a permanent +2% attack buff, which makes it an asset rather than a consumable.
| Coins reached | Rounds | Total spend |
|---|---|---|
| 11,500 | 14.2 | 0 (free to play) |
| 13,900 | 18.2 | 800 |
| 20,000 | 24.4 | 3,770 |
| 30,000 | 38.4 | 11,290 |
| 45,000 | 52.3 | 22,490 |
| 60,000 | 77.6 | 43,290 |
The 45,000 plan breaks down like this.
| Slot | Cost | Lanterns |
|---|---|---|
| Pass (Moonlit Blessing) | 800 | 186 |
| Pack 1 × 7 days | 1,050 | 105 |
| Pack 2 × 7 days | 2,240 | 210 |
| Everlasting Moon × 1 | 3,200 | 300 |
| Pack 3 × 7 days | 5,600 | 350 |
| Pack 4 × 6 days | 9,600 | 540 |
| Total | 22,490 | 1,691 |
The richest point on that curve is 800 JPY. It lifts you from 11,500 free-to-play coins to 13,900 — about 0.33 JPY per coin. Pushing to 45,000 costs over 0.5 JPY per coin, roughly 1.5 times worse.
One more frame for the decision. The shop sells Mithril at 800 coins (30 in stock) and Gem Codex at 400 coins (100 in stock). Neither appears anywhere in the board reward pools — the shop is the only source. The City Decor's 45,000 coins equals 56 Mithril or 112 Gem Codex. Permanent +2% attack against 56 Mithril is a call that depends on where your account sits. The exchange rate is the part that can be computed.
For scale: clearing every one of the shop's 15 slots would take roughly 207,800 coins. It is built on the assumption that you cannot take it all.
AnswerAbout 11,500 coins — enough to clear out all 500 Fire Crystals and still have change.
| Source | Lanterns |
|---|---|
| Starting stock | 5 |
| Daily grant 18 × 7 days | 126 |
| Mission rewards | 30 |
| Rank missions 30 × 7 days | 210 |
| Panel rewards | 162 |
| Lucky Pot missions | 35 |
| Total | 568 |
Add the lanterns the boards hand back (3.3 per round on average) and the cumulative line rewards, and that runs about 14 rounds — 11,500 coins. Fire Crystals cost 18 coins with 500 in stock, so 9,000 coins clears the whole shelf. Free-to-play does not walk away empty-handed here.
Every reward probability and quantity was read from the game's own probability tab. All nine pools were checked to sum to 100.000%. The lantern counts are an exact combinatorial result, not a simulation.
The model was also checked against a 57-round log kept during the previous event of this type. Lanterns per round measured 49.12 against a predicted 49.04; Regular-board coins measured 388.8 against 392.3; Bian measured 1,126.7 against 1,170.0. All within sampling error.
One figure is estimated. Lantern packs 5 and 6 do not display their prices until the previous pack is bought, so those carry the previous event's prices. The calculator lets you overwrite both by hand.
Added 2026-09-27. The event finished at 50 rounds and exactly 500 cumulative lines, so here is how well the numbers above held.
The money matched the plan: 20,890 JPY, exactly what the calculator returned. Coins landed at 43,455 against a predicted 44,488 — 2.3% short.
| Source | Predicted | Actual | Gap |
|---|---|---|---|
| Board rewards + grand prize | 29,623 | 29,205 | −418 |
| Cumulative line rewards | 9,000 | 9,000 | 0 |
| Daily missions | 5,866 | 5,250 | −616 |
The larger half of the gap was the daily missions. The calculator assumes an even pace across all seven days. In practice day 2 ran 11 rounds, day 6 stopped at 60 lines and day 7 at 40 — both short of the 65-line tier. Those two days alone cost 500 coins.
Section 7 of this article warned about exactly that, and it came straight back. Moving two of day 2’s eleven rounds to the end would have paid 500 more coins for the same lanterns and the same money. Not luck — just where the taps went.
The board rewards themselves came in 1.2% above expectation. Split them open, though, and the luck sits in two separate layers.
Sen appeared three times against an expectation of 1.5, so the promotions ran hot. But the reward rolls on the upper boards came in 2,743 coins below expectation (z = −1.79). The three Sen rounds paid 1,200, 600 and 1,200 — about 60% of the 1,710 they should average.
Drawing a good board and hitting the coin rolls on it are two different kinds of luck. This time they cancelled out and left +1.2%. So the feeling that “Sen showed up and it barely moved the total” was an accurate reading, not a bias.
Lanterns per round measured 49.34 against a predicted 49.04 — z = 2.45, larger than chance comfortably explains. Across 50 rounds not one came in under 47 lanterns, where theory expects about six.
Pooled with the previous event’s 57 rounds (49.12) the figure is z = 1.55 over 107 rounds, and the significance disappears. Most likely noise, but a small systematic difference cannot be ruled out. The cause is unknown. If the same tilt shows up next event, the model needs revisiting.
Disclaimer: the figures here are expected values; your actual result moves with board-rank luck. Mechanics can differ by state and by season, so trust your own screen where it disagrees with this page. Corrections will be folded in.