Two games in one
Tairyō is a 5×3, ten-line fishing slot in the style of the collector games: in free spins, a wild fisherman collects the cash values printed on every fish on screen. Designing Tairyō read its paytable. This article prices it, and the first thing the price shows is that the slot is really two games sharing a screen. One is the base game, which you play on almost every spin. The other is the free-spin round, which pays most of the money.
The base game: 29.41%
Each reel stops at one of 50 positions with equal chance and the five reels are independent, so the expected pay of a line is a short exact sum over the strips, and every line has the same one. Ten lines give the base game’s return.
| SYMBOL | PAYS 2 / 3 / 4 / 5 OF A KIND | SHARE OF THE STAKE |
|---|---|---|
| Bobber | ×0.05 / ×0.5 / ×2 / ×20 | 13.76% |
| Rod | — / ×0.3 / ×1.5 / ×10 | 7.04% |
| Dragonfly | — / ×0.2 / ×1 / ×5 | 4.16% |
| Tackle box | — / ×0.2 / ×1 / ×5 | 4.16% |
| Fish | — / ×0.1 / ×0.5 / ×2 | 0.29% |
| A, K, Q, J, 10 | — / ×0.05 / ×0.25 / ×1 | 0.00% |
| All base line wins | 29.41% |
Exact over the 50-stop strips: ten lines × one line’s expected pay. A given line pays on 6.57% of spins; about 42.8% of spins pay something on at least one line (a million-spin replay). The card ranks almost never appear on the base strips, so they carry no measurable return there.
A base game that returns 29 cents on the dollar is not a mistake; it is the shape of the product. It pays often enough to keep the screen busy — four spins in ten show a line win, mostly small ones — while almost all of the money waits behind the scatters.
One spin in 386
Free spins need a scatter visible on each of reels 2, 3 and 4. Reel 2 carries three scatters on its 50 stops and each is visible from three stopping positions, so it shows one 18% of the time; reels 3 and 4 carry two each, 12%. The trigger is the product: 0.18 × 0.12 × 0.12 = 0.2592%, one spin in 385.8. No reel can show two scatters at once and the other reels carry none, so three is also the only count possible — four or five scatters never happen.
| SPINS PLAYED | CHANCE OF NO FREE SPINS |
|---|---|
| 100 | 77.1% |
| 300 | 45.9% |
| 1,000 | 7.5% |
(1 − 0.002592) raised to the number of spins. A session without the feature returns about the base game’s 29%.
That table is the most useful fact about the game. Three sessions in four of 100 spins never see the part of the slot that pays two-thirds of its return, and those sessions lose about 71% of what they stake. The 96% is real, but it is an average over a feature most short sessions do not reach.
What the round is worth
| REGULAR ROUND | SUPER ROUND (BUY ONLY) | |
|---|---|---|
| Average payout | ×257.5 | ×685.9 |
| Middle round | ×56 | ×166 |
| Pays under ×10 | 20.7% | 10.5% |
| Pays ×1,000 or more | 4.6% | 32.3% |
| Reaches the ×2,100 cap | 0.21% | 14.6% |
| At least one retrigger | 58.5% | 57.8% |
| Average spins played | 24.1 | 22.5 |
Replay of the engine’s round rules with the published fish-value weights; standard error of the regular average about ±0.6×. The engine’s own cross-checked figures are ×258.5 and ×687.5. The super round draws fish values from a heavier table (a ×2,000 fish is 1 in 191 instead of 1 in 6,546).
The average round is worth ×258, but the typical one is worth ×56: the mean is carried by rounds in which a high-value fish meets a wild late in the ladder, when collection is multiplied by ten. That is why the return figure and the experience diverge so sharply. Multiplying the trigger rate by the round’s value gives the feature’s share of the return: 0.2592% × 257.5 ≈ 66.7% of the stake, for a total of about 96.2%, or 96.4% with the engine’s ×258.5.
Buying the feature
Tairyō sells the round directly: 270 times the bet for a regular round, 720 times for a super round with the richer fish table. The prices were set against the round’s measured value, and they return about 95.5% (270× for ×257.5–258.5) and 95.3% (720× for ×685.9–687.5). Both are a little below the roughly 96.2% the game returns when the round is earned by spinning.
The buy also compresses the variance into one decision. A regular buy returns its 270× price or more in 33.8% of rounds; the super buy returns its 720× in 36.3%. Two buys in three lose money, a few win large, and the average sits a few points below the price — the same shape as the base game’s long wait, delivered in one click. Risk of ruin and the machine zone are the two articles to read before doing that repeatedly.
Checking a spin
- Take the revealed server seed, your client seed and the nonce from the round’s fairness panel.
- For each draw i compute HMAC-SHA256 keyed by the server seed over “clientSeed-nonce-i”, read the first 13 hex digits as an integer d, and take floor(d × n ÷ 2⁵²) for a choice among n.
- A base spin uses draws 0–4, one reel stop each (n = 50). If it triggers, the free-spin round continues the same draw sequence: five reel stops per spin, then one draw per fish for its value, then the extra draws the single-wild bonus uses.
The engine does the arithmetic in integers so a verifier in a browser can match it bit for bit. Replaying a spin proves the stops were fixed before you pressed the button; the return in this article is a property of the strips and tables, which is why it has to be computed rather than replayed.
What is the RTP of the Tairyō slot?
About 96.2–96.4%: 29.41% exactly from base-game line wins, plus free spins that trigger once in 385.8 spins and pay about ×258 on average. The engine’s comment records a simulated 95.2%, about a point lower.
How often do Tairyō free spins trigger?
On 0.2592% of spins, one in 385.8. It needs a scatter on each of reels 2, 3 and 4, shown 18%, 12% and 12% of the time. Four or five scatters cannot occur.
How much do Tairyō free spins pay?
About ×258 the bet on average, but ×56 in the middle case. About 21% of rounds pay under ×10, 4.6% pay ×1,000 or more and 0.2% reach the ×2,100 cap.
Is buying the Tairyō bonus worth it?
It returns about 95.5% (regular, 270×) or 95.3% (super, 720×), slightly less than the roughly 96.2% the game returns when the round is triggered by spinning. Two buys in three pay back less than their price.
Why does Tairyō lose so fast between features?
The base game returns 29.41% on its own. Two-thirds of the return sits in the free-spin round, so a 100-spin session without the feature — 77% of them — keeps about 29% of its stakes.
What does the ×10 multiplier apply to?
Only to the fish values the wilds collect, from the ninth collected wild onward. Line wins in free spins are paid at face value.
- Betkyo engine source, house service: TairyoEngine.kt — BASE_STRIPS, FS_STRIP, PAYTABLE, PAYLINES, MONEY_WEIGHTS and SUPER_MONEY_WEIGHTS, the 3/6/9-wild retrigger ladder with multipliers 1/2/3/10, MAX_WIN_MULT1000, the integer intBelow() draw; TairyoConstants (buy prices 270× and 720×); client mirror slot/slotEngine.ts
- Exact calculation written for this article: one line’s expected pay over the five 50-stop strips ×10 lines; scatter visibility per reel and the trigger product; a million-spin replay of the base game (29.35% vs 29.41% exact)
- Replay written for this article: 300,000 regular and 300,000 super free-spin rounds under the engine’s rules (averages ×257.5 and ×685.9, against the engine’s cross-checked ×258.5 and ×687.5)
