The rules, as the engine writes them
Blackjack has more rule variants than any other table game, and casinos have learned to describe them in a font size that discourages reading. Ours are in a source comment, which is a better place, because a comment cannot be reworded for the brochure without the game changing with it.
Most of that list is favourable to the player — S17, double after split, the peek that protects a doubled bet. One line is the reason the ~99.5% figure is possible at all, and it is the first one most tables quietly change: blackjack pays 3:2.
Why one payout ratio outweighs every other rule
A natural — an ace with a ten-value card on the first two — is the best hand in the game and the only one with a special payout. At 3:2, a 10 stake wins 15. At 6:5, the same hand wins 12. Three units on a ten-unit bet sounds like a rounding difference. It is not, because naturals are common.
On an infinite shoe the frequency is exact. The chance the first card is an ace is 4/52 = 1/13; the chance the second is a ten-value card is 16/52 = 4/13; and the pair can arrive in either order. So a natural shows up on 2 × (1/13) × (4/13) = 8/169 of hands, or 4.73%. That is what the ratio is being applied to.
| 3:2 (THIS ENGINE) | 6:5 | DIFFERENCE | |
|---|---|---|---|
| Win on a 10 stake | 15 | 12 | 3 units |
| Return multiple | ×2.5 | ×2.2 | ×0.3 |
| Naturals per hand | 8/169 = 4.73% | 8/169 = 4.73% | — |
| Cost per hand, all hands | — | 0.3 × 4.73% | ≈ 1.42% of stake |
A dealer natural pushes a player natural on a small fraction of those hands (about 4.7% of them), which trims the figure by a few hundredths. Published multi-deck analyses put the 6:5 penalty at about 1.39%, in agreement.
Put that next to the house edge itself. Under these rules, with basic play, the engine states the return at about 99.5% — an edge of roughly half a percent. Switching the natural to 6:5 adds about 1.4 points to that. The one payout ratio costs nearly three times as much as the whole game. Every other rule variation in blackjack — hit or stand on soft 17, resplitting, surrender, number of decks — moves the edge by tenths of a point. This one moves it by whole ones.
It is the same lesson as the two cells that name a video poker table: the number that matters most is the one printed smallest, and the habit that pays best is reading it before sitting down.
The shoe has no memory, and no bottom
The frequency above was exact because of how the cards are drawn, and that detail is worth stating precisely, because it is easy to describe loosely.
That is not a fresh 52-card deck shuffled for each hand. It is an infinite shoe: every card is an independent draw from all fifty-two, with replacement. The deck never depletes because there is no deck — a ten dealt to you does not make the next card any less likely to be a ten, and the same card can, in principle, appear twice in one hand.
Two things follow. First, card counting is not merely impractical here but meaningless: the technique the MIT team built a business on works because a real shoe runs out of tens, and this one cannot. Second, the natural frequency, and every other probability in the game, is a closed-form number rather than something that drifts as cards leave the shoe. That is what let us write 8/169 above instead of “about 4.8%”.
What is not on the table, and why that is fine
The rule list ends with “no insurance, no surrender”. Both absences are neutral-to-good for a basic-strategy player, and one of them removes the game’s oldest trap.
- Insurance is a side bet that the dealer’s hole card is a ten, paid 2:1. On an infinite shoe the chance is exactly 4/13, so the bet returns 3 × 4/13 = 92.3% — a 7.7% house edge, the worst wager on the table by a wide margin. Basic strategy says never take it. Its absence here saves you from a mistake, not from an edge.
- Surrender lets a player forfeit half the stake instead of playing out a bad hand. Used correctly it is worth a few hundredths of a point to the player; used the way most players use it, it costs more than it saves. Its absence is a small loss for a perfect player and nothing for everyone else.
What is on the table — S17, double after split, the peek — is where the ~99.5% comes from. What decides whether that figure survives contact with a real casino is the payout on a natural, and here it is the one that keeps the number honest.
3:2, S17, every card from the committed seedBlackjack with the rules printed above and every hand recomputableBlackjack →
What does blackjack pay at Betkyo?
3:2 — a natural returns ×2.5 on the stake. The rule is stated in the engine source alongside S17, double on any first two cards, one split, dealer peek, and no insurance or surrender, at about 99.5% with basic play.
How much does 6:5 blackjack cost compared with 3:2?
About 1.4% of every initial stake. A natural arrives on 8/169 of hands (4.73%) on an infinite shoe, and 6:5 pays 0.3 stakes less on each one — nearly three times the entire house edge of a good 3:2 game.
Can you count cards on Betkyo blackjack?
No. Cards come from an infinite shoe — each card is an independent draw from all 52, derived from the committed seed pair — so nothing depletes and there is nothing to track.
Why is there no insurance?
Insurance is a 2:1 side bet that the dealer has a ten under an ace. With a 4/13 chance of that, it returns 92.3% — the worst bet on a blackjack table. Basic strategy never takes it, so leaving it out costs a correct player nothing.
Does the dealer stand on soft 17?
Yes — S17, the player-favourable version. Tables that hit soft 17 give the house roughly an extra fifth of a point.
- Betkyo engine source: the rules header, infinite-shoe draw and 3:2 payout in blackjack/derive.ts; the ~99.5% figure is the engine’s own
- Natural frequency, insurance return and the 6:5 cost are derived on the infinite-shoe model — 8/169, 4/13 and 0.3 × 8/169 — not read from a table
- Wizard of Odds — blackjack rule-variation analyses, where the published multi-deck 6:5 penalty of about 1.39% agrees with the figure above
