Queen’s Ladder
Scribe’s CardsThis board is for members only
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Stratosphynx runs free simulations of online casino games. Every board follows the real rules and the real odds of the format it simulates, and is played with practice points that have no cash value. There is no real money anywhere on this site, nothing to deposit, nothing to withdraw and nothing to win.
How to play
- Set your entry and press deal. Five cards are dealt from a fresh pack.
- Tap any card you want to keep. Kept cards are outlined and marked.
- Press replace. Every card you did not keep is exchanged once, and the final five are read against the pay table printed beside the board.
- The pay table is fixed and is the published one for this variant. It is the whole of the game: the only decision is which cards to keep, and that decision is what separates the published long-run return from a worse one.
The rules
Cards here carry numbers only, in four colour families, with no faces and no suits. On a higher-or-lower board you see one card and call the next; a correct call advances you a step and grows the running multiplier, a wrong call ends the round. You may collect at any point. On a memory board, turn two cards per move; a matching pair stays face up, and clearing the board within the move limit scores.
If this is your first board
Take the four-by-two memory board first. Eight cards, four pairs, five moves, and every mistake is visible immediately. On higher-or-lower, remember that collecting early is a real choice and usually the mathematically better one: the multiplier grows more slowly than the chance of the chain breaking.
Pay table
Every figure below is computed from this board's own settings, not typed in by hand.
Extended Bonus 9/6
| Combination | Pays | Probability | About once in | Share of the return |
|---|---|---|---|---|
| Top Run | ×250 | 0.0025% | 40,161 | 0.62% |
| Suited Run | ×50 | 0.0106% | 9,434 | 0.53% |
| Four Aces with a 2, 3 or 4 | ×400 | 0.0047% | 21,097 | 1.90% |
| Four Aces | ×160 | 0.0168% | 5,952 | 2.69% |
| Four 2s, 3s or 4s with an Ace to 4 | ×160 | 0.0122% | 8,197 | 1.95% |
| Four 2s, 3s or 4s | ×80 | 0.0363% | 2,755 | 2.90% |
| Four 5s through Kings | ×50 | 0.1710% | 585 | 8.55% |
| Three and Two | ×9 | 1.0820% | 92.4 | 9.74% |
| Same Suit | ×6 | 1.4710% | 68.0 | 8.83% |
| Run | ×4 | 1.1620% | 86.1 | 4.65% |
| Three Alike | ×3 | 7.4510% | 13.4 | 22.35% |
| Two Pairs | ×1 | 12.2750% | 8.1 | 12.28% |
| High Pair, Jacks up | ×1 | 20.7060% | 4.8 | 20.71% |
The formula
the frequencies above are the ones that follow from playing every hand correctly
keeping the wrong cards does not change the pay table; it changes the frequencies, and the return falls
What to keep, in order
Keep the highest entry your five cards contain · This chart is the published response for this board's exact rule set. Following it produces the long-run return stated above; departing from it lowers it.
- Top Run, Suited Run or Four Alike
- Four cards to a Top Run
- Three and Two, Same Suit or Run
- Three Alike
- Four cards to a Suited Run
- Two Pairs
- A high pair
- Four cards to a Same Suit
- Three cards to a Top Run
- Four cards to an open Run
- Two suited high cards
- Three cards to a Suited Run
- Two unsuited high cards, the lowest two
- A suited ten with one high card
- One high card
- Keep nothing
The maths behind it
On higher-or-lower with a top card of H, seeing a card of value v makes "higher" correct for (H − v) of the H values and "lower" correct for (v − 1). The best call is whichever side holds more, and against a low card that edge is large. Chaining calls multiplies the probabilities, which is why a five-step chain is far less likely than it feels: five calls at 70% each land together only about one time in six.
Where it comes from
Numbered cards are among the oldest portable randomisers, and the two mechanics here are the two oldest questions you can ask of them. Is the next one bigger or smaller than this one, and can you remember where you saw its twin. Both questions predate any formal theory of probability, and both were used as teaching devices long before they became pastimes.
If this is your first board
Take the four-by-two memory board first. Eight cards, four pairs, five moves, and every mistake is visible immediately. On higher-or-lower, remember that collecting early is a real choice and usually the mathematically better one: the multiplier grows more slowly than the chance of the chain breaking.