Two Kingdoms
Scribe’s CardsHave 500 practice points
Your practice points ran out. Here are 500 more, once, at no cost. Points are a scorekeeping device and carry no value of any kind.
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
- Choose one of three outcomes before the round: the Blue hand, the Amber hand, or a level result.
- Two cards go to each hand. Tens and picture cards count zero, an ace counts one, and only the last digit of the total matters, so nine plus four is three.
- Eight or nine on the first two cards is a natural and both hands stop there.
- Otherwise the Blue hand draws a third card on a total of zero to five and stops on six or seven. The Amber hand then follows the published third-card table, which depends on its own total and on the card the Blue hand drew.
- The higher final total wins. Blue pays even money, Amber pays even money less five per cent commission, and a level result pays the published multiple while returning any Blue or Amber selection.
- There is no decision after the selection is made. Every draw is forced by the table, which is why the three published edges are fixed numbers rather than a range.
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.
| Selection | Probability | Pays | Board margin |
|---|---|---|---|
| Amber hand | 45.86% | 0.95:1 | 1.06% |
| Blue hand | 44.62% | 1:1 | 1.24% |
| Level | 9.52% | 8:1 | 14.36% |
The formula
Amber wins 45.86%, Blue wins 44.62%, and the two are level 9.52% of the time
Amber edge = 1 − (0.95 × 0.4586 ÷ (1 − 0.0952) × 2) ≈ 1.06%
the level selection pays 8:1 against a 9.52% chance, which is why its edge is 14.36%
Third card table
| Your hand | When | Response |
|---|---|---|
| Amber hand | Total 0 to 5 | Takes a third card |
| Amber hand | Total 6 or 7 | Stands |
| Amber hand | Total 8 or 9 | Natural, both hands stand |
| Blue hand | Total 0, 1 or 2 | Takes a third card |
| Blue hand | Total 3 | Takes a third card unless the amber third card is an eight |
| Blue hand | Total 4 | Takes a third card if the amber third card is two to seven |
| Blue hand | Total 5 | Takes a third card if the amber third card is four to seven |
| Blue hand | Total 6 | Takes a third card if the amber third card is six or seven |
| Blue hand | Total 7 | Stands |
| Blue hand | Amber stood on 6 or 7 | Takes a third card on 0 to 5, stands on 6 or 7 |
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.