Analysis of The Three-bit Game
For the three-bit sequence game, the second player can optimise his odds by choosing sequences according to:
| 1st player's choice | 2nd player's choice | Odds in favour of 2nd player |
|---|---|---|
| HHH | THH | 7 to 1 |
| HHT | THH | 3 to 1 |
| HTH | HHT | 2 to 1 |
| HTT | HHT | 2 to 1 |
| THH | TTH | 2 to 1 |
| THT | TTH | 2 to 1 |
| TTH | HTT | 3 to 1 |
| TTT | HTT | 7 to 1 |
In each case the second player's optimal choice is to precede the first player's sequence (underlined) with the opposite of the second symbol (bolded).
An easy way to remember the sequence for using as a bar trick is for the second player to use the first two choices of the first player as the last choices, and then using the opposite of the (now) last choice as the first one.
- So for the first player's choice of XYZ
- the second player must choose xXY
where x - is the opposite of Y, and XY are the same XY chosen by the first player.
An intuitive explanation for this result, is that in any case that the sequence is not immediately the first player's choice, the chances for the first player getting their sequence-beginning, the opening two choices, are usually the chance that the second player will be getting their full sequence. So the second player will most likely "finish before" the first player.
Read more about this topic: Penney's Game
Famous quotes containing the words analysis of the, analysis of, analysis and/or game:
“Cubism had been an analysis of the object and an attempt to put it before us in its totality; both as analysis and as synthesis, it was a criticism of appearance. Surrealism transmuted the object, and suddenly a canvas became an apparition: a new figuration, a real transfiguration.”
—Octavio Paz (b. 1914)
“Cubism had been an analysis of the object and an attempt to put it before us in its totality; both as analysis and as synthesis, it was a criticism of appearance. Surrealism transmuted the object, and suddenly a canvas became an apparition: a new figuration, a real transfiguration.”
—Octavio Paz (b. 1914)
“Analysis as an instrument of enlightenment and civilization is good, in so far as it shatters absurd convictions, acts as a solvent upon natural prejudices, and undermines authority; good, in other words, in that it sets free, refines, humanizes, makes slaves ripe for freedom. But it is bad, very bad, in so far as it stands in the way of action, cannot shape the vital forces, maims life at its roots. Analysis can be a very unappetizing affair, as much so as death.”
—Thomas Mann (1875–1955)
“I have a notion that gamblers are as happy as most people, being always excited; women, wine, fame, the table, even ambition, sate now & then, but every turn of the card & cast of the dice keeps the gambler alive—besides one can game ten times longer than one can do any thing else.”
—George Gordon Noel Byron (1788–1824)