pwcrabb's Blog

The Ballad of Danny Dice

At a busy casino Craps table
near the Stickman stood Iron-Willed Dan.
He knew what he must do and did it
and boredom was part of his plan.

Temptation could not mar his pattern.
Companions could not change his mind.
Dan knew what dice do since forever.
Reliable Math just needs time.

For an hour Dan did nothing special,
made one percent Come bets each toss,
persisting with his Barefoot Buildout
and simply evading big loss.

Through choppy dice Danny broke even
and that is as good as it gets.
When Box repetitions brought money,
he used it for Odds on his bets.

Sometimes up, mostly down, Dan was hunting
by building, rebuilding his trap.
Awaiting with patience his quarry,
he stalked the elusive deep Gap.

Big Red disappears only rarely.
In each Gap, Odds wagers may win.
Dan recovers his outlay plus profit
before his Place wagers begin.

When Gap arrived, Danny was ready,
his bankroll preserved for attack.
One Shooter was all that it lasted.
"Take me down!" turned Dan's rails Black.

Near the Stickman announcing "new Shooter"
back to one percent Come bets stood Dan,
stood a player with a Will of Iron
and boredom was part of his plan.

Dice Fun Facts

NUMBERS BECOMING LIKELY

The future dice tosses that are theoretically required for a specific outcome to become likely can be easily calculated. Likelihood is anything beyond 50 percent.

Example: How many future tosses are required for the number SEVEN to become likely? Let ( x ) be the number of future tosses that are necessary for the probability to become equal to 50 percent, which is ( 0.5000 ). For any toss, the probability of a SEVEN is ( 6/36 ). The probability of anything other than SEVEN is therefore ( 30/36 ). Unlikelihood starts strong but diminishes with additional dice tosses. Simply solve the following equation for the exponent ( x ), which represents future dice tosses:

( 30/36 ) ^ ( x ) = ( 0.50000 )

For any given number to become likely, the required future dice tosses can be calculated using analogous reasoning. For all of the numbers from TWO through SEVEN, here are the solutions to the equations:

Outcome TWO requires 24.605098 future tosses to cross the likelihood threshold

Outcome THREE requires 12.126774

Outcome FOUR requires 7.966167

Outcome FIVE requires 5.884949

Outcome SIX requires 4.635452

Outcome SEVEN requires 3.801784

These data have consequences when planning strategies for multi-toss games involving two dice. Within Craps, a careful selection of specific wagering tools such as Odds bets and Place bets is necessary but not sufficient for designing a winning strategy. Just as is true when designing a skyscraper, specific tools are not as important as overall blueprints. For each of the best tools of Craps, expected outcome delays should be included in the strategy.

The single most important delay is the expected delay before the next SEVEN, because that delay is the likely window of safety for Place bets.

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DARK SIDE PLAY

Those gamblers who argue passionately for or against the Dark Side bets of Don't Pass and Don't Come are wasting their breath. As they are played in Bank Craps in licensed casinos, the Bright Side bets and the Dark Side bets are only mildly distinguished. For a model wager of 1980 units, selected for integer results, the Bright Side has an expected return of 1952 units for a casino advantage of 1.414141 percent. The same bet on the Dark Side has an expected return of 1953 units for a casino advantage of 1.363636 percent.

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BIG RED

Big Red enjoys the dominant role in Craps. Its appearance ends all working games within Craps as customarily offered by casinos. The projected behavior of Big Red over time should be carefully considered by any serious player. As do all random phenomena, Big Red tends to appear in clusters rather than at regular intervals. Both its clustered appearances and its cherished extended absences can be described mathematically. Both appearances and absences can be anticipated and responded to by alert gamblers.

Two Examples:

(1) Big Red favors the Dark Side bets of Don't Pass and Don't Come by the large but not overwhelming ratio of ( 392 ) to ( 165 ).

(2) Because the next projected appearance of Big Red is 3.8 tosses into the future, a player of Place bets should have a timing plan both for making Place bets and for taking them down. The loss of a Place bet need not be inevitable. Because they have no plan to take down their Place bets, most players of Place bets are implicitly planning for the eventual loss of every bet. Such a plan is deeply flawed mathematically. Their expected returns are only the sums of the infinite series of future winnings from their Place bets, appropriately discounted by probabilities.