Pass the pigs Version francaise Introduction
Pass the pigs is a game edited by
Winning Moves, where you throw little plastic pigs instead of dices.
This page describes probabilities found and several strategies.
Elementary probabilities
Here are results found when 844 pigs were thrown together,
that is 1688 (pigs alone) :
p=0.203 probability to have a null score.
_{0}Expected value
Expected value or expectation is the sum of the values of a random
variable (like the number of points to get) with a weight proportional
to the probability of the occurrence of the value.
Given previous results we can compute expectation of points
when throwing two pigs: E=4.919 points.
Probability to get to turn .
Then the expectation of points while playing continuously is:
^{N}E/p which is 24.23 points.
_{0}Expectations after several couple of pigs thrown
Here are probabilities after several couple of pigs were thrown.
Probability to have a null score is not represented.
One couple of pigs thrown Two couples of pigs thrown Three couples of pigs thrown Seven Couples of pigs thrown Constant point strategy
A natural strategy is to have a fixed number of points
and to stop when you reach a given number.
For instance "whatever my opponent score is, I shall stop
when I reach 20 points". 20 is named the threshold value.
Table below shows results for several threshold. Each table cell represent 20 000 plays between strategies. Cell (17x20) represents the result of the plays between threshold strategy "stop at 17 points" against strategy "stop at 20 points". The number in the cell (here 0.95) means that strategy "stop at 17 points" has won 0.95 times less than strategy "stop at 20 points". 9.3 millions plays were computed to generate the table. Since the table is symmetric, only the upper part has been represented. Diagonal figures should be 1, but their are not. This gives an idea of the precision of computation.
Stop and risk strategy
Stopping at a given threshold like in previous strategy sometimes lakes
taste of risk.
This strategy is also a threshold strategy but is different:
keep throwing pigs as long as the total score is not above the opponent
and the threshold has not been reached.
This technique (Stop_and_risk) has been compared to previous strategy (Stop_at) for thresholds from 10 to 40. ratios have been given for 10 000 plays in each cell. Stop_at are horizontal, Stop_and_risk are vertical.
Links to related sites
Optimal strategy for the pig game, I also recommend the following article by T. Neller and G. M. Presser Optimal Play of the Dice Game Pig, The UMAP Journal 25(1) (2004), pp. 25-47. Their home page.Another probability. If you have any questions: Fabrice Derepas derepas.com |