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Title: Dice - Pass the Pigs Analysis of strategies for the Pass the Pigs game.
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Pass the pigs - Analysis

Pass the pigs

Version francaiseElementary probabilitiesProbabilities after several turnsConstant point strategyLinks to other sites

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) :Pink side 0.36Black dot side 0.27Trotter 0.07Razorback 0.24Snouter 0.02Leaning Jowler 0.01If we suppose that results are the same for one or two pigs (to check) we get the following results:Double Pink Side 0.132741Pink Side Black dot side 0.203320Pink Side Trotter 0.055255Pink Side Razorback 0.177420Pink Side Snouter 0.019857Pink Side Leaning Jowler 0.007339Double Black dot side 0.077857Black dot side Trotter 0.042317Black dot side Razorback 0.135878Black dot side Snouter 0.015208Black dot side Leaning Jowler 0.005620Double Trotter 0.005750Trotter Razorback 0.036926Trotter Snouter 0.004133Trotter Leaning Jowler 0.001527Double Razorback 0.059284Razorback Snouter 0.013270Razorback Leaning Jowler 0.004904Double Snouter 0.000743Snouter Leaning Jowler 0.000549Double Leaning Jowler 0.000101We denote by p0=0.203 probability to have a null score.

Expected value

Expected value or expectation is the sum of the values of a randomvariable (like the number of points to get) with a weight proportionalto the probability of the occurrence of the value.Given previous results we can compute expectation of pointswhen throwing two pigs: E=4.919 points.Probability to get to turn N is then (1-p0)N.Then the expectation of points while playing continuously is:E/p0 which is 24.23 points.

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 thrownTwo couples of pigs thrownThree couples of pigs thrownSeven Couples of pigs thrown

Constant point strategy

A natural strategy is to have a fixed number of pointsand to stop when you reach a given number.For instance "whatever my opponent score is, I shall stopwhen 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 playsbetween 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 ideaof the precision of computation.101112131415161718192021222324252627282930313233343536373839401010.740.650.620.610.60.580.520.520.510.530.520.50.50.50.50.570.590.590.590.590.570.570.60.620.620.720.820.880.930.96101110.880.830.830.80.740.70.690.680.70.670.670.640.640.630.710.740.740.730.740.720.690.750.790.760.870.991.11.11.1111210.960.950.920.860.810.780.760.80.790.740.740.720.720.80.820.830.820.840.820.780.810.850.860.991.11.21.21.312130.980.970.970.910.860.820.830.840.780.780.750.760.780.850.860.850.860.860.840.820.830.870.8811.11.21.31.3131410.990.920.870.830.830.830.830.80.790.770.780.850.880.870.860.880.820.80.840.890.9111.21.21.31.3141510.920.840.830.850.830.820.80.770.780.790.870.90.870.890.880.830.820.850.890.9211.21.21.31.3151610.950.910.930.920.910.840.850.830.860.930.940.930.960.940.890.880.940.970.981.11.21.31.31.416170.970.970.960.950.930.880.90.890.880.960.990.990.990.980.960.910.96111.21.31.41.41.417180.990.980.990.970.940.910.930.920.9811110.980.940.96111.21.31.41.41.518190.990.970.970.970.910.90.930.9911110.970.950.99111.21.31.41.41.519200.9810.950.930.90.92111110.950.96111.11.21.31.41.51.4202110.950.940.930.93111110.970.97111.11.21.31.41.51.52122110.970.981.11.11.11.11.110.981.11.11.11.21.41.51.51.6222310.9711.11.11.11.11.11111.11.11.21.41.51.51.52324111.11.11.11.11.11111.11.11.31.41.51.51.5242511.11.11.11.11.1111.11.11.11.21.41.41.51.525260.98110.9810.940.960.98111.21.31.31.41.52627110.9710.960.940.95111.11.31.41.41.4272810.9810.970.920.96111.11.31.31.41.42829110.940.940.99111.11.31.31.41.5293010.950.981111.11.21.41.41.430310.980.9811.11.11.21.31.41.41.53132111.11.11.21.31.41.51.532330.99111.21.31.41.41.4333410.991.11.21.31.41.434350.991.11.21.31.31.4353611.11.21.21.23637111.11.137380.991138390.9913940140     <= 0.8 Very bad for vertical strategy     0.8 <...< 0.96 Bad for vertical strategy     0.96 <...< 1.05 Neutral      1.05 <...< 1.1 Good for vertical strategy     >=1.1Very good for vertical strategyNode: displayed figures are rounded. This is why some 1.1 figure appearon dark green and some other on light green.

Stop and risk strategy

Stopping at a given threshold like in previous strategy sometimes lakestaste 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 opponentand 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.10111213141516171819202122232425262728293031323334353637383940101.61.21.1110.990.90.860.830.820.840.830.790.770.750.760.860.860.860.850.840.770.760.770.80.830.911.11.21.21.310111.81.41.21.11.21.11.10.990.930.970.950.940.870.840.860.850.960.960.950.950.940.860.870.860.920.931.11.21.31.41.3111221.51.31.21.21.21.11111.10.990.910.920.910.92110.9810.980.940.870.940.990.981.11.21.31.41.412132.11.61.41.31.31.21.11.11110.990.950.940.950.94111110.950.920.94111.11.31.41.51.513142.11.51.41.31.31.31.11.11.111.110.980.970.960.93111110.960.950.95111.11.31.41.41.5141521.61.31.31.21.31.11.11.111.110.980.930.930.97111110.920.910.9911.11.11.31.41.41.515162.11.61.41.31.31.31.21.21.11.11.11.110.97111.11.11.111.110.97111.11.21.31.41.51.516172.21.61.41.41.31.41.21.11.11.11.11.110.97111.11.11.11.11.110.9911.11.11.21.41.51.51.517182.21.61.41.31.41.41.21.11.11.11.11.111111.11.11.11.11111.11.11.11.21.41.51.51.518192.21.71.41.41.41.41.21.21.11.11.11.111111.11.11.11.11.11111.11.11.21.41.51.51.519202.21.61.51.41.31.41.21.11.11.11.11.11.11111.11.11.11.11.11111.11.11.21.31.41.51.520212.11.71.41.41.31.31.21.11.11.11.11.111111.11.11.11.11.110.9911.11.11.21.31.51.51.521222.11.61.41.41.31.31.21.21.11.11.11.111111.11.11.11.11.1111.11.11.11.21.31.41.51.522232.11.61.41.41.31.41.21.11.11.11.11.11110.991.11.11.11.11.11.1111.11.11.21.41.41.41.523242.11.61.41.41.31.41.21.11.11.11.11.111111.11.11.11.11.11.1111.11.11.21.31.41.41.5242521.61.41.31.31.41.31.21.11.11.11.11110.981.11.11.11.11.1111.11.11.11.21.31.51.41.425261.81.51.31.21.21.21.21.111.11.110.990.950.950.9411.11.1111111.11.11.11.21.31.41.426271.81.41.21.21.21.21.11.111110.950.950.930.930.9911110.970.950.98111.11.21.31.31.327281.81.31.31.21.21.21.111110.990.950.930.930.910.980.991110.980.950.99111.11.21.31.31.428291.71.41.31.21.21.21.11.111110.960.920.930.92111110.980.961111.11.21.31.31.329301.71.41.31.21.21.21.1111110.930.930.930.94111110.960.970.98111.11.21.31.31.330311.81.41.21.21.21.21.111110.990.980.960.970.96111110.970.950.98111.11.21.31.31.331321.71.31.21.21.21.21.1111110.980.920.950.95111110.960.940.96111.11.21.21.31.332331.61.31.21.11.21.11.110.990.980.960.950.920.90.880.910.97110.980.990.930.920.920.950.991.11.11.21.31.233341.61.31.21.11.11.110.970.950.930.940.940.910.890.890.860.950.980.940.950.950.90.890.910.970.9511.11.21.21.334351.61.21.11.11.11.110.950.960.930.930.920.90.860.870.870.930.960.950.960.940.890.90.880.930.9511.11.11.21.235361.41.1110.9710.940.860.860.840.850.840.810.810.780.810.870.880.870.870.870.840.840.840.860.860.9511.11.11.136371.310.940.90.90.880.830.80.790.80.790.780.760.730.740.740.780.810.80.820.810.770.750.760.770.80.860.96111.137381.20.980.90.850.840.830.780.770.740.750.720.730.710.690.690.690.760.780.750.760.750.710.710.730.730.770.830.910.98138391.10.930.840.80.820.820.770.750.720.720.720.710.680.680.690.680.720.740.750.740.740.720.690.710.720.720.830.90.950.970.9739401.10.940.850.820.820.80.740.730.720.690.710.70.680.670.670.690.720.740.740.740.710.710.70.70.720.730.780.880.940.97140

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.comLast modified: Thu Nov 4 09:44:01 2004
 

Analysis

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Pass

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Pigs

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Analysis of strategies for the Pass the Pigs game.

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