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Pazaak Probabilities


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Hello, I'm new here.

 

I was just returning to Knights of the Old Republic, and I was about to start up Pazaak in Taris again, when I felt the need to seek out what other people's strategies were regarding Pazaak. After reading several pazaak guides/strategies on the internet, I felt woefully unconvinced. I'm starting this thread so I can share my ideas regarding pazaak, and perhaps hear some from other members as well.

 

So to begin, I decided to use a Monte Carlo simulation to see what I could learn about the probability of getting certain results on a pazaak table. My program is currently pretty simple, so some extrapolation on the produced data will be necessary. To begin, I'm simply rolling random values between 1 and 10 for cards, and playing a game up until the value is greater than or equal to 20, or until there are 9 cards on the table. At this point I store what the value is and simulate a new game of pazaak. I don't think the decks in KOTOR have a finite number of each type of card (though I have heard mention of there being 4 of each card between 1 and 10). In the case that they do have a finite number of each card this simulation may yield different results.

 

 

I simulated 100,000 games, and these are my results:

-----------------------

Pazaak game tester v0.1

-----------------------

100000 games simulated. Results:

Busts: 81756

g10: 23678

g11: 16053

g12: 16687

g13: 16985

g14: 17681

g15: 17876

g16: 18237

g17: 18544

g18: 18785

g19: 18774

g20: 18242

g21: 16018

g22: 14241

g23: 12586

g24: 10973

g25: 9205

g26: 7485

g27: 5618

g28: 3736

g29: 1894

g30: 0

gDouble: 25532

--Rolls--

r1: 41815

r2: 41936

r3: 42199

r4: 41652

r5: 42066

r6: 41997

r7: 41748

r8: 41878

r9: 41651

r10: 42002

 

 

A quick explanation of these values:

Busts: Whenever the game doesn't end in a 20, I count the game as a bust. This is why this number is so large, and why this number plus g20 equals the number of games simulated.

g10: Whenever the sum of the cards on the table is 10, I count that as a g10.

g11-g30: Same idea as g10, but with the sums corresponding to the variable name.

gDouble: Whenever a card is thrown such that you can use the "doubling card" from TSL (e.g. a game starting with 10) to win, I increased gDouble.

r1-r10: Just to show that the randomization was working, these values correspond to each time a 1, 2, 3... etc. card was "rolled". As you can tell they're all close to 42,000 (for a total of 418,994 rolls, corresponding to an average of 4.189 cards per game before reaching or exceeding a value of 20).

 

Obviously there's a lot more work to be done here, but I'm confident that with time we can find the most ideal pazaak hands and from there the most ideal pazaak deck.

 

 

 

--EDIT--

Did some more simulation work and expanded the program's capabilities. Tested 10,000,000 games per card type. The tested card was played whenever table value was such that playing it resulted in total card value of 20, or in the case of subtraction cards, whenever the table value exceeded 20. Direct victories are where using the card resulted in a table value of 20, luck victories are where you used a subtraction card to go below 20 and then got 20 later on in the game.

 

 

Card Probability Results:

+6

Victories without using card: 1546561

Test card +6 direct victories: 1756088

Test card +6 luck victories: 0

Chance of victory without using card: 15.47%

Total chance of victory: 33.03%

 

+5

Victories without using card: 1564440

Test card +5 direct victories: 1800038

Test card +5 luck victories: 0

Chance of victory without using card: 15.64%

Total chance of victory: 33.64%

 

+4

Victories without using card: 1583265

Test card +4 direct victories: 1834424

Test card +4 luck victories: 0

Chance of victory without using card: 15.83%

Total chance of victory: 34.18%

 

+3

Victories without using card: 1603384

Test card +3 direct victories: 1859016

Test card +3 luck victories: 0

Chance of victory without using card: 16.03%

Total chance of victory: 34.62%

 

+2

Victories without using card: 1624613

Test card +2 direct victories: 1862669

Test card +2 luck victories: 0

Chance of victory without using card: 16.24%

Total chance of victory: 34.87%

 

+1

Victories without using card: 1642042

Test card +1 direct victories: 1857887

Test card +1 luck victories: 0

Chance of victory without using card: 16.42%

Total chance of victory: 35.00%

 

-6

Victories without using card: 1827851

Test card -6 direct victories: 1343382

Test card -6 luck victories: 755766

Chance of victory without using card: 18.28%

Total chance of victory: 39.27%

 

-5

Victories without using card: 1828517

Test card -5 direct victories: 1530948

Test card -5 luck victories: 612853

Chance of victory without using card: 18.29%

Total chance of victory: 39.72%

 

-4

Victories without using card: 1828937

Test card -4 direct victories: 1559155

Test card -4 luck victories: 464965

Chance of victory without using card: 18.29%

Total chance of victory: 38.53%

 

-3

Victories without using card: 1827270

Test card -3 direct victories: 1578922

Test card -3 luck victories: 310677

Chance of victory without using card: 18.27%

Total chance of victory: 37.17%

 

-2

Victories without using card: 1825755

Test card -2 direct victories: 1591142

Test card -2 luck victories: 155946

Chance of victory without using card: 18.26%

Total chance of victory: 35.73%

 

-1

Victories without using card: 1826087

Test card -1 direct victories: 1591168

Test card -1 luck victories: 0

Chance of victory without using card: 18.26%

Total chance of victory: 34.17%

 

+/-6

Victories without using card: 1546192

Test card +/-6 direct victories: 2893080

Test card +/-6 luck victories: 610858

Chance of victory without using card: 15.46%

Total chance of victory: 50.50%

 

+/-5

Victories without using card: 1564809

Test card +/-5 direct victories: 2954220

Test card +/-5 luck victories: 497123

Chance of victory without using card: 15.64%

Total chance of victory: 50.16%

 

+/-4

Victories without using card: 1585434

Test card +/-4 direct victories: 3074411

Test card +/-4 luck victories: 387313

Chance of victory without using card: 15.85%

Total chance of victory: 50.47%

 

+/-3

Victories without using card: 1603198

Test card +/-3 direct victories: 3165574

Test card +/-3 luck victories: 265437

Chance of victory without using card: 16.03%

Total chance of victory: 50.34%

 

+/-2

Victories without using card: 1622371

Test card +/-2 direct victories: 3231314

Test card +/-2 luck victories: 136824

Chance of victory without using card: 16.22%

Total chance of victory: 49.91%

 

+/-1

Victories without using card: 1643193

Test card +/-1 direct victories: 3264196

Test card +/-1 luck victories: 0

Chance of victory without using card: 16.43%

Total chance of victory: 49.07%

 

 

Show spoiler
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-----------------------

Pazaak game tester v0.4

-----------------------

10000000 games simulated. Results:

Busts: 6697351

9 cards: 4320

g10: 2359855

g11: 1594229

g12: 1653916

g13: 1707651

g14: 0

g15: 1625516

g16: 1642501

g17: 1644493

g18: 1629537

g19: 1601081

g20: 1546561

g21: 1310413

g22: 1149495

g23: 983114

g24: 814495

g25: 813440

g26: 652041

g27: 487916

g28: 322109

g29: 160008

g30: 0

gDouble: 2328667

--Rolls--

r1: 3734940

r2: 3735893

r3: 3743647

r4: 3665867

r5: 3689967

r6: 3708140

r7: 3728153

r8: 3743483

r9: 3758528

r10: 3768384

--Victories--

Victories without using card: 1546561

Test card +6 direct victories: 1756088

Test card +6 luck victories: 0

 

 

10000000 games simulated. Results:

Busts: 6635522

9 cards: 4366

g10: 2358693

g11: 1593700

g12: 1653403

g13: 1708566

g14: 1757097

g15: 0

g16: 1654343

g17: 1659789

g18: 1649201

g19: 1618603

g20: 1564440

g21: 1329042

g22: 1169752

g23: 1005576

g24: 831966

g25: 657961

g26: 657293

g27: 491981

g28: 326572

g29: 161013

g30: 0

gDouble: 2504961

--Rolls--

r1: 3746528

r2: 3753170

r3: 3757902

r4: 3762394

r5: 3687527

r6: 3710528

r7: 3730608

r8: 3743900

r9: 3762060

r10: 3773521

--Victories--

Victories without using card: 1564440

Test card +5 direct victories: 1800038

Test card +5 luck victories: 0

 

 

10000000 games simulated. Results:

Busts: 6582311

9 cards: 4456

g10: 2357602

g11: 1593084

g12: 1650598

g13: 1708296

g14: 1760235

g15: 1801141

g16: 0

g17: 1671419

g18: 1665643

g19: 1635787

g20: 1583265

g21: 1349430

g22: 1189966

g23: 1023501

g24: 851540

g25: 677854

g26: 497097

g27: 495336

g28: 329107

g29: 164024

g30: 0

gDouble: 2340575

--Rolls--

r1: 3762173

r2: 3767584

r3: 3770382

r4: 3775287

r5: 3782044

r6: 3705527

r7: 3730971

r8: 3746967

r9: 3763485

r10: 3780040

--Victories--

Victories without using card: 1583265

Test card +4 direct victories: 1834424

Test card +4 luck victories: 0

 

 

10000000 games simulated. Results:

Busts: 6537600

9 cards: 4388

g10: 2357677

g11: 1593131

g12: 1654436

g13: 1707533

g14: 1759852

g15: 1798795

g16: 1835143

g17: 0

g18: 1679589

g19: 1653858

g20: 1603384

g21: 1365843

g22: 1206770

g23: 1043074

g24: 872512

g25: 697120

g26: 517781

g27: 332873

g28: 332423

g29: 164816

g30: 0

gDouble: 2528165

--Rolls--

r1: 3780483

r2: 3781549

r3: 3785523

r4: 3794656

r5: 3796194

r6: 3802847

r7: 3723004

r8: 3744394

r9: 3765229

r10: 3785450

--Victories--

Victories without using card: 1603384

Test card +3 direct victories: 1859016

Test card +3 luck victories: 0

 

 

10000000 games simulated. Results:

Busts: 6512718

9 cards: 4366

g10: 2357631

g11: 1591668

g12: 1652661

g13: 1708989

g14: 1757998

g15: 1800713

g16: 1836761

g17: 1856598

g18: 0

g19: 1671631

g20: 1624613

g21: 1388374

g22: 1226792

g23: 1061883

g24: 891907

g25: 717092

g26: 535651

g27: 352726

g28: 166069

g29: 167858

g30: 0

gDouble: 2358279

--Rolls--

r1: 3793019

r2: 3793517

r3: 3801775

r4: 3806546

r5: 3810567

r6: 3819580

r7: 3820664

r8: 3749217

r9: 3766314

r10: 3783956

--Victories--

Victories without using card: 1624613

Test card +2 direct victories: 1862669

Test card +2 luck victories: 0

 

 

10000000 games simulated. Results:

Busts: 6500071

9 cards: 4385

g10: 2355804

g11: 1592775

g12: 1653761

g13: 1706482

g14: 1759051

g15: 1802045

g16: 1836086

g17: 1858140

g18: 1865046

g19: 0

g20: 1642042

g21: 1405875

g22: 1247986

g23: 1081025

g24: 911371

g25: 735178

g26: 555791

g27: 371812

g28: 186648

g29: 0

g30: 0

gDouble: 2544931

--Rolls--

r1: 3810653

r2: 3813134

r3: 3817661

r4: 3816814

r5: 3828385

r6: 3832022

r7: 3834158

r8: 3842902

r9: 3760691

r10: 3787407

--Victories--

Victories without using card: 1642042

Test card +1 direct victories: 1857887

Test card +1 luck victories: 0

 

 

10000000 games simulated. Results:

Busts: 6048588

9 cards: 274268

g10: 2355855

g11: 1592881

g12: 1652651

g13: 1708731

g14: 1759644

g15: 3391083

g16: 3425294

g17: 3432570

g18: 3427086

g19: 3388953

g20: 1827851

g21: 1312948

g22: 1127226

g23: 940644

g24: 755678

g25: 755712

g26: 0

g27: 444445

g28: 293170

g29: 144497

g30: 0

gDouble: 2850522

--Rolls--

r1: 4941331

r2: 4944904

r3: 4941640

r4: 4943741

r5: 4943445

r6: 4940668

r7: 4611431

r8: 4602831

r9: 4605096

r10: 4602520

--Victories--

Victories without using card: 1827851

Test card -6 direct victories: 1343382

Test card -6 luck victories: 755766

 

 

10000000 games simulated. Results:

Busts: 6007958

9 cards: 187208

g10: 2358108

g11: 1595624

g12: 1652601

g13: 1708108

g14: 1758441

g15: 1800906

g16: 3424208

g17: 3446291

g18: 3443252

g19: 3414451

g20: 1828517

g21: 1352835

g22: 1168709

g23: 984256

g24: 798236

g25: 0

g26: 610642

g27: 456236

g28: 301417

g29: 148419

g30: 0

gDouble: 2853136

--Rolls--

r1: 4796146

r2: 4794222

r3: 4800835

r4: 4798443

r5: 4795422

r6: 4462604

r7: 4460548

r8: 4456123

r9: 4458333

r10: 4619405

--Victories--

Victories without using card: 1828517

Test card -5 direct victories: 1530948

Test card -5 luck victories: 612853

 

 

10000000 games simulated. Results:

Busts: 6132005

9 cards: 121551

g10: 2358626

g11: 1595477

g12: 1653737

g13: 1705493

g14: 1759386

g15: 1802301

g16: 1833766

g17: 3447805

g18: 3455345

g19: 3434137

g20: 1828937

g21: 1383348

g22: 1202995

g23: 1019579

g24: 372465

g25: 646896

g26: 463327

g27: 463638

g28: 306293

g29: 151913

g30: 0

gDouble: 2703071

--Rolls--

r1: 4650821

r2: 4650895

r3: 4652172

r4: 4646044

r5: 4310678

r6: 4305992

r7: 4306478

r8: 4466817

r9: 4468594

r10: 4472252

--Victories--

Victories without using card: 1828937

Test card -4 direct victories: 1559155

Test card -4 luck victories: 464965

 

 

10000000 games simulated. Results:

Busts: 6273314

9 cards: 70916

g10: 2355969

g11: 1594854

g12: 1651727

g13: 1708986

g14: 1758467

g15: 1802267

g16: 1834043

g17: 1857474

g18: 3455463

g19: 3445781

g20: 1827270

g21: 1407238

g22: 1231775

g23: 741335

g24: 866565

g25: 683699

g26: 495814

g27: 310778

g28: 310573

g29: 154621

g30: 0

gDouble: 2703117

--Rolls--

r1: 4497545

r2: 4492862

r3: 4497921

r4: 4158490

r5: 4150466

r6: 4311050

r7: 4313805

r8: 4318330

r9: 4320944

r10: 4323995

--Victories--

Victories without using card: 1827270

Test card -3 direct victories: 1578922

Test card -3 luck victories: 310677

 

 

10000000 games simulated. Results:

Busts: 6422191

9 cards: 33858

g10: 2358602

g11: 1593698

g12: 1654648

g13: 1708687

g14: 1760120

g15: 1799583

g16: 1834156

g17: 1857656

g18: 1865710

g19: 3447721

g20: 1825755

g21: 1425456

g22: 1095700

g23: 1077017

g24: 895757

g25: 712770

g26: 527838

g27: 340623

g28: 156740

g29: 156432

g30: 0

gDouble: 2545675

--Rolls--

r1: 4342581

r2: 4339029

r3: 4002456

r4: 4155213

r5: 4156305

r6: 4160404

r7: 4161796

r8: 4165049

r9: 4170059

r10: 4175932

--Victories--

Victories without using card: 1825755

Test card -2 direct victories: 1591142

Test card -2 luck victories: 155946

 

 

10000000 games simulated. Results:

Busts: 6582745

9 cards: 7673

g10: 2359311

g11: 1592319

g12: 1651898

g13: 1709826

g14: 1760736

g15: 1800941

g16: 1833336

g17: 1857809

g18: 1864104

g19: 1858465

g20: 1826087

g21: 1432705

g22: 1269187

g23: 1096448

g24: 921424

g25: 740502

g26: 557858

g27: 371417

g28: 185531

g29: 0

g30: 0

gDouble: 2548799

--Rolls--

r1: 4185031

r2: 3996734

r3: 4000947

r4: 4003240

r5: 4001998

r6: 4004154

r7: 4010051

r8: 4013512

r9: 4021872

r10: 4028237

--Victories--

Victories without using card: 1826087

Test card -1 direct victories: 1591168

Test card -1 luck victories: 0

 

 

10000000 games simulated. Results:

Busts: 4934432

9 cards: 192605

g10: 2356566

g11: 1591464

g12: 1652423

g13: 1707460

g14: 0

g15: 2935837

g16: 2920443

g17: 2880271

g18: 2817366

g19: 2902005

g20: 1546192

g21: 1097890

g22: 932225

g23: 772814

g24: 609632

g25: 611230

g26: 0

g27: 356789

g28: 237383

g29: 123864

g30: 0

gDouble: 2564104

--Rolls--

r1: 4343835

r2: 4344947

r3: 4357964

r4: 4276831

r5: 4301971

r6: 4317154

r7: 4052141

r8: 4073496

r9: 4085831

r10: 4090344

--Victories--

Victories without using card: 1546192

Test card +/-6 direct victories: 2893080

Test card +/-6 luck victories: 610858

 

 

10000000 games simulated. Results:

Busts: 4971580

9 cards: 131128

g10: 2359278

g11: 1591665

g12: 1653627

g13: 1707894

g14: 1757044

g15: 0

g16: 2982631

g17: 2959382

g18: 2908315

g19: 2833653

g20: 1564809

g21: 1153603

g22: 988906

g23: 822656

g24: 657500

g25: 0

g26: 497500

g27: 366104

g28: 238014

g29: 116169

g30: 0

gDouble: 2757608

--Rolls--

r1: 4242605

r2: 4254316

r3: 4252159

r4: 4260313

r5: 4187149

r6: 3925343

r7: 3936321

r8: 3949945

r9: 3958791

r10: 4271760

--Victories--

Victories without using card: 1564809

Test card +/-5 direct victories: 2954220

Test card +/-5 luck victories: 497123

 

 

10000000 games simulated. Results:

Busts: 4943436

9 cards: 83365

g10: 2360340

g11: 1592612

g12: 1652849

g13: 1708849

g14: 1758938

g15: 1798828

g16: 0

g17: 3019872

g18: 2981540

g19: 2924331

g20: 1585434

g21: 1064308

g22: 883337

g23: 883821

g24: 329154

g25: 549711

g26: 386170

g27: 386352

g28: 252878

g29: 124340

g30: 0

gDouble: 2471865

--Rolls--

r1: 4147254

r2: 4151000

r3: 4156431

r4: 4163629

r5: 3880584

r6: 3795031

r7: 3816419

r8: 4133506

r9: 3969249

r10: 3992034

--Victories--

Victories without using card: 1585434

Test card +/-4 direct victories: 3074411

Test card +/-4 luck victories: 387313

 

 

10000000 games simulated. Results:

Busts: 4959442

9 cards: 48084

g10: 2357782

g11: 1594409

g12: 1653640

g13: 1708357

g14: 1757885

g15: 1800984

g16: 1833924

g17: 0

g18: 3048803

g19: 2994978

g20: 1603198

g21: 1139207

g22: 963675

g23: 516556

g24: 598754

g25: 598429

g26: 430986

g27: 266369

g28: 266387

g29: 130995

g30: 0

gDouble: 2661294

--Rolls--

r1: 4042161

r2: 4046363

r3: 4049587

r4: 3761166

r5: 3761731

r6: 4066985

r7: 3808971

r8: 3832791

r9: 3856138

r10: 3881044

--Victories--

Victories without using card: 1603198

Test card +/-3 direct victories: 3165574

Test card +/-3 luck victories: 265437

 

 

10000000 games simulated. Results:

Busts: 5006299

9 cards: 22770

g10: 2356091

g11: 1593181

g12: 1652562

g13: 1708130

g14: 1759087

g15: 1798747

g16: 1834903

g17: 1858026

g18: 0

g19: 3054988

g20: 1622371

g21: 1199065

g22: 892465

g23: 850986

g24: 673964

g25: 488339

g26: 302453

g27: 303376

g28: 136619

g29: 136262

g30: 0

gDouble: 2360673

--Rolls--

r1: 3929209

r2: 3933291

r3: 3630553

r4: 3938814

r5: 3759423

r6: 3771040

r7: 3776843

r8: 3707323

r9: 3729676

r10: 3758783

--Victories--

Victories without using card: 1622371

Test card +/-2 direct victories: 3231314

Test card +/-2 luck victories: 136824

 

 

10000000 games simulated. Results:

Busts: 5092611

9 cards: 4350

g10: 2357816

g11: 1594868

g12: 1653943

g13: 1707816

g14: 1759160

g15: 1800853

g16: 1833956

g17: 1856109

g18: 1865916

g19: 0

g20: 1643193

g21: 1245526

g22: 1083084

g23: 910488

g24: 734690

g25: 555176

g26: 372815

g27: 186482

g28: 0

g29: 0

g30: 0

gDouble: 2545534

--Rolls--

r1: 3814814

r2: 3815490

r3: 3630655

r4: 3632534

r5: 3639025

r6: 3649851

r7: 3661274

r8: 3668711

r9: 3596569

r10: 3630574

--Victories--

Victories without using card: 1643193

Test card +/-1 direct victories: 3264196

Test card +/-1 luck victories: 0

 

More advanced simulation is still possible, but this is quite a good start.

 

 

Results:

  • +/-x cards have the best chance of victory, with +/-4, 5, and 6 having the highest percentages by small margins.
  • Chance of victory without using a card is highest for the lower +/- cards.
  • Getting an 11, or another value less than 15 but more than 10, on the table is less likely than getting a value larger than 15 but less than or equal to 20. (I'm not certain why this is)
  • Cards by total chance of victory: +/-6, +/-4, +/-3, +/-5, +/-2, +/-1, -5, -6, -4, -3, -2, +1, +2, +3, +4, -1, +5, +6

 

Card Costs:

(from Matthew Brown's Pazaak Guide)

 

Tatooine

Junix Nard, Cantina

 

Qty Card Price

--- ------ -----

2 [+/-1] 200c

2 [+/-2] 150c

2 [+/-3] 125c

2 [+/-4] 100c

 

Korriban

Mika Dorin, Cantina

 

Qty Card Price

--- ------ -----

1 [+/-1] 300c

1 [+/-2] 225c

1 [+/-3] 187c

1 [+/-4] 150c

 

Manaan

Shady Rodian, Ahto East

 

Qty Card Price

--- ------ -----

1 [+/-1] 200c

1 [+/-2] 150c

2 [+/-3] 125c

2 [+1] 100c

1 [-1] 100c

2 [+2] 75c

1 [-2] 75c

3 [+/-6] 50c

3 [+3] 50c

3 [+4] 50c

2 [-3] 25c

2 [-4] 25c

4 [+5] 12c

4 [-5] 12c

5 [+6] 5c

5 [-6] 5c

 

Dantooine

Crattis Yurkal, Aratech Mercantile

 

Qty Card Price

--- ------ -----

1 [+/-1] 200c

1 [+/-3] 125c

1 [-2] 75c

1 [+/-5] 75c

1 [-4] 25c

1 [-6] 5c

 

Dantooine

Sol'aa, Jedi Enclave

 

Qty Card Price

--- ------ -----

1 [+/-2] 150c

2 [+/-4] 100c

2 [+1] 100c

1 [-1] 100c

3 [+/-5] 75c

2 [+2] 75c

1 [-2] 75c

3 [+3] 50c

3 [+4] 25c

2 [-3] 25c

2 [-4] 25c

4 [+5] 12c

4 [-5] 12c

5 [+6] 5c

5 [+6] 5c

 

Taris

Uriah, Lower City Cantina

-need a Pazaak deck in order to buy cards from Uriah

inf = infinite/unlimited quantity

 

Qty Card Price

--- ------ -----

2 [+/-1] 200c

1 [+/-3] 125c

inf [+1] 100c

inf [+2] 75c

inf [-2] 75c

inf [+/-6] 50c

inf [+3] 50c

inf [+4] 25c

inf [-4] 25c

inf [+5] 12c

inf [-5] 12c

inf [+6] 6c

inf [-6] 6c

 

Taris

Igear, Undercity

 

Qty Card Price

--- ------ -----

1 [-2] 56c

1 [+2] 56c

1 [-3] 18c

 

 

The best deck:

  • -6 cards only cost 6c, and you can buy as many as you want from Uriah. With a 39.27% chance of victory they're a pretty good investment.
  • -5 cards only cost 12c, and you can buy as many as you want from Uriah. With a 39.72% chance of victory they're a pretty good investment, just like -6 cards.
  • +/-6 cards cost 50c. These are the best bang-for-you-buck cards, along with +/-5 cards, which cost 75c apiece.
  • Generally speaking, any +/- cards you can pick up for free should be used. -5 or -6 cards should take up the rest of your deck.
  • A good deck will have a variety of cards because having a duplicate card in your hand limits your options in the game. So the best hand would be +/-6, +/-5, +/-4, and +/-3. Because +/-2 and +/-1 are equally valuable and having them decreases your chances for duplicate cards, I'd say the best deck is: two +/-6 cards, two +/-5 cards, two +/-4 cards, two +/-3 cards, one +/-2, and one +/-1.

 

 

Note: Variety is important in a pazaak deck to increase the chances of winning the first few games.

 

Possible improvements to this investigation: This investigation into Pazaak probabilities could be improved by actually simulating full games with a procedure which decides whether or not to stand based on what another simulation is doing. With two different simulations with two different decks you could simulate actual pazaak games and discover deeper probability behaviors. There's also the fact that my simulation assumed that the pazaak deck in KOTOR had no limit to card types (even though several people have suggested there's 4 of each number 1-10). If I was wrong about this certain values found in my simulations may be slightly off.

Edited by Mator
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Hi again!

 

I've made an entirely new program that actually allows you to put two hands against each other and see which will win. It's still in need of a bit of work, but it's capable of better simulations than before. Here's what it looks like:

 

5Rjxy.png

 

The "match" play of 3 games with 1 hand is not yet coded, but soon I'll have written the code to do this as well! :)

 

Here's some sample data:

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Simulating 1000000 side-by-side games

Player 1's hand: +/-6, +/-5, +/-4, +/-3

Player 2's hand: -5, +5, +3, -4

p1wins: 297820

p1busts: 49159

p1full: 9238

p2wins: 58397

p2busts: 275154

p2full: 22666

ties: 643783

 

 

-Mator

Edited by Mator
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Even though I don't understand half of this stuff, I just wanted to say that what you're doing is nothing short of amazing. I'm surprised no one else thought of this earlier.

 

Keep the simulations coming!

 

Thanks LordDeathRay!

 

It's really not all that complicated, I'm just having the computer play pazaak games over and over again and seeing what the chance of winning is.

 

Between yesterday and today I've actually found a few other attempted pazaak simulations, though I don't really agree with their techniques or results. I feel their simulations weren't nearly as in-depth or accurate as mine are.

 

Anywho, I'll keep working on this until there's no more work to be done, next update will probably be around midnight PST! :p

Edited by Mator
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