Main     Study 7Z79 by Richard Pavlicek    

Let’s Make a Deal

Would you trade your wallet for what’s behind Door Number 2? I didn’t think so, but you might be interested in the makeup of a bridge deal. For example, what are the chances of all four hands being balanced? Or a deal having a void suit? Or a seven-card suit? Or various other items of interest — or noninterest for that matter. Check out the following tables for answers.

General CriteriaSuit LengthsFreakness
The number of possible bridge deals is mind-boggling: 53,644,737,765,488,792,839,237,440,000. That’s 29 digits or 53+ octillion. Nobody ever listed or counted each individual deal — such a feat would be impossible even by the most powerful computers — but the number is easily calculated.*

*The formula is 52!/(13!)^4 which means “52 factorial divided by 13 factorial to the fourth power.” The factorial of a number is the product of all integers from 1 through that number. See my article Mapping Bridge Deals for a more detailed explanation of this calculation.

Each table lists a description of various deal types, the number of generic dealprints*, the number of actual deals, the approximate odds against such a deal type, and the percent probability rounded to 12 decimal places. (In the few cases where the odds are in favor of the deal, it is indicated simply as “favored.”)

*The shape of all four hands. There are 37,478,624 specific dealprints; but all my references are to generic dealprints, which reduce the number to 393,197. Each generic dealprint contains 96, 48, 24 or 16 specific dealprints. See my article Dealprints and Matrices for an explanation.

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General Criteria

This table lists deal types based on general characteristics. Some terms may need clarification: “Balanced” includes generic hand patterns 4-3-3-3, 4-4-3-2 and 5-3-3-2; “semibalanced” includes 5-4-2-2 and 6-3-2-2; “quasibalanced” includes 4-4-4-1 and 5-4-3-1. “Symmetrical” means that a like rotation of each specific hand pattern produces the next hand pattern.

Deal TypeDealprintsNumber of Deals — Odds AgainstPercent
No singleton or void46111065866297144810274506240000 — 4 to 120.628055533648
At least 1 singleton or void39273642578871468343982564731200000 (favored)79.371944466352
…in each hand2221531184748234815985942742387200 — 44 to 12.208507831645
All hands balanced914651440732749946606831360000 — 10 to 18.670823880404
…at least semibalanced42310953740328040921416445440000 — 4 to 120.419039749856
…at least quasibalanced128220531630725871382306549360000 — 8 to 538.273335989872
All hand patterns same252285229338401870353594581216 — 187 to 10.531700499029
…and symmetrical5783265059027355742533946896 — 643 to 10.155215707068
Each hand 1 card each rank393197876488338465357824 — 61204166000 to 10.000000001634
…and symmetrical5767108864 — 799368884645235431777 to 10.000000000000
One side entirely 2 suits28649034882160000 — 82653088824683 to 10.000000000001
…specified (e.g. S + C)28108172480360000 — 495918532948103 to 10.000000000000

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Suit Lengths

The following 14 tables show the chances of each specific suit length from a void through 13 cards. Each table caption shows the average number per deal, and the table lists a variety of pertinent holdings. Ostensibly missing entries (e.g., 11 voids) are impossible. The shorthand “1+ voids” means “at least 1 void.”

Voids — 0.204655168601
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No void2454743786641333457372963248979200 (favored)81.623367281379
1 void753908799457894227700441632304128 — 5 to 116.403207958057
1+ voids3686509858096432031419875988460800 — 9 to 218.376632718621
2 voids113242998506861918196340608870400 — 52 to 11.861332357114
2+ voids2932601058638537803719434356156672 — 49 to 11.973424760564
3 voids9734658348592829119872339137792 — 918 to 10.108768530260
3+ voids18001860131675885523093747286272 — 891 to 10.112092403450
4 voids559361760151254006403709124544 — 30476 to 10.003281125656
4+ voids826721783083056403221408148480 — 30084 to 10.003323873190
5 voids2017822741159103390139399936 — 2358926 to 10.000042392153
5+ voids2673622931802396817699023936 — 2339315 to 10.000042747534
6 voids5483189905533721240847744 — 282481171 to 10.000000354006
6+ voids6558190643293427559624000 — 281388013 to 10.000000355381
7 voids792733838125172226048 — 73101595467 to 10.000000001368
7+ voids1075737759706318776256 — 72713022011 to 10.000000001375
8 voids2583920126156514360 — 13684441679597 to 10.000000000007
8+ voids2833921581146550208 — 13679364460601 to 10.000000000007
9 voids121454241192768 — 36888473543636524 to 10.000000000000
9+ voids251454990035848 — 36869488067815849 to 10.000000000000
10 voids12748843056 — 71636823411351487298 to 10.000000000000
10+ voids13748843080 — 71636821115431543866 to 10.000000000000
12 voids124 — 2235197406895366368301559999 to 10.000000000000
Shortest suit 03686509858096432031419875988460800 — 9 to 218.376632718621

Singletons — 1.280989759022
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No singleton2391913436267408464750462079611896 — 3 to 125.046757553746
1 singleton7408719692753394437851528571129216 — 5 to 336.709571552994
1+ singletons36927840208470357024042377157828104 (favored)74.953242446254
2 singletons11517113982420636500124063619552240 — 3 to 126.064850382204
2+ singletons29519120515716962586190848586698888 — 8 to 538.243670893261
3 singletons962445234722137247397227258877376 — 9 to 19.758127926976
3+ singletons1800206533296326086066784967146648 — 7 to 112.178820511057
4 singletons553001148260368984438039385190616 — 45 to 12.140490226654
4+ singletons837761298574188838669557708269272 — 40 to 12.420692584081
5 singletons20868138766430185365695589766656 — 385 to 10.258676686597
5+ singletons28476150313819854231518323078656 — 355 to 10.280202357427
6 singletons627111122755677912332785217536 — 4821 to 10.020734103924
6+ singletons760811547389668865822733312000 — 4644 to 10.021525670830
7 singletons1036408790415278227335528448 — 131226 to 10.000762032647
7+ singletons1337424633990953489948094464 — 126330 to 10.000791566906
8 singletons26815665802824130246567936 — 3424320 to 10.000029202870
8+ singletons30115843575675262612566016 — 3385897 to 10.000029534259
9 singletons22174134142810284507136 — 308065590 to 10.000000324606
9+ singletons33177772851132365998080 — 301760011 to 10.000000331389
10 singletons103638500218106490880 — 14743640111 to 10.000000006783
10+ singletons113638708322081490944 — 14742796897 to 10.000000006783
12 singletons1208103975000064 — 257778534818818 to 10.000000000000
Shortest suit 12408632720775036312562688742739200 (favored)60.995311747731

Doubletons — 3.293973666058
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No doubleton30734804259249659202740664528512 — 65 to 11.499232325778
1 doubleton811954243260184157275735384000512 — 11 to 17.909928095290
1+ doubletons36246352840478515829590098572911488 (favored)98.500767674222
2 doubletons11333910928139270707171912961848832 — 4 to 120.371316415937
2+ doubletons28126848597218331672314363188910976 (favored)90.590839578931
3 doubletons8970914440004290394498870749274112 — 8 to 326.917839273481
3+ doubletons16792937669079060965142450227062144 (favored)70.219523162995
4 doubletons5066213058442226453447625951590272 — 3 to 124.342447685250
4+ doubletons7822023229074770570643579477788032 — 4 to 343.301683889514
5 doubletons196626697224638661855788498511360 — 7 to 112.484401858649
5+ doubletons2755810170632544117195953526197760 — 4 to 118.959236204264
6 doubletons63482855610546731060215809254400 — 17 to 15.323188565511
6+ doubletons78963473407905455340165027686400 — 14 to 16.474834345616
7 doubletons1263520926012825773891491584000 — 101 to 10.971066379526
7+ doubletons1548617797358724279949218432000 — 85 to 11.151645780104
8 doubletons24488573369500118130779008000 — 604 to 10.165111012169
8+ doubletons28596871345898506057726848000 — 552 to 10.180579400578
9 doubletons326829571339090287856640000 — 7853 to 10.012731111426
9+ doubletons418297976398387926947840000 — 6463 to 10.015468388409
10 doubletons81454751357497884892160000 — 36874 to 10.002711824902
10+ doubletons91468405059297639091200000 — 36531 to 10.002737276983
12 doubletons113653701799754199040000 — 3928950 to 10.000025452080
Shortest suit 246011015900532747294908106240000 — 4 to 120.534913565808

Tripletons — 4.581273719460
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No tripleton42267298481305036862547953966208 — 178 to 10.556403698610
1 tripleton940201641241485067199149856037888 — 31 to 13.059464084328
1+ tripletons35093053346256460451930291283473792 (favored)99.443596301390
2 tripletons1129605355205218885833912073927168 — 9 to 19.982722335780
2+ tripletons25691051705014975384731141427435904 (favored)96.384132217062
3 tripletons792738872474055429629157573119488 — 5 to 116.539318533378
3+ tripletons14395046349809756498897229353508736 (favored)86.401409881282
4 tripletons4182411257865437176662107015225728 — 4 to 120.985964152516
4+ tripletons6467737477335701069268071780389248 (favored)69.862091347904
5 tripletons160929975568326621327582382264320 — 4 to 118.595613926253
5+ tripletons2285326219470263892605964765163520 — 1 to 148.876127195388
6 tripletons52057474355676760133808619315200 — 6 to 113.933064058277
6+ tripletons676116243901937271278382382899200 — 7 to 330.280513269135
7 tripletons12485087619301709484239192064000 — 9 to 19.483911215952
7+ tripletons15568769546260511144573763584000 — 5 to 116.347449210858
8 tripletons2582208867758155132312043520000 — 23 to 14.117585154039
8+ tripletons3083681926958801660334571520000 — 13 to 16.863537994905
9 tripletons401078084931631556552704000000 — 48 to 12.009675089371
9+ tripletons501473059200646528022528000000 — 35 to 12.745952840866
10 tripletons9345008504617456103424000000 — 154 to 10.643135783654
10+ tripletons10394974269014971469824000000 — 134 to 10.736277751495
12 tripletons149965764397515366400000000 — 1072 to 10.093141967840
Shortest suit 3149965764397515366400000000 — 1072 to 10.093141967840

4-Card Suits — 3.817728099550
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No 4-card suit58548827527196765622468298731000 — 63 to 11.542606472201
1 4-card suit1122133264522488820600040694232000 — 15 to 16.085447752754
1+ 4-card suits33464952817210568723170370938709000 (favored)98.457393527799
2 4-card suits1105898107219615979748529508958000 — 11 to 215.112795688220
2+ 4-card suits22243649552688079902570330244477000 (favored)92.371945775045
3 4-card suits6571611328128521386758622862464000 — 4 to 121.116942673685
3+ 4-card suits11184741445468463922821800735519000 (favored)77.259150086825
4 4-card suits3108812122462049388925454412335000 — 7 to 222.597672305498
4+ 4-card suits4613130117339942536063177873055000 (favored)56.142207413141
5 4-card suits105849405039628729954030309488000 — 9 to 217.532082400784
5+ 4-card suits1504317994877893147137723460720000 — 2 to 133.544535107642
6 4-card suits34025219103350668664679414192000 — 9 to 19.729012701086
6+ 4-card suits44598589838264417183693151232000 — 5 to 116.012452706859
7 4-card suits8392635160299611246929602080000 — 19 to 14.912243790120
7+ 4-card suits10573370734913748519013737040000 — 14 to 16.283440005773
8 4-card suits181585877783479958092483360000 — 90 to 11.092143997499
8+ 4-card suits218735574614137272084134960000 — 71 to 11.371196215653
9 4-card suits29124079826585336167145600000 — 431 to 10.231299157669
9+ 4-card suits37149696830657313991651600000 — 357 to 10.279052218154
10 4-card suits724628911563140240356000000 — 2177 to 10.045911141687
10+ 4-card suits825617004071977824506000000 — 2093 to 10.047753060485
12 4-card suits1988092508837584150000000 — 54290 to 10.001841918798
Longest suit 4291571494042604960223750000000 — 33 to 12.929446779058
Longest 4 shortest 19226907515517134602150000000 — 235 to 10.422981871044
Longest 4 shortest 2191294620762690310255200000000 — 40 to 12.413322940173
Longest 4 shortest 3149965764397515366400000000 — 1072 to 10.093141967840

5-Card Suits — 1.995070813313
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No 5-card suit870064597881752913411186598943736 — 10 to 18.570983743109
1 5-card suit12114314162753528304985663093951488 — 3 to 126.401011764133
1+ 5-card suits30619149046856012575381652638496264 (favored)91.429016256891
2 5-card suits10450818067215541367691851979855600 — 2 to 133.679380856235
2+ 5-card suits18504834884102484270395989544544776 (favored)65.028004492758
3 5-card suits5479811640282689397513831787179072 — 7 to 221.698834171366
3+ 5-card suits8054016816886942902704137564689176 — 9 to 431.348623636523
4 5-card suits200554206420083748200765168830680 — 11 to 17.841253884280
4+ 5-card suits257425176604253505190305777510104 — 9 to 19.649789465157
5 5-card suits4722847666043311209636417007104 — 62 to 11.580147613018
5+ 5-card suits5687970184169756989540608679424 — 54 to 11.808535580877
6 5-card suits878115132376736925239588728832 — 464 to 10.214620075580
6+ 5-card suits965122518126445779904191672320 — 436 to 10.228387967859
7 5-card suits756872885114033959677296640 — 7804 to 10.012811853316
7+ 5-card suits877385749708854664602943488 — 7262 to 10.013767892279
8 5-card suits12512864594820704925646848 — 104597 to 10.000956038963
Longest suit 5329721583251210971361009130800768 — 3 to 240.233678287932
Longest 5 shortest 015881609503787729626328278490752 — 32 to 13.000301343192
Longest 5 shortest 1149112670231342665127083546710016 — 3 to 123.618777666607
Longest 5 shortest 22187303516080576607597305600000 — 6 to 113.614599278133

6-Card Suits — 0.665023604438
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No 6-card suit11385326905653785695390696041730560 (favored)50.155252698438
1 6-card suit14462119066726906544846134962690048 — 7 to 435.542585723685
1+ 6-card suits27934426739083979793402143195709440 — 1 to 149.844747301562
2 6-card suits933536485428597816725021394136064 — 7 to 112.089589525385
2+ 6-card suits1347237672357073248556008233019392 — 6 to 114.302161577877
3 6-card suits326841111477008094705239177535488 — 47 to 12.071921784675
3+ 6-card suits413701186928475431830986838883328 — 44 to 12.212572052492
4 6-card suits742374270503985138725291822080 — 721 to 10.138448815445
4+ 6-card suits868675451467337125747661347840 — 709 to 10.140650267817
5 6-card suits10921166137252500210225371136 — 46001 to 10.002173814807
5+ 6-card suits12631180963351987022369525760 — 45423 to 10.002201452372
6 6-card suits15414747938755361745117184 — 3637438 to 10.000027491865
6+ 6-card suits17114826099486812144154624 — 3618262 to 10.000027637565
7 6-card suits1273663812654622654464 — 728237322 to 10.000000137318
7+ 6-card suits1778160731450399037440 — 686338736 to 10.000000145701
8 6-card suits54496918795776382976 — 11929220917 to 10.000000008383
Longest suit 63287322642122348654241172787919872 — 4 to 342.207536641591
Longest 6 shortest 0256115023219452210248132366595072 — 9 to 19.363862442892
Longest 6 shortest 1707715313265176067504842881484800 — 5 to 228.545698634991
Longest 6 shortest 21852305637720376488197539840000 — 22 to 14.297975563709

7-Card Suits — 0.141065613063
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No 7-card suit14861246668614955529607643028925952 (favored)86.995699670570
1 7-card suit1666306414841838510523780739153920 — 7 to 111.958007636375
1+ 7-card suits2445856976122809959185196208514048 — 13 to 213.004300329430
2 7-card suits67357531829247712684682606230528 — 99 to 10.991391271289
2+ 7-card suits77955561280971448661415469360128 — 94 to 11.046292693055
3 7-card suits1013628879408411913023879090176 — 1856 to 10.053834559763
3+ 7-card suits1059829451723735976732863129600 — 1820 to 10.054901421766
4 7-card suits462572315324063708984039424 — 93731 to 10.001066862003
Longest suit 7848376782984599117957218132857856 — 13 to 212.644268350738
Longest 7 shortest 0765322601365526899294160773154816 — 19 to 14.849246422401
Longest 7 shortest 182674069493103114774199298903040 — 12 to 17.586006144545
Longest 7 shortest 238112125969103888858060800000 — 477 to 10.209015783792

8-Card Suits — 0.018670448788
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No 8-card suit21802052659418358646318763250088120 (favored)98.163250585454
1 8-card suit135330969336127795929767968558464 — 54 to 11.806954732510
1+ 8-card suits175177985319406842474075987351880 — 53 to 11.836749414546
2 8-card suits3533215717541316474557292763888 — 3412 to 10.029299316151
2+ 8-card suits3984715983279046544308018793416 — 3355 to 10.029794682037
3 8-card suits4277262832169584598962242752 — 204101 to 10.000489949584
3+ 8-card suits4515265737730069750726029528 — 201869 to 10.000495365885
4 8-card suits2382905560485151763786776 — 18462783 to 10.000005416301
Longest suit 8101924981975954511555218232092504 — 53 to 11.830516832433
Longest 8 shortest 096759559206840312485595147564504 — 94 to 11.042426272558
Longest 8 shortest 15165422769114199069623084528000 — 125 to 10.788090559874

9-Card Suits — 0.001481781650
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No 9-card suit28224053565418928084244786753267000 (favored)99.852140506770
1 9-card suit9375679148608957994535139752000 — 676 to 10.147542167703
1+ 9-card suits11095779318837404548052484173000 — 675 to 10.147859493230
2 9-card suits15568169510962571319297214000 — 316466 to 10.000315988053
2+ 9-card suits17201170228446553517344421000 — 315132 to 10.000317325526
3 9-card suits1521712788941101915392000 — 75260338 to 10.000001328721
3+ 9-card suits1633717483982198047207000 — 74767853 to 10.000001337473
4 9-card suits1124695041096131815000 — 11425829223 to 10.000000008752
Longest suit 98484479298562143148725113050600 — 675 to 10.147821697796
Longest 9 shortest 08302561390081488049420251922920 — 872 to 10.114438217140
Longest 9 shortest 1181917908480655099304861127680 — 2994 to 10.033383480656

10-Card Suits — 0.000065856962
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No 10-card suit33359353641205490163369327919048832 (favored)99.993415429970
1 10-card suit536773531671663756659651717632 — 15188 to 10.006583444734
1+ 10-card suits596043532275325423511318391168 — 15186 to 10.006584570030
2 10-card suits5447603182972886040115712 — 88936093 to 10.000001124403
2+ 10-card suits5927603661666851666673536 — 88865568 to 10.000001125295
3 10-card suits433476472744726730752 — 112587211668 to 10.000000000888
3+ 10-card suits480478693965626557824 — 112064787979 to 10.000000000892
4 10-card suits472221220899827072 — 24151014322647 to 10.000000000004
Longest suit 10528733532238785856985879197952 — 15186 to 10.006584501916
Longest 10 shortest 0526153331934692003952959212288 — 16099 to 10.006211111902
Longest 10 shortest 1258200304093853032919985664 — 267815 to 10.000373390014

11-Card Suits — 0.000001456296
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No 11-card suit36780753644659643413038984236251264 (favored)99.999854371409
1 11-card suit2390178121509765066018800640 — 686682 to 10.000145627536
1+ 11-card suits2539078122075753855001188736 — 686677 to 10.000145628591
2 11-card suits1385565933048294288896 — 94789901255 to 10.000000001055
2+ 11-card suits1489565988788982388096 — 94780565992 to 10.000000001055
3 11-card suits8755476844780032 — 966975284520818 to 10.000000000000
3+ 11-card suits10455740688099200 — 962398197704679 to 10.000000000000
4 11-card suits17263843319168 — 203320432500058718 to 10.000000000000
Longest suit 112431978122061820624147552512 — 686677 to 10.000145628565
Longest 11 shortest 02431978122061820624147552512 — 686677 to 10.000145628565

12-Card Suits — 0.000000012775
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No 12-card suit38586153644737080202550239380997624 (favored)99.999998722547
1 12-card suit7113685286153633192746752 — 78280783 to 10.000001277453
1+ 12-card suits7336685286242599856442376 — 78280773 to 10.000001277453
2 12-card suits20988966097766000 — 602979551902859 to 10.000000000000
2+ 12-card suits22388966663695624 — 602975716264015 to 10.000000000000
3 12-card suits9559760448 — 95835170128863397005 to 10.000000000000
3+ 12-card suits14565929624 — 94790474805554255344 to 10.000000000000
4 12-card suits56169176 — 8695608257162511304464 to 10.000000000000
Longest suit 127269685286242093646948664 — 78280773 to 10.000001277453
Longest 12 shortest 07269685286242093646948664 — 78280773 to 10.000001277453

13-Card Suits — 0.000000000025
Deal ContainsDealprintsNumber of Deals — Odds AgainstPercent
No 13-card suit39226553644737764137143270820420728 (favored)99.999999997480
1 13-card suit9191351649567668176192 — 39688347517 to 10.000000002520
1+ 13-card suits9321351649568417019272 — 39688347495 to 10.000000002520
2 13-card suits12748843056 — 71636823411351487298 to 10.000000000000
2+ 13-card suits13748843080 — 71636821115431543866 to 10.000000000000
4 13-card suits124 — 2235197406895366368301559999 to 10.000000000000
Longest suit 139321351649568417019272 — 39688347495 to 10.000000002520
Longest 13 shortest 09321351649568417019272 — 39688347495 to 10.000000002520

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Freakness

The flattest deal (each hand 4-3-3-3) has a freakness of zero, and the wildest deal (each hand 13-0-0-0) has a freakness of 80. All others fall in between, with the great majority on the low end. The average deal freakness is 11.931421228644. See Patterns and Freakness for an explanation. The following table shows a breakdown of deals by freakness (missing freakness numbers are impossible).

FreaknessDealprintsNumber of Deals — Odds AgainstPercent
0149965764397515366400000000 — 1072 to 10.093141967840
13224845939788819148800000000 — 237 to 10.419138855281
24337268909683228723200000000 — 158 to 10.628708282922
3171277249852411486553600000000 — 41 to 12.380941552916
4191059656755610994244704000000 — 49 to 11.975322836404
5542182129845650489839104000000 — 23 to 14.067742590503
6612100679403961990102451200000 — 24 to 13.915909540178
71443900852209396223412531200000 — 12 to 17.271640000272
81692935429792437846953208960000 — 17 to 15.471980877734
92773902968973315092438517760000 — 12 to 17.275585893209
104494319233756510792955996160000 — 11 to 18.051551627287
115924177391033763705615137280000 — 11 to 17.787140375307
128533990368759941243838222064000 — 12 to 17.438509211072
1312063836417947826698802760192000 — 12 to 17.151527079129
1416013648437681407219980639360000 — 13 to 16.801110105816
1522263264937827762008134953216000 — 15 to 16.086221992612
1627492663243649725330822345395200 — 19 to 14.964594405080
1735432289468162846201949464652800 — 22 to 14.267833637019
1846081932541204471813293546988800 — 26 to 13.602480476128
1953911480279600703791494954547200 — 35 to 12.759412502257
2066851174583424431230888775500800 — 44 to 12.189559448619
217689856279205971843936824622080 — 61 to 11.596203545099
229282651189608460944685643230720 — 81 to 11.213892798410
2310881468514461078731756738649600 — 113 to 10.873365180993
2411530309869707607739903405614976 — 172 to 10.577632999088
2513463224014273521217767999290880 — 238 to 10.417588533102
2614828146819296583833277172307968 — 364 to 10.273688161597
271594393044009812336198278474240 — 575 to 10.173444803140
281724660185626811626055142978432 — 890 to 10.112192974220
291706435602130280545690996040192 — 1505 to 10.066366491409
301882822690215766463274527427072 — 2363 to 10.042297188339
311893012814634946132905421279744 — 4185 to 10.023887962697
32188117271032073391375174407808 — 7376 to 10.013554045329
33189604027998015429852085509888 — 13316 to 10.007508654498
34178242134460884602256692932736 — 25131 to 10.003978882130
35182641204090604570608544934144 — 44551 to 10.002244564248
3616955588171565475675378600832 — 91204 to 10.001096419873
3715676281495292714510093483264 — 190569 to 10.000524739806
3814636136548415355635932352704 — 392861 to 10.000254542050
391279666675424468034146976640 — 804564 to 10.000124290708
401224431568800006311999095808 — 1699295 to 10.000058847897
411029612551152845439469866176 — 4274087 to 10.000023396802
4287945539188505944246918336 — 9684583 to 10.000010325688
4374942281818876604493219136 — 23509637 to 10.000004253574
4466081080773542988045704512 — 49635501 to 10.000002014687
455400364042919909640464064 — 147358276 to 10.000000678618
464335149341040837809172352 — 359209613 to 10.000000278389
47366456213864818077979584 — 954297269 to 10.000000104789
48292722667027728510788480 — 2366641907 to 10.000000042254
4924057918128597821105664 — 6774926309 to 10.000000014760
5019212786029111818995328 — 19254909266 to 10.000000005193
5115451050155184192903360 — 51082676705 to 10.000000001958
521176381937032300814848 — 140454402763 to 10.000000000712
53914123106992036215616 — 435757034414 to 10.000000000229
5483248759791163887232 — 1100183911476 to 10.000000000091
5550012332598988387392 — 4349832327799 to 10.000000000023
564956378802488829056 — 8409844615729 to 10.000000000012
572881201770056710080 — 44638104823765 to 10.000000000002
58350776728909674432 — 69064942861433 to 10.000000000001
59126101120237302656 — 530504468704205 to 10.000000000000
6020787806733670656 — 610941046579621 to 10.000000000000
61567741853982720 — 6929184906512716 to 10.000000000000
621429610252313376 — 5582032189812906 to 10.000000000000
6321384475703040 — 139526990499859266 to 10.000000000000
6487927265749696 — 57852603509917176 to 10.000000000000
65613029299712 — 4117238758126189063 to 10.000000000000
664877879337120 — 688818623132738764 to 10.000000000000
671361924992 — 148220595292542806325 to 10.000000000000
68305262221952 — 10194313021156427427 to 10.000000000000
7012288527616 — 185925834445908958811 to 10.000000000000
721014638104 — 3664732657008639427566 to 10.000000000000
742421824 — 127173270761001727827807 to 10.000000000000
76224336 — 2204336693190696615682010 to 10.000000000000
80124 — 2235197406895366368301559999 to 10.000000000000
Totals39319753644737765488792839237440000100.000000000000

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Photo is Monty Hall of the old TV show Let’s Make a Deal.
© 2004 Richard Pavlicek