Study 7Z79 Main

Let’s Make a Deal

by Richard Pavlicek

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 Criteria Suit Lengths Freakness

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 four 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.

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 Type Dealprints Number of Deals — Odds Against Percent
No singleton or void 461 11065866297144810274506240000 — 4:1 20.6281
At least 1 singleton or void 392736 42578871468343982564731200000 (favored) 79.3719
…in each hand 222153 1184748234815985942742387200 — 44:1 2.2085
All hands balanced 91 4651440732749946606831360000 — 10:1 8.6708
…at least semibalanced 423 10953740328040921416445440000 — 4:1 20.4190
…at least quasibalanced 1282 20531630725871382306549360000 — 8:5 38.2733
All hand patterns same 252 285229338401870353594581216 — 187:1 0.5317
…and symmetrical 57 83265059027355742533946896 — 643:1 0.1552
Each hand 1 card each rank 393197 876488338465357824 — 61204166000:1 0.0000
…and symmetrical 57 67108864 — 799368884645235431777:1 0.0000
One side entirely 2 suits 28 649034882160000 — 82653088824683:1 0.0000
…and specified 28 108172480360000 — 495918532948103:1 0.0000

Deal Type	Dealprints	Number of Deals — Odds Against	Percent
No singleton or void	461	11065866297144810274506240000 — 4:1	20.6281
At least 1 singleton or void	392736	42578871468343982564731200000 (favored)	79.3719
…in each hand	222153	1184748234815985942742387200 — 44:1	2.2085
All hands balanced	91	4651440732749946606831360000 — 10:1	8.6708
…at least semibalanced	423	10953740328040921416445440000 — 4:1	20.4190
…at least quasibalanced	1282	20531630725871382306549360000 — 8:5	38.2733
All hand patterns same	252	285229338401870353594581216 — 187:1	0.5317
…and symmetrical	57	83265059027355742533946896 — 643:1	0.1552
Each hand 1 card each rank	393197	876488338465357824 — 61204166000:1	0.0000
…and symmetrical	57	67108864 — 799368884645235431777:1	0.0000
One side entirely 2 suits	28	649034882160000 — 82653088824683:1	0.0000
…and specified	28	108172480360000 — 495918532948103:1	0.0000

Study 7Z79 Main Top Let’s Make a Deal

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. The shorthand “1+ voids” means at least 1 void. Ostensibly missing entries (e.g., 11 voids) are impossible.

Voids — 0.2047
Deal Contains Dealprints Number of Deals — Odds Against Percent
No void 24547 43786641333457372963248979200 (favored) 81.6234
1 void 75390 8799457894227700441632304128 — 5:1 16.4032
1+ voids 368650 9858096432031419875988460800 — 9:2 18.3766
2 voids 113242 998506861918196340608870400 — 52:1 1.8613
2+ voids 293260 1058638537803719434356156672 — 49:1 1.9734
3 voids 97346 58348592829119872339137792 — 918:1 0.1088
3+ voids 180018 60131675885523093747286272 — 891:1 0.1121
4 voids 55936 1760151254006403709124544 — 30476:1 0.0033
4+ voids 82672 1783083056403221408148480 — 30084:1 0.0033
5 voids 20178 22741159103390139399936 — 2358926:1 0.0000
5+ voids 26736 22931802396817699023936 — 2339315:1 0.0000
6 voids 5483 189905533721240847744 — 282481171:1 0.0000
6+ voids 6558 190643293427559624000 — 281388013:1 0.0000
7 voids 792 733838125172226048 — 73101595467:1 0.0000
7+ voids 1075 737759706318776256 — 72713022011:1 0.0000
8 voids 258 3920126156514360 — 13684441679597:1 0.0000
8+ voids 283 3921581146550208 — 13679364460601:1 0.0000
9 voids 12 1454241192768 — 36888473543636524:1 0.0000
9+ voids 25 1454990035848 — 36869488067815849:1 0.0000
10 voids 12 748843056 — 71636823411351487298:1 0.0000
10+ voids 13 748843080 — 71636821115431543866:1 0.0000
12 voids 1 24 — 2235197406895366368301559999:1 0.0000
Shortest suit 0 368650 9858096432031419875988460800 — 9:2 18.3766

Voids — 0.2047
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No void	24547	43786641333457372963248979200 (favored)	81.6234
1 void	75390	8799457894227700441632304128 — 5:1	16.4032
1+ voids	368650	9858096432031419875988460800 — 9:2	18.3766
2 voids	113242	998506861918196340608870400 — 52:1	1.8613
2+ voids	293260	1058638537803719434356156672 — 49:1	1.9734
3 voids	97346	58348592829119872339137792 — 918:1	0.1088
3+ voids	180018	60131675885523093747286272 — 891:1	0.1121
4 voids	55936	1760151254006403709124544 — 30476:1	0.0033
4+ voids	82672	1783083056403221408148480 — 30084:1	0.0033
5 voids	20178	22741159103390139399936 — 2358926:1	0.0000
5+ voids	26736	22931802396817699023936 — 2339315:1	0.0000
6 voids	5483	189905533721240847744 — 282481171:1	0.0000
6+ voids	6558	190643293427559624000 — 281388013:1	0.0000
7 voids	792	733838125172226048 — 73101595467:1	0.0000
7+ voids	1075	737759706318776256 — 72713022011:1	0.0000
8 voids	258	3920126156514360 — 13684441679597:1	0.0000
8+ voids	283	3921581146550208 — 13679364460601:1	0.0000
9 voids	12	1454241192768 — 36888473543636524:1	0.0000
9+ voids	25	1454990035848 — 36869488067815849:1	0.0000
10 voids	12	748843056 — 71636823411351487298:1	0.0000
10+ voids	13	748843080 — 71636821115431543866:1	0.0000
12 voids	1	24 — 2235197406895366368301559999:1	0.0000
Shortest suit 0	368650	9858096432031419875988460800 — 9:2	18.3766

Singletons — 1.2810
Deal Contains Dealprints Number of Deals — Odds Against Percent
No singleton 23919 13436267408464750462079611896 — 3:1 25.0468
1 singleton 74087 19692753394437851528571129216 — 5:3 36.7096
1+ singletons 369278 40208470357024042377157828104 (favored) 74.9532
2 singletons 115171 13982420636500124063619552240 — 3:1 26.0649
2+ singletons 295191 20515716962586190848586698888 — 8:5 38.2437
3 singletons 96244 5234722137247397227258877376 — 9:1 9.7581
3+ singletons 180020 6533296326086066784967146648 — 7:1 12.1788
4 singletons 55300 1148260368984438039385190616 — 45:1 2.1405
4+ singletons 83776 1298574188838669557708269272 — 40:1 2.4207
5 singletons 20868 138766430185365695589766656 — 385:1 0.2587
5+ singletons 28476 150313819854231518323078656 — 355:1 0.2802
6 singletons 6271 11122755677912332785217536 — 4821:1 0.0207
6+ singletons 7608 11547389668865822733312000 — 4644:1 0.0215
7 singletons 1036 408790415278227335528448 — 131226:1 0.0008
7+ singletons 1337 424633990953489948094464 — 126330:1 0.0008
8 singletons 268 15665802824130246567936 — 3424320:1 0.0000
8+ singletons 301 15843575675262612566016 — 3385897:1 0.0000
9 singletons 22 174134142810284507136 — 308065590:1 0.0000
9+ singletons 33 177772851132365998080 — 301760011:1 0.0000
10 singletons 10 3638500218106490880 — 14743640111:1 0.0000
10+ singletons 11 3638708322081490944 — 14742796897:1 0.0000
12 singletons 1 208103975000064 — 257778534818818:1 0.0000
Shortest suit 1 24086 32720775036312562688742739200 (favored) 60.9953

Singletons — 1.2810
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No singleton	23919	13436267408464750462079611896 — 3:1	25.0468
1 singleton	74087	19692753394437851528571129216 — 5:3	36.7096
1+ singletons	369278	40208470357024042377157828104 (favored)	74.9532
2 singletons	115171	13982420636500124063619552240 — 3:1	26.0649
2+ singletons	295191	20515716962586190848586698888 — 8:5	38.2437
3 singletons	96244	5234722137247397227258877376 — 9:1	9.7581
3+ singletons	180020	6533296326086066784967146648 — 7:1	12.1788
4 singletons	55300	1148260368984438039385190616 — 45:1	2.1405
4+ singletons	83776	1298574188838669557708269272 — 40:1	2.4207
5 singletons	20868	138766430185365695589766656 — 385:1	0.2587
5+ singletons	28476	150313819854231518323078656 — 355:1	0.2802
6 singletons	6271	11122755677912332785217536 — 4821:1	0.0207
6+ singletons	7608	11547389668865822733312000 — 4644:1	0.0215
7 singletons	1036	408790415278227335528448 — 131226:1	0.0008
7+ singletons	1337	424633990953489948094464 — 126330:1	0.0008
8 singletons	268	15665802824130246567936 — 3424320:1	0.0000
8+ singletons	301	15843575675262612566016 — 3385897:1	0.0000
9 singletons	22	174134142810284507136 — 308065590:1	0.0000
9+ singletons	33	177772851132365998080 — 301760011:1	0.0000
10 singletons	10	3638500218106490880 — 14743640111:1	0.0000
10+ singletons	11	3638708322081490944 — 14742796897:1	0.0000
12 singletons	1	208103975000064 — 257778534818818:1	0.0000
Shortest suit 1	24086	32720775036312562688742739200 (favored)	60.9953

Doubletons — 3.2940
Deal Contains Dealprints Number of Deals — Odds Against Percent
No doubleton 30734 804259249659202740664528512 — 65:1 1.4992
1 doubleton 81195 4243260184157275735384000512 — 11:1 7.9099
1+ doubletons 362463 52840478515829590098572911488 (favored) 98.5008
2 doubletons 113339 10928139270707171912961848832 — 4:1 20.3713
2+ doubletons 281268 48597218331672314363188910976 (favored) 90.5908
3 doubletons 89709 14440004290394498870749274112 — 8:3 26.9178
3+ doubletons 167929 37669079060965142450227062144 (favored) 70.2195
4 doubletons 50662 13058442226453447625951590272 — 3:1 24.3424
4+ doubletons 78220 23229074770570643579477788032 — 4:3 43.3017
5 doubletons 19662 6697224638661855788498511360 — 7:1 12.4844
5+ doubletons 27558 10170632544117195953526197760 — 4:1 18.9592
6 doubletons 6348 2855610546731060215809254400 — 17:1 5.3232
6+ doubletons 7896 3473407905455340165027686400 — 14:1 6.4748
7 doubletons 1263 520926012825773891491584000 — 101:1 0.9711
7+ doubletons 1548 617797358724279949218432000 — 85:1 1.1516
8 doubletons 244 88573369500118130779008000 — 604:1 0.1651
8+ doubletons 285 96871345898506057726848000 — 552:1 0.1806
9 doubletons 32 6829571339090287856640000 — 7853:1 0.0127
9+ doubletons 41 8297976398387926947840000 — 6463:1 0.0155
10 doubletons 8 1454751357497884892160000 — 36874:1 0.0027
10+ doubletons 9 1468405059297639091200000 — 36531:1 0.0027
12 doubletons 1 13653701799754199040000 — 3928950:1 0.0000
Shortest suit 2 460 11015900532747294908106240000 — 4:1 20.5349

Doubletons — 3.2940
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No doubleton	30734	804259249659202740664528512 — 65:1	1.4992
1 doubleton	81195	4243260184157275735384000512 — 11:1	7.9099
1+ doubletons	362463	52840478515829590098572911488 (favored)	98.5008
2 doubletons	113339	10928139270707171912961848832 — 4:1	20.3713
2+ doubletons	281268	48597218331672314363188910976 (favored)	90.5908
3 doubletons	89709	14440004290394498870749274112 — 8:3	26.9178
3+ doubletons	167929	37669079060965142450227062144 (favored)	70.2195
4 doubletons	50662	13058442226453447625951590272 — 3:1	24.3424
4+ doubletons	78220	23229074770570643579477788032 — 4:3	43.3017
5 doubletons	19662	6697224638661855788498511360 — 7:1	12.4844
5+ doubletons	27558	10170632544117195953526197760 — 4:1	18.9592
6 doubletons	6348	2855610546731060215809254400 — 17:1	5.3232
6+ doubletons	7896	3473407905455340165027686400 — 14:1	6.4748
7 doubletons	1263	520926012825773891491584000 — 101:1	0.9711
7+ doubletons	1548	617797358724279949218432000 — 85:1	1.1516
8 doubletons	244	88573369500118130779008000 — 604:1	0.1651
8+ doubletons	285	96871345898506057726848000 — 552:1	0.1806
9 doubletons	32	6829571339090287856640000 — 7853:1	0.0127
9+ doubletons	41	8297976398387926947840000 — 6463:1	0.0155
10 doubletons	8	1454751357497884892160000 — 36874:1	0.0027
10+ doubletons	9	1468405059297639091200000 — 36531:1	0.0027
12 doubletons	1	13653701799754199040000 — 3928950:1	0.0000
Shortest suit 2	460	11015900532747294908106240000 — 4:1	20.5349

Tripletons — 4.5813
Deal Contains Dealprints Number of Deals — Odds Against Percent
No tripleton 42267 298481305036862547953966208 — 178:1 0.5564
1 tripleton 94020 1641241485067199149856037888 — 31:1 3.0595
1+ tripletons 350930 53346256460451930291283473792 (favored) 99.4436
2 tripletons 112960 5355205218885833912073927168 — 9:1 9.9827
2+ tripletons 256910 51705014975384731141427435904 (favored) 96.3841
3 tripletons 79273 8872474055429629157573119488 — 5:1 16.5393
3+ tripletons 143950 46349809756498897229353508736 (favored) 86.4014
4 tripletons 41824 11257865437176662107015225728 — 4:1 20.9860
4+ tripletons 64677 37477335701069268071780389248 (favored) 69.8621
5 tripletons 16092 9975568326621327582382264320 — 4:1 18.5956
5+ tripletons 22853 26219470263892605964765163520 — 1:1 48.8761
6 tripletons 5205 7474355676760133808619315200 — 6:1 13.9331
6+ tripletons 6761 16243901937271278382382899200 — 7:3 30.2805
7 tripletons 1248 5087619301709484239192064000 — 9:1 9.4839
7+ tripletons 1556 8769546260511144573763584000 — 5:1 16.3474
8 tripletons 258 2208867758155132312043520000 — 23:1 4.1176
8+ tripletons 308 3681926958801660334571520000 — 13:1 6.8635
9 tripletons 40 1078084931631556552704000000 — 48:1 2.0097
9+ tripletons 50 1473059200646528022528000000 — 35:1 2.7460
10 tripletons 9 345008504617456103424000000 — 154:1 0.6431
10+ tripletons 10 394974269014971469824000000 — 134:1 0.7363
12 tripletons 1 49965764397515366400000000 — 1072:1 0.0931
Shortest suit 3 1 49965764397515366400000000 — 1072:1 0.0931

Tripletons — 4.5813
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No tripleton	42267	298481305036862547953966208 — 178:1	0.5564
1 tripleton	94020	1641241485067199149856037888 — 31:1	3.0595
1+ tripletons	350930	53346256460451930291283473792 (favored)	99.4436
2 tripletons	112960	5355205218885833912073927168 — 9:1	9.9827
2+ tripletons	256910	51705014975384731141427435904 (favored)	96.3841
3 tripletons	79273	8872474055429629157573119488 — 5:1	16.5393
3+ tripletons	143950	46349809756498897229353508736 (favored)	86.4014
4 tripletons	41824	11257865437176662107015225728 — 4:1	20.9860
4+ tripletons	64677	37477335701069268071780389248 (favored)	69.8621
5 tripletons	16092	9975568326621327582382264320 — 4:1	18.5956
5+ tripletons	22853	26219470263892605964765163520 — 1:1	48.8761
6 tripletons	5205	7474355676760133808619315200 — 6:1	13.9331
6+ tripletons	6761	16243901937271278382382899200 — 7:3	30.2805
7 tripletons	1248	5087619301709484239192064000 — 9:1	9.4839
7+ tripletons	1556	8769546260511144573763584000 — 5:1	16.3474
8 tripletons	258	2208867758155132312043520000 — 23:1	4.1176
8+ tripletons	308	3681926958801660334571520000 — 13:1	6.8635
9 tripletons	40	1078084931631556552704000000 — 48:1	2.0097
9+ tripletons	50	1473059200646528022528000000 — 35:1	2.7460
10 tripletons	9	345008504617456103424000000 — 154:1	0.6431
10+ tripletons	10	394974269014971469824000000 — 134:1	0.7363
12 tripletons	1	49965764397515366400000000 — 1072:1	0.0931
Shortest suit 3	1	49965764397515366400000000 — 1072:1	0.0931

4-Card Suits — 3.8177
Deal Contains Dealprints Number of Deals — Odds Against Percent
No 4-card suit 58548 827527196765622468298731000 — 63:1 1.5426
1 4-card suit 112213 3264522488820600040694232000 — 15:1 6.0854
1+ 4-card suits 334649 52817210568723170370938709000 (favored) 98.4574
2 4-card suits 110589 8107219615979748529508958000 — 11:2 15.1128
2+ 4-card suits 222436 49552688079902570330244477000 (favored) 92.3719
3 4-card suits 65716 11328128521386758622862464000 — 4:1 21.1169
3+ 4-card suits 111847 41445468463922821800735519000 (favored) 77.2592
4 4-card suits 31088 12122462049388925454412335000 — 7:2 22.5977
4+ 4-card suits 46131 30117339942536063177873055000 (favored) 56.1422
5 4-card suits 10584 9405039628729954030309488000 — 9:2 17.5321
5+ 4-card suits 15043 17994877893147137723460720000 — 2:1 33.5445
6 4-card suits 3402 5219103350668664679414192000 — 9:1 9.7290
6+ 4-card suits 4459 8589838264417183693151232000 — 5:1 16.0125
7 4-card suits 839 2635160299611246929602080000 — 19:1 4.9122
7+ 4-card suits 1057 3370734913748519013737040000 — 14:1 6.2834
8 4-card suits 181 585877783479958092483360000 — 90:1 1.0921
8+ 4-card suits 218 735574614137272084134960000 — 71:1 1.3712
9 4-card suits 29 124079826585336167145600000 — 431:1 0.2313
9+ 4-card suits 37 149696830657313991651600000 — 357:1 0.2791
10 4-card suits 7 24628911563140240356000000 — 2177:1 0.0459
10+ 4-card suits 8 25617004071977824506000000 — 2093:1 0.0478
12 4-card suits 1 988092508837584150000000 — 54290:1 0.0018
Longest suit 4 29 1571494042604960223750000000 — 33:1 2.9294
Longest 4 shortest 1 9 226907515517134602150000000 — 235:1 0.4230
Longest 4 shortest 2 19 1294620762690310255200000000 — 40:1 2.4133
Longest 4 shortest 3 1 49965764397515366400000000 — 1072:1 0.0931

4-Card Suits — 3.8177
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No 4-card suit	58548	827527196765622468298731000 — 63:1	1.5426
1 4-card suit	112213	3264522488820600040694232000 — 15:1	6.0854
1+ 4-card suits	334649	52817210568723170370938709000 (favored)	98.4574
2 4-card suits	110589	8107219615979748529508958000 — 11:2	15.1128
2+ 4-card suits	222436	49552688079902570330244477000 (favored)	92.3719
3 4-card suits	65716	11328128521386758622862464000 — 4:1	21.1169
3+ 4-card suits	111847	41445468463922821800735519000 (favored)	77.2592
4 4-card suits	31088	12122462049388925454412335000 — 7:2	22.5977
4+ 4-card suits	46131	30117339942536063177873055000 (favored)	56.1422
5 4-card suits	10584	9405039628729954030309488000 — 9:2	17.5321
5+ 4-card suits	15043	17994877893147137723460720000 — 2:1	33.5445
6 4-card suits	3402	5219103350668664679414192000 — 9:1	9.7290
6+ 4-card suits	4459	8589838264417183693151232000 — 5:1	16.0125
7 4-card suits	839	2635160299611246929602080000 — 19:1	4.9122
7+ 4-card suits	1057	3370734913748519013737040000 — 14:1	6.2834
8 4-card suits	181	585877783479958092483360000 — 90:1	1.0921
8+ 4-card suits	218	735574614137272084134960000 — 71:1	1.3712
9 4-card suits	29	124079826585336167145600000 — 431:1	0.2313
9+ 4-card suits	37	149696830657313991651600000 — 357:1	0.2791
10 4-card suits	7	24628911563140240356000000 — 2177:1	0.0459
10+ 4-card suits	8	25617004071977824506000000 — 2093:1	0.0478
12 4-card suits	1	988092508837584150000000 — 54290:1	0.0018
Longest suit 4	29	1571494042604960223750000000 — 33:1	2.9294
Longest 4 shortest 1	9	226907515517134602150000000 — 235:1	0.4230
Longest 4 shortest 2	19	1294620762690310255200000000 — 40:1	2.4133
Longest 4 shortest 3	1	49965764397515366400000000 — 1072:1	0.0931

5-Card Suits — 1.9951
Deal Contains Dealprints Number of Deals — Odds Against Percent
No 5-card suit 87006 4597881752913411186598943736 — 10:1 8.5710
1 5-card suit 121143 14162753528304985663093951488 — 3:1 26.4010
1+ 5-card suits 306191 49046856012575381652638496264 (favored) 91.4290
2 5-card suits 104508 18067215541367691851979855600 — 2:1 33.6794
2+ 5-card suits 185048 34884102484270395989544544776 (favored) 65.0280
3 5-card suits 54798 11640282689397513831787179072 — 7:2 21.6988
3+ 5-card suits 80540 16816886942902704137564689176 — 9:4 31.3486
4 5-card suits 20055 4206420083748200765168830680 — 11:1 7.8413
4+ 5-card suits 25742 5176604253505190305777510104 — 9:1 9.6498
5 5-card suits 4722 847666043311209636417007104 — 62:1 1.5801
5+ 5-card suits 5687 970184169756989540608679424 — 54:1 1.8085
6 5-card suits 878 115132376736925239588728832 — 464:1 0.2146
6+ 5-card suits 965 122518126445779904191672320 — 436:1 0.2284
7 5-card suits 75 6872885114033959677296640 — 7804:1 0.0128
7+ 5-card suits 87 7385749708854664602943488 — 7262:1 0.0138
8 5-card suits 12 512864594820704925646848 — 104597:1 0.0010
Longest suit 5 3297 21583251210971361009130800768 — 3:2 40.2337
Longest 5 shortest 0 1588 1609503787729626328278490752 — 32:1 3.0003
Longest 5 shortest 1 1491 12670231342665127083546710016 — 3:1 23.6188
Longest 5 shortest 2 218 7303516080576607597305600000 — 6:1 13.6146

5-Card Suits — 1.9951
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No 5-card suit	87006	4597881752913411186598943736 — 10:1	8.5710
1 5-card suit	121143	14162753528304985663093951488 — 3:1	26.4010
1+ 5-card suits	306191	49046856012575381652638496264 (favored)	91.4290
2 5-card suits	104508	18067215541367691851979855600 — 2:1	33.6794
2+ 5-card suits	185048	34884102484270395989544544776 (favored)	65.0280
3 5-card suits	54798	11640282689397513831787179072 — 7:2	21.6988
3+ 5-card suits	80540	16816886942902704137564689176 — 9:4	31.3486
4 5-card suits	20055	4206420083748200765168830680 — 11:1	7.8413
4+ 5-card suits	25742	5176604253505190305777510104 — 9:1	9.6498
5 5-card suits	4722	847666043311209636417007104 — 62:1	1.5801
5+ 5-card suits	5687	970184169756989540608679424 — 54:1	1.8085
6 5-card suits	878	115132376736925239588728832 — 464:1	0.2146
6+ 5-card suits	965	122518126445779904191672320 — 436:1	0.2284
7 5-card suits	75	6872885114033959677296640 — 7804:1	0.0128
7+ 5-card suits	87	7385749708854664602943488 — 7262:1	0.0138
8 5-card suits	12	512864594820704925646848 — 104597:1	0.0010
Longest suit 5	3297	21583251210971361009130800768 — 3:2	40.2337
Longest 5 shortest 0	1588	1609503787729626328278490752 — 32:1	3.0003
Longest 5 shortest 1	1491	12670231342665127083546710016 — 3:1	23.6188
Longest 5 shortest 2	218	7303516080576607597305600000 — 6:1	13.6146

6-Card Suits — 0.6650
Deal Contains Dealprints Number of Deals — Odds Against Percent
No 6-card suit 113853 26905653785695390696041730560 (favored) 50.1553
1 6-card suit 144621 19066726906544846134962690048 — 7:4 35.5426
1+ 6-card suits 279344 26739083979793402143195709440 — 1:1 49.8447
2 6-card suits 93353 6485428597816725021394136064 — 7:1 12.0896
2+ 6-card suits 134723 7672357073248556008233019392 — 6:1 14.3022
3 6-card suits 32684 1111477008094705239177535488 — 47:1 2.0719
3+ 6-card suits 41370 1186928475431830986838883328 — 44:1 2.2126
4 6-card suits 7423 74270503985138725291822080 — 721:1 0.1384
4+ 6-card suits 8686 75451467337125747661347840 — 709:1 0.1407
5 6-card suits 1092 1166137252500210225371136 — 46001:1 0.0022
5+ 6-card suits 1263 1180963351987022369525760 — 45423:1 0.0022
6 6-card suits 154 14747938755361745117184 — 3637438:1 0.0000
6+ 6-card suits 171 14826099486812144154624 — 3618262:1 0.0000
7 6-card suits 12 73663812654622654464 — 728237322:1 0.0000
7+ 6-card suits 17 78160731450399037440 — 686338736:1 0.0000
8 6-card suits 5 4496918795776382976 — 11929220917:1 0.0000
Longest suit 6 32873 22642122348654241172787919872 — 4:3 42.2075
Longest 6 shortest 0 25611 5023219452210248132366595072 — 9:1 9.3639
Longest 6 shortest 1 7077 15313265176067504842881484800 — 5:2 28.5457
Longest 6 shortest 2 185 2305637720376488197539840000 — 22:1 4.2980

6-Card Suits — 0.6650
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No 6-card suit	113853	26905653785695390696041730560 (favored)	50.1553
1 6-card suit	144621	19066726906544846134962690048 — 7:4	35.5426
1+ 6-card suits	279344	26739083979793402143195709440 — 1:1	49.8447
2 6-card suits	93353	6485428597816725021394136064 — 7:1	12.0896
2+ 6-card suits	134723	7672357073248556008233019392 — 6:1	14.3022
3 6-card suits	32684	1111477008094705239177535488 — 47:1	2.0719
3+ 6-card suits	41370	1186928475431830986838883328 — 44:1	2.2126
4 6-card suits	7423	74270503985138725291822080 — 721:1	0.1384
4+ 6-card suits	8686	75451467337125747661347840 — 709:1	0.1407
5 6-card suits	1092	1166137252500210225371136 — 46001:1	0.0022
5+ 6-card suits	1263	1180963351987022369525760 — 45423:1	0.0022
6 6-card suits	154	14747938755361745117184 — 3637438:1	0.0000
6+ 6-card suits	171	14826099486812144154624 — 3618262:1	0.0000
7 6-card suits	12	73663812654622654464 — 728237322:1	0.0000
7+ 6-card suits	17	78160731450399037440 — 686338736:1	0.0000
8 6-card suits	5	4496918795776382976 — 11929220917:1	0.0000
Longest suit 6	32873	22642122348654241172787919872 — 4:3	42.2075
Longest 6 shortest 0	25611	5023219452210248132366595072 — 9:1	9.3639
Longest 6 shortest 1	7077	15313265176067504842881484800 — 5:2	28.5457
Longest 6 shortest 2	185	2305637720376488197539840000 — 22:1	4.2980

Study 7Z79 Main Top Let’s Make a Deal

7-Card Suits — 0.1411
Deal Contains Dealprints Number of Deals — Odds Against Percent
No 7-card suit 148612 46668614955529607643028925952 (favored) 86.9957
1 7-card suit 166630 6414841838510523780739153920 — 7:1 11.9580
1+ 7-card suits 244585 6976122809959185196208514048 — 13:2 13.0043
2 7-card suits 67357 531829247712684682606230528 — 99:1 0.9914
2+ 7-card suits 77955 561280971448661415469360128 — 94:1 1.0463
3 7-card suits 10136 28879408411913023879090176 — 1856:1 0.0538
3+ 7-card suits 10598 29451723735976732863129600 — 1820:1 0.0549
4 7-card suits 462 572315324063708984039424 — 93731:1 0.0011
Longest suit 7 84837 6782984599117957218132857856 — 13:2 12.6443
Longest 7 shortest 0 76532 2601365526899294160773154816 — 19:1 4.8492
Longest 7 shortest 1 8267 4069493103114774199298903040 — 12:1 7.5860
Longest 7 shortest 2 38 112125969103888858060800000 — 477:1 0.2090

7-Card Suits — 0.1411
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No 7-card suit	148612	46668614955529607643028925952 (favored)	86.9957
1 7-card suit	166630	6414841838510523780739153920 — 7:1	11.9580
1+ 7-card suits	244585	6976122809959185196208514048 — 13:2	13.0043
2 7-card suits	67357	531829247712684682606230528 — 99:1	0.9914
2+ 7-card suits	77955	561280971448661415469360128 — 94:1	1.0463
3 7-card suits	10136	28879408411913023879090176 — 1856:1	0.0538
3+ 7-card suits	10598	29451723735976732863129600 — 1820:1	0.0549
4 7-card suits	462	572315324063708984039424 — 93731:1	0.0011
Longest suit 7	84837	6782984599117957218132857856 — 13:2	12.6443
Longest 7 shortest 0	76532	2601365526899294160773154816 — 19:1	4.8492
Longest 7 shortest 1	8267	4069493103114774199298903040 — 12:1	7.5860
Longest 7 shortest 2	38	112125969103888858060800000 — 477:1	0.2090

8-Card Suits — 0.0187
Deal Contains Dealprints Number of Deals — Odds Against Percent
No 8-card suit 218020 52659418358646318763250088120 (favored) 98.1633
1 8-card suit 135330 969336127795929767968558464 — 54:1 1.8070
1+ 8-card suits 175177 985319406842474075987351880 — 53:1 1.8367
2 8-card suits 35332 15717541316474557292763888 — 3412:1 0.0293
2+ 8-card suits 39847 15983279046544308018793416 — 3355:1 0.0298
3 8-card suits 4277 262832169584598962242752 — 204101:1 0.0005
3+ 8-card suits 4515 265737730069750726029528 — 201869:1 0.0005
4 8-card suits 238 2905560485151763786776 — 18462783:1 0.0000
Longest suit 8 101924 981975954511555218232092504 — 53:1 1.8305
Longest 8 shortest 0 96759 559206840312485595147564504 — 94:1 1.0424
Longest 8 shortest 1 5165 422769114199069623084528000 — 125:1 0.7881

8-Card Suits — 0.0187
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No 8-card suit	218020	52659418358646318763250088120 (favored)	98.1633
1 8-card suit	135330	969336127795929767968558464 — 54:1	1.8070
1+ 8-card suits	175177	985319406842474075987351880 — 53:1	1.8367
2 8-card suits	35332	15717541316474557292763888 — 3412:1	0.0293
2+ 8-card suits	39847	15983279046544308018793416 — 3355:1	0.0298
3 8-card suits	4277	262832169584598962242752 — 204101:1	0.0005
3+ 8-card suits	4515	265737730069750726029528 — 201869:1	0.0005
4 8-card suits	238	2905560485151763786776 — 18462783:1	0.0000
Longest suit 8	101924	981975954511555218232092504 — 53:1	1.8305
Longest 8 shortest 0	96759	559206840312485595147564504 — 94:1	1.0424
Longest 8 shortest 1	5165	422769114199069623084528000 — 125:1	0.7881

9-Card Suits — 0.0015
Deal Contains Dealprints Number of Deals — Odds Against Percent
No 9-card suit 282240 53565418928084244786753267000 (favored) 99.8521
1 9-card suit 93756 79148608957994535139752000 — 676:1 0.1475
1+ 9-card suits 110957 79318837404548052484173000 — 675:1 0.1479
2 9-card suits 15568 169510962571319297214000 — 316466:1 0.0003
2+ 9-card suits 17201 170228446553517344421000 — 315132:1 0.0003
3 9-card suits 1521 712788941101915392000 — 75260338:1 0.0000
3+ 9-card suits 1633 717483982198047207000 — 74767853:1 0.0000
4 9-card suits 112 4695041096131815000 — 11425829223:1 0.0000
Longest suit 9 84844 79298562143148725113050600 — 675:1 0.1478
Longest 9 shortest 0 83025 61390081488049420251922920 — 872:1 0.1144
Longest 9 shortest 1 1819 17908480655099304861127680 — 2994:1 0.0334

9-Card Suits — 0.0015
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No 9-card suit	282240	53565418928084244786753267000 (favored)	99.8521
1 9-card suit	93756	79148608957994535139752000 — 676:1	0.1475
1+ 9-card suits	110957	79318837404548052484173000 — 675:1	0.1479
2 9-card suits	15568	169510962571319297214000 — 316466:1	0.0003
2+ 9-card suits	17201	170228446553517344421000 — 315132:1	0.0003
3 9-card suits	1521	712788941101915392000 — 75260338:1	0.0000
3+ 9-card suits	1633	717483982198047207000 — 74767853:1	0.0000
4 9-card suits	112	4695041096131815000 — 11425829223:1	0.0000
Longest suit 9	84844	79298562143148725113050600 — 675:1	0.1478
Longest 9 shortest 0	83025	61390081488049420251922920 — 872:1	0.1144
Longest 9 shortest 1	1819	17908480655099304861127680 — 2994:1	0.0334

10-Card Suits — 0.0001
Deal Contains Dealprints Number of Deals — Odds Against Percent
No 10-card suit 333593 53641205490163369327919048832 (favored) 99.9934
1 10-card suit 53677 3531671663756659651717632 — 15188:1 0.0066
1+ 10-card suits 59604 3532275325423511318391168 — 15186:1 0.0066
2 10-card suits 5447 603182972886040115712 — 88936093:1 0.0000
2+ 10-card suits 5927 603661666851666673536 — 88865568:1 0.0000
3 10-card suits 433 476472744726730752 — 112587211668:1 0.0000
3+ 10-card suits 480 478693965626557824 — 112064787979:1 0.0000
4 10-card suits 47 2221220899827072 — 24151014322647:1 0.0000
Longest suit 10 52873 3532238785856985879197952 — 15186:1 0.0066
Longest 10 shortest 0 52615 3331934692003952959212288 — 16099:1 0.0062
Longest 10 shortest 1 258 200304093853032919985664 — 267815:1 0.0004

10-Card Suits — 0.0001
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No 10-card suit	333593	53641205490163369327919048832 (favored)	99.9934
1 10-card suit	53677	3531671663756659651717632 — 15188:1	0.0066
1+ 10-card suits	59604	3532275325423511318391168 — 15186:1	0.0066
2 10-card suits	5447	603182972886040115712 — 88936093:1	0.0000
2+ 10-card suits	5927	603661666851666673536 — 88865568:1	0.0000
3 10-card suits	433	476472744726730752 — 112587211668:1	0.0000
3+ 10-card suits	480	478693965626557824 — 112064787979:1	0.0000
4 10-card suits	47	2221220899827072 — 24151014322647:1	0.0000
Longest suit 10	52873	3532238785856985879197952 — 15186:1	0.0066
Longest 10 shortest 0	52615	3331934692003952959212288 — 16099:1	0.0062
Longest 10 shortest 1	258	200304093853032919985664 — 267815:1	0.0004

11-Card Suits — 0.0000
Deal Contains Dealprints Number of Deals — Odds Against Percent
No 11-card suit 367807 53644659643413038984236251264 (favored) 99.9999
1 11-card suit 23901 78121509765066018800640 — 686682:1 0.0001
1+ 11-card suits 25390 78122075753855001188736 — 686677:1 0.0001
2 11-card suits 1385 565933048294288896 — 94789901255:1 0.0000
2+ 11-card suits 1489 565988788982388096 — 94780565992:1 0.0000
3 11-card suits 87 55476844780032 — 966975284520818:1 0.0000
3+ 11-card suits 104 55740688099200 — 962398197704679:1 0.0000
4 11-card suits 17 263843319168 — 203320432500058718:1 0.0000
Longest suit 11 24319 78122061820624147552512 — 686677:1 0.0001
Longest 11 shortest 0 24319 78122061820624147552512 — 686677:1 0.0001

11-Card Suits — 0.0000
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No 11-card suit	367807	53644659643413038984236251264 (favored)	99.9999
1 11-card suit	23901	78121509765066018800640 — 686682:1	0.0001
1+ 11-card suits	25390	78122075753855001188736 — 686677:1	0.0001
2 11-card suits	1385	565933048294288896 — 94789901255:1	0.0000
2+ 11-card suits	1489	565988788982388096 — 94780565992:1	0.0000
3 11-card suits	87	55476844780032 — 966975284520818:1	0.0000
3+ 11-card suits	104	55740688099200 — 962398197704679:1	0.0000
4 11-card suits	17	263843319168 — 203320432500058718:1	0.0000
Longest suit 11	24319	78122061820624147552512 — 686677:1	0.0001
Longest 11 shortest 0	24319	78122061820624147552512 — 686677:1	0.0001

12-Card Suits — 0.0000
Deal Contains Dealprints Number of Deals — Odds Against Percent
No 12-card suit 385861 53644737080202550239380997624 (favored) 100.0000
1 12-card suit 7113 685286153633192746752 — 78280783:1 0.0000
1+ 12-card suits 7336 685286242599856442376 — 78280773:1 0.0000
2 12-card suits 209 88966097766000 — 602979551902859:1 0.0000
2+ 12-card suits 223 88966663695624 — 602975716264015:1 0.0000
3 12-card suits 9 559760448 — 95835170128863397005:1 0.0000
3+ 12-card suits 14 565929624 — 94790474805554255344:1 0.0000
4 12-card suits 5 6169176 — 8695608257162511304464:1 0.0000
Longest suit 12 7269 685286242093646948664 — 78280773:1 0.0000
Longest 12 shortest 0 7269 685286242093646948664 — 78280773:1 0.0000

12-Card Suits — 0.0000
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No 12-card suit	385861	53644737080202550239380997624 (favored)	100.0000
1 12-card suit	7113	685286153633192746752 — 78280783:1	0.0000
1+ 12-card suits	7336	685286242599856442376 — 78280773:1	0.0000
2 12-card suits	209	88966097766000 — 602979551902859:1	0.0000
2+ 12-card suits	223	88966663695624 — 602975716264015:1	0.0000
3 12-card suits	9	559760448 — 95835170128863397005:1	0.0000
3+ 12-card suits	14	565929624 — 94790474805554255344:1	0.0000
4 12-card suits	5	6169176 — 8695608257162511304464:1	0.0000
Longest suit 12	7269	685286242093646948664 — 78280773:1	0.0000
Longest 12 shortest 0	7269	685286242093646948664 — 78280773:1	0.0000

13-Card Suits — 0.0000
Deal Contains Dealprints Number of Deals — Odds Against Percent
No 13-card suit 392265 53644737764137143270820420728 (favored) 100.0000
1 13-card suit 919 1351649567668176192 — 39688347517:1 0.0000
1+ 13-card suits 932 1351649568417019272 — 39688347495:1 0.0000
2 13-card suits 12 748843056 — 71636823411351487298:1 0.0000
2+ 13-card suits 13 748843080 — 71636821115431543866:1 0.0000
4 13-card suits 1 24 — 2235197406895366368301559999:1 0.0000
Longest suit 13 932 1351649568417019272 — 39688347495:1 0.0000
Longest 13 shortest 0 932 1351649568417019272 — 39688347495:1 0.0000

13-Card Suits — 0.0000
Deal Contains	Dealprints	Number of Deals — Odds Against	Percent
No 13-card suit	392265	53644737764137143270820420728 (favored)	100.0000
1 13-card suit	919	1351649567668176192 — 39688347517:1	0.0000
1+ 13-card suits	932	1351649568417019272 — 39688347495:1	0.0000
2 13-card suits	12	748843056 — 71636823411351487298:1	0.0000
2+ 13-card suits	13	748843080 — 71636821115431543866:1	0.0000
4 13-card suits	1	24 — 2235197406895366368301559999:1	0.0000
Longest suit 13	932	1351649568417019272 — 39688347495:1	0.0000
Longest 13 shortest 0	932	1351649568417019272 — 39688347495:1	0.0000

Study 7Z79 Main Top Let’s Make a Deal

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 11.9314. See Patterns and Freakness for an explanation. The following table shows a breakdown of deals by freakness (missing freakness numbers are impossible).

Freakness Dealprints Number of Deals — Odds Against Percent
0 1 49965764397515366400000000 — 1072:1 0.0931
1 3 224845939788819148800000000 — 237:1 0.4191
2 4 337268909683228723200000000 — 158:1 0.6287
3 17 1277249852411486553600000000 — 41:1 2.3809
4 19 1059656755610994244704000000 — 49:1 1.9753
5 54 2182129845650489839104000000 — 23:1 4.0677
6 61 2100679403961990102451200000 — 24:1 3.9159
7 144 3900852209396223412531200000 — 12:1 7.2716
8 169 2935429792437846953208960000 — 17:1 5.4720
9 277 3902968973315092438517760000 — 12:1 7.2756
10 449 4319233756510792955996160000 — 11:1 8.0516
11 592 4177391033763705615137280000 — 11:1 7.7871
12 853 3990368759941243838222064000 — 12:1 7.4385
13 1206 3836417947826698802760192000 — 12:1 7.1515
14 1601 3648437681407219980639360000 — 13:1 6.8011
15 2226 3264937827762008134953216000 — 15:1 6.0862
16 2749 2663243649725330822345395200 — 19:1 4.9646
17 3543 2289468162846201949464652800 — 22:1 4.2678
18 4608 1932541204471813293546988800 — 26:1 3.6025
19 5391 1480279600703791494954547200 — 35:1 2.7594
20 6685 1174583424431230888775500800 — 44:1 2.1896
21 7689 856279205971843936824622080 — 61:1 1.5962
22 9282 651189608460944685643230720 — 81:1 1.2139
23 10881 468514461078731756738649600 — 113:1 0.8734
24 11530 309869707607739903405614976 — 172:1 0.5776
25 13463 224014273521217767999290880 — 238:1 0.4176
26 14828 146819296583833277172307968 — 364:1 0.2737
27 15943 93044009812336198278474240 — 575:1 0.1734
28 17246 60185626811626055142978432 — 890:1 0.1122
29 17064 35602130280545690996040192 — 1505:1 0.0664
30 18828 22690215766463274527427072 — 2363:1 0.0423
31 18930 12814634946132905421279744 — 4185:1 0.0239
32 18811 7271032073391375174407808 — 7376:1 0.0136
33 18960 4027998015429852085509888 — 13316:1 0.0075
34 17824 2134460884602256692932736 — 25131:1 0.0040
35 18264 1204090604570608544934144 — 44551:1 0.0022
36 16955 588171565475675378600832 — 91204:1 0.0011
37 15676 281495292714510093483264 — 190569:1 0.0005
38 14636 136548415355635932352704 — 392861:1 0.0003
39 12796 66675424468034146976640 — 804564:1 0.0001
40 12244 31568800006311999095808 — 1699295:1 0.0001
41 10296 12551152845439469866176 — 4274087:1 0.0000
42 8794 5539188505944246918336 — 9684583:1 0.0000
43 7494 2281818876604493219136 — 23509637:1 0.0000
44 6608 1080773542988045704512 — 49635501:1 0.0000
45 5400 364042919909640464064 — 147358276:1 0.0000
46 4335 149341040837809172352 — 359209613:1 0.0000
47 3664 56213864818077979584 — 954297269:1 0.0000
48 2927 22667027728510788480 — 2366641907:1 0.0000
49 2405 7918128597821105664 — 6774926309:1 0.0000
50 1921 2786029111818995328 — 19254909266:1 0.0000
51 1545 1050155184192903360 — 51082676705:1 0.0000
52 1176 381937032300814848 — 140454402763:1 0.0000
53 914 123106992036215616 — 435757034414:1 0.0000
54 832 48759791163887232 — 1100183911476:1 0.0000
55 500 12332598988387392 — 4349832327799:1 0.0000
56 495 6378802488829056 — 8409844615729:1 0.0000
57 288 1201770056710080 — 44638104823765:1 0.0000
58 350 776728909674432 — 69064942861433:1 0.0000
59 126 101120237302656 — 530504468704205:1 0.0000
60 207 87806733670656 — 610941046579621:1 0.0000
61 56 7741853982720 — 6929184906512716:1 0.0000
62 142 9610252313376 — 5582032189812906:1 0.0000
63 21 384475703040 — 139526990499859266:1 0.0000
64 87 927265749696 — 57852603509917176:1 0.0000
65 6 13029299712 — 4117238758126189063:1 0.0000
66 48 77879337120 — 688818623132738764:1 0.0000
67 1 361924992 — 148220595292542806325:1 0.0000
68 30 5262221952 — 10194313021156427427:1 0.0000
70 12 288527616 — 185925834445908958811:1 0.0000
72 10 14638104 — 3664732657008639427566:1 0.0000
74 2 421824 — 127173270761001727827807:1 0.0000
76 2 24336 — 2204336693190696615682010:1 0.0000
80 1 24 — 2235197406895366368301559999:1 0.0000
Totals 393197 53644737765488792839237440000 100.0000

Freakness	Dealprints	Number of Deals — Odds Against	Percent
0	1	49965764397515366400000000 — 1072:1	0.0931
1	3	224845939788819148800000000 — 237:1	0.4191
2	4	337268909683228723200000000 — 158:1	0.6287
3	17	1277249852411486553600000000 — 41:1	2.3809
4	19	1059656755610994244704000000 — 49:1	1.9753
5	54	2182129845650489839104000000 — 23:1	4.0677
6	61	2100679403961990102451200000 — 24:1	3.9159
7	144	3900852209396223412531200000 — 12:1	7.2716
8	169	2935429792437846953208960000 — 17:1	5.4720
9	277	3902968973315092438517760000 — 12:1	7.2756
10	449	4319233756510792955996160000 — 11:1	8.0516
11	592	4177391033763705615137280000 — 11:1	7.7871
12	853	3990368759941243838222064000 — 12:1	7.4385
13	1206	3836417947826698802760192000 — 12:1	7.1515
14	1601	3648437681407219980639360000 — 13:1	6.8011
15	2226	3264937827762008134953216000 — 15:1	6.0862
16	2749	2663243649725330822345395200 — 19:1	4.9646
17	3543	2289468162846201949464652800 — 22:1	4.2678
18	4608	1932541204471813293546988800 — 26:1	3.6025
19	5391	1480279600703791494954547200 — 35:1	2.7594
20	6685	1174583424431230888775500800 — 44:1	2.1896
21	7689	856279205971843936824622080 — 61:1	1.5962
22	9282	651189608460944685643230720 — 81:1	1.2139
23	10881	468514461078731756738649600 — 113:1	0.8734
24	11530	309869707607739903405614976 — 172:1	0.5776
25	13463	224014273521217767999290880 — 238:1	0.4176
26	14828	146819296583833277172307968 — 364:1	0.2737
27	15943	93044009812336198278474240 — 575:1	0.1734
28	17246	60185626811626055142978432 — 890:1	0.1122
29	17064	35602130280545690996040192 — 1505:1	0.0664
30	18828	22690215766463274527427072 — 2363:1	0.0423
31	18930	12814634946132905421279744 — 4185:1	0.0239
32	18811	7271032073391375174407808 — 7376:1	0.0136
33	18960	4027998015429852085509888 — 13316:1	0.0075
34	17824	2134460884602256692932736 — 25131:1	0.0040
35	18264	1204090604570608544934144 — 44551:1	0.0022
36	16955	588171565475675378600832 — 91204:1	0.0011
37	15676	281495292714510093483264 — 190569:1	0.0005
38	14636	136548415355635932352704 — 392861:1	0.0003
39	12796	66675424468034146976640 — 804564:1	0.0001
40	12244	31568800006311999095808 — 1699295:1	0.0001
41	10296	12551152845439469866176 — 4274087:1	0.0000
42	8794	5539188505944246918336 — 9684583:1	0.0000
43	7494	2281818876604493219136 — 23509637:1	0.0000
44	6608	1080773542988045704512 — 49635501:1	0.0000
45	5400	364042919909640464064 — 147358276:1	0.0000
46	4335	149341040837809172352 — 359209613:1	0.0000
47	3664	56213864818077979584 — 954297269:1	0.0000
48	2927	22667027728510788480 — 2366641907:1	0.0000
49	2405	7918128597821105664 — 6774926309:1	0.0000
50	1921	2786029111818995328 — 19254909266:1	0.0000
51	1545	1050155184192903360 — 51082676705:1	0.0000
52	1176	381937032300814848 — 140454402763:1	0.0000
53	914	123106992036215616 — 435757034414:1	0.0000
54	832	48759791163887232 — 1100183911476:1	0.0000
55	500	12332598988387392 — 4349832327799:1	0.0000
56	495	6378802488829056 — 8409844615729:1	0.0000
57	288	1201770056710080 — 44638104823765:1	0.0000
58	350	776728909674432 — 69064942861433:1	0.0000
59	126	101120237302656 — 530504468704205:1	0.0000
60	207	87806733670656 — 610941046579621:1	0.0000
61	56	7741853982720 — 6929184906512716:1	0.0000
62	142	9610252313376 — 5582032189812906:1	0.0000
63	21	384475703040 — 139526990499859266:1	0.0000
64	87	927265749696 — 57852603509917176:1	0.0000
65	6	13029299712 — 4117238758126189063:1	0.0000
66	48	77879337120 — 688818623132738764:1	0.0000
67	1	361924992 — 148220595292542806325:1	0.0000
68	30	5262221952 — 10194313021156427427:1	0.0000
70	12	288527616 — 185925834445908958811:1	0.0000
72	10	14638104 — 3664732657008639427566:1	0.0000
74	2	421824 — 127173270761001727827807:1	0.0000
76	2	24336 — 2204336693190696615682010:1	0.0000
80	1	24 — 2235197406895366368301559999:1	0.0000
Totals	393197	53644737765488792839237440000	100.0000

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