Cards 1-180 come in both gray back and white back variations. The gray backs are slightly more rare than the white backs in series I (card numbers 1 through 100) and command a bit of a premium, but they're not super difficult to find. Most collectors agree (and it's essentially proven by looking at the PSA pop report), that white backs are, at least, twice as common as gray backs in Series I. In Series II (cards 101 through 180), however, the white backs are significantly more scarce, and command a significant premium, and are EXTREMELY difficult to find in mid and higher grades. The consensus seems to be that, in Series II, Topps printed around one tenth as many white backs as gray.
Based on the difficulty of finding them (and the cost), I believe this to be true. For example, the total pop, according to PSA. For card # 135, Mickey Mantle, is 6,125 in the gray back version and 484 in the white back. That would suggest about a 13 to 1 ratio.
Another example: The white back Mantle in this set (PSA 7) has a total pop of 10 with only 4 graded higher. PSA 8.5, 8 -- 335. PSA 7.5, 7 -- 76. PSA 6.5, 6 -- 74. PSA 5.5, 5 -- 28.PSA 4.5, 4 -- 21. Condition breakdown by back variation. 17,18,26,29,36,44,50(Rhodes), 54,78,84. 4,6,7,8(Alston), 9,12(Carey), 14(Boyer), 16,19,21(Collins), 22,23,24(Groat), 27,28,31(Aaron), 34,37(Grammas), 39,41,42. (Amaros), 43,45,46,48,49,51,52,53,55,58,59,60,65,66,67,69,70,71,73,75,77,79(Koufax), 80,81,83,86,87,89.
90(Redlegs Team Name Left), 91,92,93,94,96,98(Pasqual). 85 (Indians Team with Date). 13,90(Redlegs Name Centered). 35,47(Fowler), 57,61(Skowron), 62,63,72(Phillies Team Dated), 72(Phillies Left), 72(Phillies Centered), 74,82,85(Indians Centered), 85(Indians Left), 88,90(Reds Dated), 95(Braves Left), 104,107(Mathews).56,76,139,152,156. 3,5(Williams), 10(Spahn), 15(Banks), 30(Robinson), 32,38,40(Turley), 68,95(Braves Dated), 97,103,105,106,108,109(Slaughter), 112,114,116,118(Fox), 120(Ashburn), 123,126,130(Mays), 133,137,138,144,146(Nationals Team), 148,149,150(Snider), 154,155,157,171,172,178. 100(Orioles Centered), 113(Rizzuto). 11(Cubs Team Centered), 64(Arroyo), 95(Braves Centered), 100(Orioles Left), 111(Red Sox Team), 115,121(Pirates Team), 122,140(Score), 141,147,153,158,160,162,169,174,175,176,177(Bauer).
101(Campanella), 102,110(Berra), 125(Minoso), 131,136,142,145(Hodges), 151,159,161,163,164(Killebrew), 167,170,173(Podres), 179. 128,129,132,134(Cardinals Team), 165(Schoendienst). 29,47(Fowler), 48,56,81,107(Mathews), 131,145,150,164,171,179.
3,5(Williams), 10(Spahn), 12(Carey), 13,14(Boyer), 16,18,19,21(Collins), 22,23,25(Kluszewski), 26,28. 30(Robinson), 32,34,35,36,37(Grammas), 39,41,42(Amaros), 43,45,50(Rhodes), 53,54,57,58,60. 62,65,66,68,70,71,74,76,78,82,83,84,86,89,90(Redlegs Name Left), 92,93,95(Braves Name Left), 97. 102,103,104,105,106,108,109(Slaughter), 110(Berra), 112. 114,115,116,117,118(Fox), 119,120(Ashburn).126,127,128,129,132,133,134(Cardinals Team), 135(Mantle), 136,137,138,139,140(Score). 144,147,148,149,151,152,153,154,155,156,157,158,159,160,161,162,163(Woodling).
169,170,172,173(Podres), 174,175,176,177(Bauer), 178,180(Roberts). 183,184,186,189,191(Lary), 193,196,197,198,199,201,202. 203,204,206,207,208(Howard). 209,210,211,212,214,216,217,218,219,220,221,222,223,224,225(McDougald), 226(Giants Team), 227,229. 230,231,234,235(Newcomb), 237,238,239,241,242,243,244,245,246,247,248,249,250(Doby), 252,254. 255(Lemon), 256,257(Thompson), 258. 259,261(Shantz), 262,264,265,266,267,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284. 285,286,287,288(Cerv), 289,291,293,294,295(Labine), 296,297,298,299,300,301,302,303,305,306,307(Wilhelm), 308,309,310. 311,312(Pafko), 313,314,315,316,317,318,319,320(Adcock), 321,322,323,324,325,327,328,329,330,331,333,335,336. 337,338,339, Checklist 1/3. 130(Mays), 194(Irvin), 205,326,72(Phillies Left). 15(Banks), 24(Groat), 51,91.4,6,8(Alston), 38,40(Turley). 46,49,55,59,63,64(Arroyo), 67,69,72(Phillies Name Centered), 73,85(Indians Centered), 85(Indians Left), 88. 90(Redlegs Centered), 95(Braves Centered), 96,111(Red Sox Team), 113(Rizzuto), 125(Minoso), 146(Nationals Team), 166(Dodgers Team).
181(Martin), 185,190(Furillo), 192(Burgess). 195,200(Feller), 213(Tigers Team), 215,228,233,263,290,304,332(Larsen), 340, Checklist 2/4. 7,27,77,98(Pasqual), 268. 11(Cubs Name Left), 17,20(Kaline), 31(Aaron), 33(Clemente), 44,52,61(Skowron), 75,87,94,99(Zimmer), 100(Orioles Centered).
100(Orioles Left), 101(Campanella), 121(Pirates Team), 187(Wynn), 188(White Sox Team), 236(A's Team), 240(Ford), 251(Yankees Team), 253,260(Reese), 292(Aparicio). 1(Harridge), 11(Cubs Centered), 334.
These are 100 Percent PSA graded. Not as described is impossible. The item "High-End 1956 Topps Complete Super Master Set 540/540 #4 on PSA Set Registry" is in sale since Friday, February 7, 2020. This item is in the category "Sports Mem, Cards & Fan Shop\Sports Trading Cards\Baseball Cards". The seller is "overthetoppscollectibles" and is located in Olathe, Kansas. This item can be shipped to United States.