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Here's what I've discovered about Mystery Gifts in Pokemon Stadium 2. Similarities with GameBoy Color Infra-Red Mystery Gifts The logic is the mostly the same between Pokemon Stadium 2 and Mystery Gift between GameBoy Color using infra-red system. The game chooses a random item and decoration separately. The game first tries to give the decoration but you already have that decoration, you will get the item instead. Choosing a specific item or decoration gift to send occurs in two stages. First, the game selects a set from which the gift will come. Then, it uses a part of the player's Trainer ID number to determine which gift from that set to send. (Below, bit 0 refers to the least significant bit of the Trainer ID and bit 15 refers to the most significant bit. Given the Trainer ID 32768, which translates to 1000000000000000 in binary, bit 15 is 1 and bit 0 is 0.) The logic for determining the item given is the same as the logic for Mystery Gift between GameBoy Color using infra-red system. See https://bulbapedia.bulbagarden.net/wiki/Mystery_Gift for more info. Decoration Logic The logic for determining decoration is different however. Random number. Range . Gift set . Overall rate 1st 36-255 Common 223/256 0-35 N/A (pick a 2nd number) 2nd 72-255 Uncommon 25/256 0-71 N/A (pick a 3rd number) 3rd 72-255 Rare 7/256 0-71 N/A (pick a 4th number) 4th 154-255 Very Rare 1/256 77-153 Tentacool Doll 0/256 0-76 Tentacool Doll or Pikachu Bed 0/256 Common, Uncommon, Rare and Very Rare follows a similar logic as GameBoy Color Infra-Red Mystery Gifts (using Trainer ID). The exact bit used for each item and decoration is slightly different. Check https://bulbapedia.bulbagarden.net/wiki/Mystery_Gift for the detailed list. Upon reaching the 4th roll with 0-76, Tentacool Doll is given if Round 2 has not been unlocked and Pikachu Bed is given if Round 2 has been unlocked. No code exists to return Unown Doll (internal decoration ID 35). Why Tentacool Doll and Pikachu Bed are unobtainable You may have noticed that Overall rate for Tentacool Doll and Pikachu Bed is 0/256. Here's why: To obtain Tentacool Doll, the game must roll 0-35, 0-71, 0-71, 0-153 (assuming Round 2 hasn't been unlocked). To obtain Pikachu Bed, the game must roll 0-35, 0-71, 0-71, 0-76 (assuming Round 2 has been unlocked). Those sequences of numbers are not possible. The game uses a 32-bit linear congruential generator: result = (seed * 0x19660D) + 0x3C6EF35F; Mystery Gift logic only uses the last 8 bits of the generated random number. The last 8 bits of the generator follows a cyclic pattern: 0,95,50,233,52,3,134,45,168,231,26,177,92,11,238,117,80,111,2,121,132,19,86,189,248,247,234,65,172,27,190,5,160,127,210,9,212,35,38,77,72,7,186,209,252,43,142,149,240,143,162,153,36,51,246,221,152,23,138,97,76,59,94,37,64,159,114,41,116,67,198,109,232,39,90,241,156,75,46,181,144,175,66,185,196,83,150,253,56,55,42,129,236,91,254,69,224,191,18,73,20,99,102,141,136,71,250,17,60,107,206,213,48,207,226,217,100,115,54,29,216,87,202,161,140,123,158,101,128,223,178,105,180,131,6,173,40,103,154,49,220,139,110,245,208,239,130,249,4,147,214,61,120,119,106,193,44,155,62,133,32,255,82,137,84,163,166,205,200,135,58,81,124,171,14,21,112,15,34,25,164,179,118,93,24,151,10,225,204,187,222,165,192,31,242,169,244,195,70,237,104,167,218,113,28,203,174,53,16,47,194,57,68,211,22,125,184,183,170,1,108,219,126,197,96,63,146,201,148,227,230,13,8,199,122,145,188,235,78,85,176,79,98,89,228,243,182,157,88,215,74,33,12,251,30,229,0 The first random number is selected randomly in that list, then at every new roll, the next random number is the next one in the list. The issue is that there are no 4 consecutive numbers that are 0-35, 0-71, 0-71, 0-153 respectively. This means Tentacool Doll (and Pikachu Bed) can't be obtained. The sequence to obtain a Very Rare decoration (0-35, 0-71, 0-71, 154-255) appears once (15,34,25,164). In short, none of the Pokemon Stadium 2 exclusive decorations are actually obtainable. Special thanks to Lincoln for providing the initial disassembly of Mystery Gift functions of Pokemon Stadium 2. https://github.com/Lincoln-LM/stad2

Even though this isn't directed to me, I am popping in to say that our general stance is to NOT look at one's (in this case, yours) hacked Pokémon and explain why it is/isn't legal and whether would it get you banned. You may continue to provide legal Pokemon to others seeking them, or bring up something to our attention to mention how a hack checked is missed/incorrect, but you shouldn't do so with the intentions along the lines of getting feedback on getting free hack checks, ban evasions, etc.

By using hacks, it is possible to receive Pikachu Bed, Unown Doll, and Tentacool Doll. In Pokemon Stadium 2 USA 1.0, place a breakpoint at command 0x801454F8 and alter the register V0 to 0x22 for Pikachu Bed, 0x23 for Unown Doll, or 0x24 for Tentacool Doll. Note that the Unown Doll is displayed as "DECORATION".