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Grandia III Gambling FAQ (version 1.7) Table of Contents: I. About this guide II. Version history III. Dealer menu IV. Instructions V. Probabilities VI. Prize exchange I. About this guide =========================================================== Legal information: (c) Copyright 2006 Pete Strege. This may be not be reproduced under any circumstances except for personal, private use. It may not be placed on any web site or otherwise distributed publicly without advance written permission. Use of this guide on any other web site or as a part of any public display is strictly prohibited, and a violation of copyright. Contact information: Author: Pete Strege gamefaqs.com username: Rose4256 If you want to contact me, you may post on the message board here: http://boards.gamefaqs.com/gfaqs/gentopic.php?board=927215 II. Version history =========================================================== Version History: FAQ started November 9, 2005 1.7 February 23, 2006: Edited instructions to make them easier to understand. 1.6 February 20, 2006: Finished corrections to prize names and descriptions. 1.5 February 18, 2006: Corrected prize names and descriptions. 1.4 February 07, 2006: Corrected a typo. 1.3 December 20, 2005: Calculated probabilities for 4 sequences. 1.2 December 14, 2005: Rounded probabilities to 3 decimal places. 1.1 November 16, 2005: Added two more probability tables. 1.0 November 11, 2005: First full draft. III. Dealer menu ============================================================== Talk to the dealer: * Play Game 1) Place your bet (1-1000 Medals) Accept? (Y/N) 2) Arrange sequence: (Start) [] [] <- Discard [] [] [] [] [] [] [] <- Sequence 3) Roll 5x 4) Roll again/Change bet/Exit * Buy Medals Exchange rate: Purchase each medal (M) for 5 gold (G). 20M for 100G 200M for 1000G 2000M for 10000G * Prize Exchange (see "VI. Prize Exchange") * Quit IV. Instructions ============================================================== THE OBJECTIVE OF THE GAME IS TO ASSEMBLE A RUN OF 3-5 ADJACENT CARDS. How to play: ------------------------------------------------------------------------------- 1) Buy some medals. Caution: You cannot exchange medals back into gold when you are finished playing! 2) Save your game in the neighboring tent. Reload as necessary. 3) Reenter the gambling tent, talk to the dealer, and place your bet. I recommend betting no more than 10-20% of your total medals at a time. For example, bet 10 medals if you have 50-100 total, or bet 1000 medals if you have >5000 total). 4) Arrange a sequence of 7 cards. You must choose from 9 cards (III IV V VI VII VIII IX X XI) and discard 2. For starters, try one of the first three sequences (I'll explain the theory later): ---------------------------------------------------------------------------- Sequence Discard Predicted Observed Max bonus Comment ---------------------------------------------------------------------------- IV V VI VII VIII IX X III XI 31% 30% x200 default III V VI VII VIII IX XI IV X 29% 30% x400 recommended V III VI VII VIII XI IX IV X 21% 15% x400 recommended V VI III VII XI VIII IX IV X 14% 9% x800 best bonus ---------------------------------------------------------------------------- 5) Roll one pair of dice 5 times per bet. Each time you roll a number that matches the number on a card, that card is placed forward. IF 3-5 ADJACENT CARDS ARE PLACED FORWARD AT THE END OF YOUR TURN, YOU WIN. YOUR WINNINGS = (BET)*(BONUS)*(DEUCE)^n, where n = the number of deuces rolled. If you roll one deuce in addition to a 3- or 4-card run, your reward will be multiplied by 10. If you roll two deuces in addition to a 3- card run, your reward will be multiplied by 100. If a 3-5 card run includes one red card ("Lucky," III OR XI), your reward will be multiplied by 2. If a 3-5 card run includes both red cards ("Fever," III AND XI), your reward will be multiplied by 4. If you roll a 12 at any time, you automatically lose. The bonuses are summarized below: --------------------------- 10 Grade Up x 10 3 Card Row x 2 Lucky 3 Card Row x 4 Fever 3 Card Row x 8 4 Card Row x 15 Lucky 4 Card Row x 30 Fever 4 Card Row x 60 Absolute Card x 100 Lucky Absolute Card x 200 Fever Absolute Card x 400 --------------------------- 6) Save your game after every big win (>8x bonus or >15,000). 7) Exchange your medals for prizes. I recommend keeping >10,000M in reserve. Tip: ------------------------------------------------------------------------------- You'll have to press the X button intermittently, approximately once every 2-3 seconds. The repetition can become boring, so you'll have a few options. If you're low on medals, you'll want to pay attention to whether you run out and are forced to reload your save file. However, if you've accumulated a sizable amount, you could flip your switcher and watch television while tapping X. The easiest option would be to screw a C-clamp onto a turbo controller; you could check back later to see how much you've won. The theory behind choosing a sequence: ------------------------------------------------------------------------------- The red cards III and XI double your reward if included in a winning run, but there are only 2 of 36 possible combinations to roll each (see table below). By comparison, there are more combinations to roll the middle numbers (IV, V, VI, VII, VIII, IX, and X). Therefore, the middle numbers will appear more often due to chance. When picking a sequence, you'll want to keep open the possibility of a red card bonus while getting rid of the least probable green cards. For example, there are 2/36 chances to roll a III versus 3/36 chances to roll a IV; similarly, there are 2/36 chances to roll a XI versus 3/36 chances to roll a X. It would not be a huge sacrifice to switch the IV and X for a III and XI, respectively. Second, you'll want to place the numbers with the highest probability in the middle of the sequence. Based on the above criteria, this would be a good set-up for beginners: III V VI VII VIII IX XI If you want to try for the Fever Absolute Card (x400) jackpot, you could slightly alter the previous sequence by flanking the III and XI to the sides of the 3 most common numbers, VI-VII-VIII: V III VI VII VIII XI IX V. Probabilities ============================================================== Probability of circumstance x = "P(x)" P(getting a given card per roll) or "P(card)": ------------------------------------------------- Card Combinations Probability ------------------------------------------------- II 1+1 1/36 = 0.028 III 1+2, 2+1 2/36 = 0.055 IV 1+3, 2+2, 3+1 3/36 = 0.083 V 1+4, 2+3, 3+2, 4+1 4/36 = 0.111 VI 1+5, 2+4, 3+3, 4+2, 5+1 5/36 = 0.139 VII 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 6/36 = 0.167 VIII 2+6, 3+5, 4+4, 5+3, 6+2 5/36 = 0.139 IX 3+6, 4+5, 5+4, 6+3 4/36 = 0.111 X 4+6, 5+5, 6+4 3/36 = 0.083 XI 5+6, 6+5 2/36 = 0.055 XII 6+6 1/36 = 0.028 ------------------------------------------------- Total 36/36 = 1.000 P(not getting a card in any of 5 rolls) or "P(0/5)" = P(getting any except the given card)^5 = (1-P(card))^5: ------------------------------------------------- Card Equation Probability ------------------------------------------------- II (1-1/36)^5 = 0.869 III (1-2/36)^5 = 0.751 IV (1-3/36)^5 = 0.647 V (1-4/36)^5 = 0.555 VI (1-5/36)^5 = 0.473 VII (1-6/36)^5 = 0.402 VIII (1-5/36)^5 = 0.473 IX (1-4/36)^5 = 0.555 X (1-3/36)^5 = 0.647 XI (1-2/36)^5 = 0.751 XII (1-1/36)^5 = 0.869 ------------------------------------------------- P(getting a card in at least 1 of 5 rolls) or "P(>0/5)" = 1-P(0/5) = 1-(1-P(card))^5: ------------------------------------------------- Card Equation Probability ------------------------------------------------- II 1-(1-1/36)^5 = 0.131 III 1-(1-2/36)^5 = 0.248 IV 1-(1-3/36)^5 = 0.353 V 1-(1-4/36)^5 = 0.445 VI 1-(1-5/36)^5 = 0.526 VII 1-(1-6/36)^5 = 0.598 VIII 1-(1-5/36)^5 = 0.526 IX 1-(1-4/36)^5 = 0.445 X 1-(1-3/36)^5 = 0.353 XI 1-(1-2/36)^5 = 0.248 XII 1-(1-1/36)^5 = 0.131 ------------------------------------------------- You would like to know the probability of "a AND b AND c" as long as the remaining 2 slots are "NOT f OR f OR xii," in any order but regardless of the position of f's. Therefore, instead of multiplying all probabilities by 5! (120), you need to multiply by 5!/2 (60) instead. For example, multiplying 3! by 10 possible combinations for the sequence "o-o-o-x-x" yields 60: 123xx 132xx 213xx 231xx 312xx 321xx xxooo xoxoo xooxo xooox oxxoo oxoxo oxoox ooxxo ooxox oooxx In equation form, this becomes: P(a-b-c) = P(a)*P(b)*P(c)*(1-(P(f)+P(f)+P(xii)))^2*5!/2, where a-b-c = sequence and f = card(s) flanking the sequence. Unfortunately, when I tested my prediction for P(3 in a row), the observed probability after 100 tries was much lower than expected. However, the equation somehow fits if you multiply by 5!/4 instead of 5!/2. I also observed xii appearing in 68/400 or 17% of turns, which was much more common than predicted by 1-(35/36)^5 = 13%. P(a-b-c-d) = P(a)*P(b)*P(c)*P(d)*(1-(P(f)+P(xii)))*5!, where a-b-c-d = sequence and f = card(s) flanking the sequence. P(a-b-c-d-e) = P(a)*P(b)*P(c)*P(d)*P(e)*5! P(any winning hand for 4-5-6-7-8-9-10): --------------------------------------------------------------------------- Card II III IV V VI VII VIII IX X XI XII Pred Obs x/36 1 2 3 4 5 6 5 4 3 2 1 36 P(card) .03 .06 .08 .11 .14 .17 .14 .11 .08 .06 .03 .999 --------------------------------------------------------------------------- P(a-b-c) = P(a)*P(b)*P(c)*(1-(P(f)+P(f)+P(xii)))^2*5!/4 4-5-6 .08 .11 .14 .17 .03 .025 .04 5-6-7 .08 .11 .14 .17 .14 .03 .043 .06 6-7-8 .11 .14 .17 .14 .11 .03 .054 .03 7-8-9 .14 .17 .14 .11 .08 .03 .043 .08 8-9-10 .17 .14 .11 .08 .03 .025 .00 P(a-b-c-d) = P(a)*P(b)*P(c)*P(d)*(1-(P(f)+P(xii)))*5! 4-5-6-7 .08 .11 .14 .17 .14 .03 .021 .00 5-6-7-8 .08 .11 .14 .17 .14 .11 .03 .033 .01 6-7-8-9 .11 .14 .17 .14 .11 .08 .03 .033 .08 7-8-9-10 .14 .17 .14 .11 .08 .03 .021 .00 P(a-b-c-d-e) = P(a)*P(b)*P(c)*P(d)*P(e)*5! 4-5-6-7-8 .35 .45 .53 .60 .53 .004 .00 5-6-7-8-9 .45 .53 .60 .53 .45 .005 .00 6-7-8-9-10 .53 .60 .53 .45 .35 .004 .00 --------------------------------------------------------------------------- Sum total .313 .30 P(any winning hand for 3-5-6-7-8-9-11): --------------------------------------------------------------------------- Card II III IV V VI VII VIII IX X XI XII Pred Obs x/36 1 2 3 4 5 6 5 4 3 2 1 36 P(card) .03 .06 .08 .11 .14 .17 .14 .11 .08 .06 .03 .999 --------------------------------------------------------------------------- P(a-b-c) = P(a)*P(b)*P(c)*(1-(P(f)+P(f)+P(xii)))^2*5!/4 3-5-6 .06 .11 .14 .17 .03 .017 .02 5-6-7 .06 .11 .14 .17 .14 .03 .047 .07 6-7-8 .11 .14 .17 .14 .11 .03 .054 .02 7-8-9 .14 .17 .14 .11 .06 .03 .047 .10 8-9-11 .17 .14 .11 .06 .03 .017 .02 P(a-b-c-d) = P(a)*P(b)*P(c)*P(d)*(1-(P(f)+P(xii)))*5! 3-5-6-7 .06 .11 .14 .17 .14 .03 .014 .02 5-6-7-8 .06 .11 .14 .17 .14 .11 .03 .035 .01 6-7-8-9 .11 .14 .17 .14 .11 .06 .03 .035 .01 7-8-9-11 .14 .17 .14 .11 .06 .03 .014 .02 P(a-b-c-d-e) = P(a)*P(b)*P(c)*P(d)*P(e)*5! 3-5-6-7-8 .06 .11 .14 .17 .14 .002 .00 5-6-7-8-9 .11 .14 .17 .14 .11 .005 .01 6-7-8-9-11 .14 .17 .14 .11 .06 .002 .01 --------------------------------------------------------------------------- Sum total .288 .30 P(any winning hand for 5-3-6-7-8-11-9): --------------------------------------------------------------------------- Card II III IV V VI VII VIII IX X XI XII Pred Obs x/36 1 2 3 4 5 6 5 4 3 2 1 36 P(card) .03 .06 .08 .11 .14 .17 .14 .11 .08 .06 .03 .999 --------------------------------------------------------------------------- P(a-b-c) = P(a)*P(b)*P(c)*(1-(P(f)+P(f)+P(xii)))^2*5!/4 5-3-6 .06 .11 .14 .17 .03 .017 .01 3-6-7 .06 .11 .14 .17 .14 .03 .020 .01 6-7-8 .06 .14 .17 .14 .06 .03 .072 .07 7-8-11 .14 .17 .14 .11 .06 .03 .020 .03 8-11-9 .17 .14 .11 .06 .03 .017 .00 P(a-b-c-d) = P(a)*P(b)*P(c)*P(d)*(1-(P(f)+P(xii)))*5! 5-3-6-7 .06 .11 .14 .17 .03 .014 .00 3-6-7-8 .06 .11 .14 .17 .14 .06 .03 .017 .01 6-7-8-11 .06 .14 .17 .14 .11 .06 .03 .017 .02 7-8-11-9 .14 .17 .14 .11 .06 .03 .014 .00 P(a-b-c-d-e) = P(a)*P(b)*P(c)*P(d)*P(e)*5! 5-3-6-7-8 .06 .11 .14 .17 .14 .002 .00 3-6-7-8-11 .06 .14 .17 .14 .06 .001 .00 6-7-8-11-9 .14 .17 .14 .11 .06 .002 .00 --------------------------------------------------------------------------- Sum total .214 .15 P(any winning hand for 5-6-3-7-11-8-9): --------------------------------------------------------------------------- Card II III IV V VI VII VIII IX X XI XII Pred Obs x/36 1 2 3 4 5 6 5 4 3 2 1 36 P(card) .03 .06 .08 .11 .14 .17 .14 .11 .08 .06 .03 .999 --------------------------------------------------------------------------- P(a-b-c) = P(a)*P(b)*P(c)*(1-(P(f)+P(f)+P(xii)))^2*5!/4 5-6-3 .06 .11 .14 .17 .03 .017 .01 6-3-7 .06 .11 .14 .17 .06 .03 .025 .00 3-7-11 .06 .14 .17 .14 .06 .03 .007 .00 7-11-8 .06 .17 .14 .11 .06 .03 .025 .04 11-8-9 .17 .14 .11 .06 .03 .017 .01 P(a-b-c-d) = P(a)*P(b)*P(c)*P(d)*(1-(P(f)+P(xii)))*5! 5-6-3-7 .06 .11 .14 .17 .06 .03 .016 .01 6-3-7-11 .06 .11 .14 .17 .14 .06 .03 .006 .00 3-7-11-8 .06 .14 .17 .14 .11 .06 .03 .006 .01 7-11-8-9 .06 .17 .14 .11 .06 .03 .016 .01 P(a-b-c-d-e) = P(a)*P(b)*P(c)*P(d)*P(e)*5! 5-6-3-7-11 .06 .11 .14 .17 .06 .001 .00 6-3-7-11-8 .06 .14 .17 .14 .06 .001 .00 3-7-11-8-9 .06 .17 .14 .11 .06 .001 .00 --------------------------------------------------------------------------- Sum total .138 .09 VI. Prize Exchange ============================================================ A maximum 9 of each item may be purchased in exchange for medals earned. Early in the game, I recommend the jade charm, magic pendant, and staff of healing. After you can fly freely, revisit to pick up 3 mysterious clogs and 3 rune armors. (Dahna doesn't need to warp because she can throw her cards, and she can't equip rune armor.) Do not waste your time trying to win the gambler. It's too inconsistent to be worth its price. Later in the game, buy 3 ninja shoes and a master book. Stock up on platinum and golden feathers to use during your fight against the last boss. ------------------------------------------------------------------------------- Prize Exchange Sell Effect Type Range Target ------------------------------------------------------------------------------- White Sulfur 16M 5G Restores 40 MP REC Single Ally Panacea 24M 60G Cure poi,sleep,para,conf,sil,sick SUP Single Ally Mogay Bomb 36M 5G Non-elemental, Pow 120, Cancel ATK Single Enemy Revival Elixir 48M 120G Revives one ally 100% HP SUP Single Ally Silver Feather 64M 5G Moves IP symbol far ahead SUP Single Ally Manana Fruit 240M 50G Restores 80 MP REC Single Ally Big Mogay Bomb 360M 20G Non-elemental, Pow 600, Cancel ATK Single Enemy Warrior's Tonic 480M 32G Restores 100 SP REC Single Ally Golden Feather 640M 25G Moves IP symbol far ahead SUP All Ally Jade Charm 800M 16G ATK +5 --- ------ ----- Magic Pendant 800M 16G MAG +5 --- ------ ----- Holy Water 1600M 150G Restores 160 MP REC Single Ally Fat Mogay Bomb 3600M 80G Non-elemental, Pow 1800, Cancel ATK Circle Enemy Staff of Healing 4000M 108G ATK +20, +10 MAG, Restore HP --- ------ ----- Platinum Feather 6400M 100G Moves IP symbol far ahead SUP All Ally Rune Armor 8000M 175G DEF +25, RES +50 --- ------ ----- Volcano Egg 12000M ---- Fire*** Magic Level 6 --- ------ ----- Lake Egg 12000M ---- Water*** Magic Level 6 --- ------ ----- Indigo Elixir 24000M 1375G Restores 320 MP REC Single Ally Mysterious Clog 45000M 160G Warp movement --- ------ ----- The Gambler 80000M 1G ATK +??? Variable attack bonus --- ------ ----- Alluring Cards 120000M 450G ATK +99, Confuse an enemy --- ------ ----- Ninja Slippers 160000M 900G INI +10, Warp movement --- ------ ----- Master Book 999999M ---- Mind*** Tech*** Body***, Critical --- ------ ----- ------------------------------------------------------------------------------- 1234567890123456789012345678901234567890123456789012345678901234567890123456789