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 --- ------ -----
-------------------------------------------------------------------------------

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