|===========================|
                         |=|        Xenosaga       |=|
                         |=|       EPISODE  I      |=|
                         |=|  Der Wille zur Macht  |=|
                         |===========================|
                         |=| Poker Mini-Game Guide |=|
                         |===========================|


Xenosaga(TM) EPISODE I Der Wille zur Macht 
   is Copyright (c)  2001  NAMCO LTD.

This guide is Copyright (C)  2003  James Doyle / "Kadamony",
   see chapter 8 for licensing information.

This is version 1.0.  The latest version will always be available
at GameFAQs, http://www.gamefaqs.com.

===============================================
  0 :: INTRODUCTION AND TABLE OF CONTENTS
===============================================

This is a guide to the Poker mini-game, and especially the "High & Low"
game that takes place after a winning Poker hand.  It is meant as a
guide to earning money quickly and securely in Xenosaga, a game in which
money can be hard to come by later in the game.

This guide was written March 2, 2003, after experiencing the immense
power of the AG-05 AGWS in annihilating the final boss. 

To quickly access a chapter, use your text editor's search feature
and search for the chapter number, followed by a space and two colons.
For example, to go to chapter 9, you would search specicifically 
for "9 ::".

* CONTENTS:

  0:  Introduction and Table of Contents
      - Right here
  1:  Money In Xenosaga
      - Why you want to play Poker to make money
  2:  Accessing the Poker Game
      - How to first get access to the Poker game, and where to play it
  3:  How to Play Poker
      - An introduction to the game of Poker, inside and outside of
        Xenosaga
  4:  Poker in Xenosaga
      - How to use the Poker game
  5:  Making Lots of Money
      - Using the "High & Low" game to get rich
  6:  Cashing Out
      - Getting G for your Coins, and otherwise spending your winnings
  7:  The Mathematical Evidence
      - An in-depth look at the mathematics behind "High & Low"
  8:  Copyright Information
      - Licensed under the GNU Free Document License

* Revision History:

 2 March 2003 - Version 1.0, Initial revision



==============================
  1 :: MONEY IN XENOSAGA
==============================

Xenosaga differs from most console RPGs in that defeating enemies rarely
yields much money.  There are a handful of creatures around the Xenosaga
world that drop money, but the vast majority is earned through other 
mechanisms.  Throughout the game, money is earned by investing in companies
through e-mail, or by successfully completing a long side-quest to track
down a hacker.  Some money is earned from bosses, and a little bit is 
available from selling "Barter Items", such as "Scrap Iron".  However, you
can't get much money this way, and you can't do it very quickly.

Near the end of the game, a new AGWS unit is available for sale at the Dock
Colony, for 300000 G.  This AGWS unit is extremely powerful, able to take
out almost any enemy in the game all on its own.  The AG-05 unit comes 
built in with 6000 HP, and is capable of equipping the most powerful 
AGWS weapons available in the game.  However, it can be quite difficult to
earn enough money to pay for all of this.  

This guide presents a mechanism for earning money through the Poker game
available through the "Casino Passport" item, first acquired at Durandal.
This Poker game is heavily weighted in favor of the player, such that over
time it provides a consistent and guaranteed source of cash, which is 
otherwise lacking in the game.  This guide attempts to explain how gambling
can be profitable, and the quickest way to take advantage of this game
to make as much money as you want.

In addition to cold hard G, you can acquire thousands of Xenocard boosters,
making it trivial to create any deck you want in a matter of under an
hour.



=====================================
  2 :: ACCESSING THE POKER GAME
=====================================

The Poker game is first accessible when you arrive at the Durandal, after
completing the Cathedral Ship.  In order to access the Poker game, you must
first acquire the "Casino Passport", which is available inside the Casino
in the Residential Area of the Durandal.  

* Getting the Casino Passport

After arriving at the Durandal and being allowed to leave the Isolation
Area, enter the Durandal Train.  Select "Residential Area" as your 
destination, and enter the Train.  When you exit the train, proceed
westward until you come to a wall.  Turn to the north, and continue down
a hallway, past some vending machines.  When you reach the north wall,
make a right turn, and enter the first door to the north.  This is the
casino.  At the far right of the casino, up the staircase and behind the
table, lies a treasure chest containing the "Casino Passport".

* Use the Casino Passport at EVS Save Points

The actual physical casino at the Durandal has very little to do with 
the Poker game, other than being the location of the passport and 
containing an EVS-enabled UMN Plate (save point).  You can play Poker
from any EVS-enabled save point in the game.  To do so, enter the main
menu, and select "Items".  Use the R1 button to scroll over to "Special
Items", and select the Casino Passport.  If you hear a buzzing sound, 
you are not properly positioned on the EVS-enabled save point.  Exit
the menu and try again when you hear a sound indicating you have touched
the save point.  *** This will not work if the save point does not have
the blue EVS plate on top of it! ***

 - EVS-enabled UMN Plates -

1.  Onboard the Elsa, to the starboard side of the ship, just outside the
    bridge.
2.  The Durandal casino inside the residential area.
3.  The "Our Treasure" Inn in Sector 26 of the Kukai Foundation (except
    during the Gnosis attack).



==============================
  3 :: HOW TO PLAY POKER
==============================

The common card game of Poker takes on many forms.  The form used in this
game is a simple one, known as "Five-Card Draw".  Ordinarily a game of 
Poker is played between several players at a table, with each betting on 
the value of his hand.  After each player has decided whether or not to
invest in his hand, the hands are revealed and the player with the highest
valued hand takes all of the money that had been bet.  This game uses a 
slightly different version, to allow play by a single player.  It is a form
commonly used in American casinos, known as "Video Poker".  In Video Poker,
there are no opponents, and the goal is simply to make your hand as highly
valued as possible.  Depending on the value of your hand, you will either
lose your initial bet or be returned some multiple of it.

* The Deck of Cards         

A Poker hand consists of five cards taken from a standard 52-card deck.  The
deck contains 13 denominations of cards in four different suits -- the 
shape of the icon appearing on the card.

Denominations of a standard deck:  
  [A]   [K]    [Q]     [J]    [T]  [9] [8] [7] [6] [5] [4] [3] [2]
  (Ace) (King) (Queen) (Jack) (10)

The Ace is normally considered either the highest -or- the lowest 
denomination, with the King being the next highest and the [2] being the
lowest.  The King, Queen, and Jack appear with a picture on them, while
the Ace and the numbered Ten through Two cards appear with a number of
suit symbols equal to their denomination, with an Ace considered 1.

Suits in a standard deck:
  <Clubs> <Diamonds> <Hearts> <Spades>

Clubs are represented by a clover symbol.  Diamonds are represented by
a geometrical diamond.  Hearts are represented by a heart, and Spades by
a pointed leaf-shaped object.  Clubs and Spades are black, and Diamonds
and Hearts are red.

Xenosaga ** does not use a standard deck **.
In Xenosaga, the Ace does not exist, and is a [1] card.  As such, it is
always considered the lowest card, and the [K] is now the highest card.

* The Value of a Poker Hand

A Poker hand is more highly valued based on the presence of less probable
card patterns.  For example, having five cards of seperate denominations
and suits is the most common result, and thus the least valuable.  Having
five cards all of the same suit is significantly rarer, and thus is a
highly valued hand.

The hand ranks are as follows:

No Pairs:                         [x0]

A hand consisting of five cards of seperate denominations, without being
all in sequence or all of the same suit.  In ordinary poker, the higest
card is considered the "value" of the hand for purposes of comparing with
the other players.  Thus, [7] [4] [3] [8] [2] would be considered worth
an [8].  If another player had [9] [3] [7] [4] [5], the other player would
win due to having a hand valued at [9].  In the case of a tie, the second-
highest card is compared.  Such a hand is considered "9-high".
In Xenosaga, such a hand is always a loser, and returns 0x the bet.

One Pair:                         [x1]

A hand consisting of two cards of the same denomination, and no other
pattern of note.  Such a hand beats a hand without a pair, but loses to
any other patterned hand.  In the case of two hands with One Pair, the
higher-valued denomination wins.  In Xenosaga, any pair is valued the
same, and returns 1x the bet.

Two Pairs:                        [x2]

A hand consisting of four cards of two denominations, with no other
pattern.  Such a hand beats a single pair, but loses to any other patterned
hand.  Again, the highest valued pair is used as a tiebreaker if another
hand also has Two Pairs.  In Xenosaga, two of any pair is valued at
2x the bet.

Three of a Kind:                  [x3]

A hand consisting of three cards of the same denomination, and no other
pattern of note.  Such a hand beats a hand with only pairs, but loses to
other patterned hands.  In Xenosaga, three of a kind is valued at 3x the bet.

Straight:                         [x5]

A hand consisting of five cards in numerical sequence, with no other pattern.
For instance, [3] [4] [5] [6] [7] would be considered a straight.  A straight
cannot "wrap", so a [K] is always the highest card in a straight and cannot
be the bottom of a [4] [3] [2] [1] [K].  The highest card in a straight
breaks any ties, and a straight beats any paired or three of a kind hand.
In Xenosaga, all straights pay out 5x the bet.

Flush:                            [x7]

This hand type is a bit different than the others, in the the denomination
of the card isn't considered (unless there is a straight).  A flush is
a hand with five cards all of the same suit.  Ties are broken by the highest
denomination card.  Flushes beat straights, pairs, and threes of a kind.
In Xenosaga, a flush is worth 7x the initial bet.

Full House:                       [x10]

A hand consisting of both a three of a kind -and- a pair.  Such a hand
beats anything except four of a kind or a straight flush.  It pays out
10x the initial bet.

Four of a Kind:                   [x20]

Four cards of the same denomination consititutes a Four of a Kind.  Such
a hand beats anything except a straight flush.  It pays out 20x the initial
bet.

Straight Flush:                   [x50]

A straight flush is a hand with both a straight -and- a flush, with five
cards in sequence all of the same suit.  It is the highest possible hand
and beats anything, with ties broken by the highest valued denomination.

Royal Flush:                      [x100]

A royal flush is just a certain straight flush--that which consists of the
highest cards available, the [K] [Q] [J] [T] [9], all of the same suit.
(Normally it would be [A] [K] [Q] [J] [T], but Xenosaga doesn't have an [A]).
While technically it is not a different hand type, since it cannot be
beaten (only tied), it receives special payout in Xenosaga, of 100x the bet.

* Playing your hand

In Five-card Draw Poker, you are dealt five cards to start with.  If you
have one of the patterned hand types listed above, you are welcome to keep
it and receive your prize.  However, you usually don't get more than just
a pair (if anything) on your initial deal.  You have one opportunity to
improve your hand by discarding unwanted cards and replacing them with
new cards dealt at random.  After this second deal, known as the "Draw",
you are stuck with whatever you are left with.  As such, it is usually
a good idea to hang on to cards that form a pattern and discard other 
cards in an attempt to improve your pattern.  

 - Hang on to pairs

Holding [2] [2] [3] [8] [J], you would likely keep the two [2]s and
discard the rest, hoping to draw another [2] to get a three of a kind,
or perhaps another pair for two pairs.  If you're really lucky, you might
draw two more [2]s or even a brand new three of a kind for a full house.

 - High cards are irrelevant

In Xenosaga, you are not competing against other players, but rather 
attempting to acquire as valuable a pattern as possible.  As such, you
don't have to worry about breaking ties, and a pair of [1]s is just as
valuable as a pair of [K]s.  Don't hang on to high cards in an attempt
to match them up; pitch them to allow for more chances to improve your
pairs.

 - When to go for a straight or flush

If you are not dealt any pairs, you often want to throw away the entire
hand and get a new one, since you have nothing you want to work with.
However, sometimes you will be dealt no pairs, but several cards that
look like they might make up a superior pattern, such as a straight
or a flush.  In that case, you can choose to hang on to the partially
completed pattern in an attempt to finish it off.  For example, holding
[2] [3] [4] [5] [8], you might discard the [8] in an attempt to draw
either a [1] or a [6].  Either card would complete a straight.  However,
the odds are against you, in that only two denominations will complete
your straight, while eleven will not.  Still, four others will get you
at least one pair, so it's not all that bad a deal.  Avoid drawing to
inside straights, however, such as [2] [3] [5] [6] [T], since only one
card is capable of completing the straight, the [4].  Similarly, straights
that are blocked off by an extreme card, such as [K] [Q] [J] [T] [5],
have only one card that will complete them, and are thus bad news.
It's better to discard the entire jumble and hope for at least a pair
then to hold on to a faint hope at a better pattern.

Flushes pay out extremely highly, but are relatively rare.  However,
sometimes you are dealt four cards of the same suit, and one card of
a different suit.  In that case, you can choose to pitch only the
extraneous card and holding on to the almost-flush.  Still, be aware
that although it might appear you have 1 in 4 odds to complete the flush,
it's actually a bit lower than that, since 4 cards of that suit have 
already been removed from the deck.  Assuming 4 Diamonds and a Club
are your initial hand, there are only 9 Diamonds and 38 other cards left
in the deck, for about 19.1%, a bit lower than 25%.  If your fifth
card makes a pair with a card in the almost-flush, it's usually not
a good idea to break up that pair in a futile atempt at a flush, when
you could go for a three of a kind or two pair instead.

 - High Valued Hands

Extremely high valued hands such as Straight Flushes are extremely rare,
and generally occur more by fluke than by actually attempting to 
complete them.  Still, holding [K] [Q] [J] [8] [4] with the high
cards all being of the same suit, it is very, very tempting to take
that tiny chance at getting the missing [9] and [T].  It's probably
not a very good move from a probability standpoint, but it can be fun
as long as it's not ridiculous, such as trying for a royal flush holding
two of the required cards, or done regularly with only three.  Still,
in general you should go for the common patterns, especially due to
the presence of the "High & Low" game (to be discussed in extreme detail
later).



==============================
  4 :: POKER IN XENOSAGA
==============================

* About Coins

In Xenosaga, you can't directly gamble away G, the currency of the 
Xenosaga universe.  Instead, you must buy "Coins", which can be gambled
at either the Slot machine or the Poker game.  Coins can be used to buy
a variety of "prizes", which will be detailed below.  To buy coins,
access the Casino using the Casino Passport (see chapter 2), and select
"Exchange".  You can then select "Purchase Coins" from the menu.

Coins are available in the following packages:

 - 10 Coins   [ 100 G]
 - 100 Coins  [ 950 G]
 - 500 Coins  [4500 G]
 - 1000 Coins [8000 G]

While it might seem like a better deal to purchase the Coins in bulk,
it really is a waste of G.  These are horrifically high prices for Coins,
which can easily be acquired by simply winning the Poker game.  If you have
a bit of money to spare, you can start with 100 Coins so you don't have to
worry about coming back for more, but if you want to be cost-efficient,
you can buy just 10 and start at the low-stakes machines.  You may have to
buy a few batches of 10 before you win, but once you hit a x16 on the 
"High & Low" game, you will not need to buy another Coin ever again.  Still,
you will soon be racking in a virtually unlimited amount of cash, so if
you want to get started immediately on the high-stakes (well, if you call
100 Coins high) game, feel free to buy a larger package.

* The Poker Game

Heading back to the main Casino menu, once you have Coins, select "Poker"
to begin the Poker game.  The Poker game can be played in 4 different
levels of stakes:

 - LEVEL-1:   5 Coins
 - LEVEL-2:  10 Coins
 - LEVEL-3:  30 Coins
 - LEVEL-4: 100 Coins

Since the Poker game is biased heavily in your favor, you will want to
play for as high of stakes as you can afford.  However, if you initially
purchased just a few Coins, you might want to start out at a lower level,
such that you don't run out of coins and have to buy more.

-----------------------------------------------------------------------------
"But if this is such as sure way of gaining money, how come I can run out
 of coins?"

Consider the old saying - "The House Always Wins".  This is an old axiom
about casinos -- they turn a profit.  In order to do such, they have to 
be making money on the gambling taking place within.  Yet, it is still 
possible to show up at a casino and go home a winner.  How is this possible?
Statistical sample size is the answer.  In a casino, the games are set up
such that the probabilities favor the house ever so slightly.  Thus, any
game can be won or lost by anyone, and 5 or 10 or even 50 games can go
either way, but over the long haul the casino WILL make money.  This is
the principle of the law of averages.  

In Xenosaga, the probabilities favor you.  And it's not just a slight
favoring, it's hugely, immensely in your favor.  And yet, after two or three
or even ten hands it's possible you might lose some money.  Due to the
overwhelming odds, the law of averages will kick in pretty soon after that,
and you'll be sure to turn a profit over even a short time.  Still, a 
couple hands here and there can go against you.  Once you have about 1000
Coins, you will never have to worry about running out again, and you should
get there very quickly.

Over time, you WILL make a ton of money with the Xenosaga Poker game.
-----------------------------------------------------------------------------

Once you select a level, you will be presented with a screen detailing
how many Coins you have, what the payout levels are, and a dialog box
asking you if you want to play that level of Poker.  Select "Yes", and you
will be given your hand.

Below each card is a "DRAW" button, with a seperate draw button in the 
middle of the screen.  The "DRAW" buttons below the cards are used to toggle
whether or not you wish to keep each card.  By selecting one, it changes
to "HOLD".  Now, the card will not be pitched when you go to make your draw.
If you mistakenly choose to HOLD a card, you can select the "HOLD" button
to toggle it back to "DRAW".  When you eventually select the main "DRAW"
button in the center, all the cards that are marked "DRAW" will be 
jettisoned, and new cards will be dealt in their place. 

After the second deal, your hand will be evaluated, and, if you have at
least a Pair, the value of your hand will light up on the chart.  If you
do not have at least a Pair, you have lost, and will be given the option
to play again.

If you won at least a 1x payout, you will be given the option to play a
"Double or Nothing" game, entitled "High & Low".  By playing "High & Low",
you can multiply your payout by anywhere from 2 to 16 times--or you can
lose it all.

* High & Low

When you win at least a 1x payout in the Poker portion of the Poker game,
you will be given the option to play "High & Low".  If you choose to do
so, you will enter a different screen, in which five card slots appear
at the top of the screen, and a set of indicators from 2x - 16x appear
where the payouts normally are.

This game is very similar to the old television game show "Card Sharks".
In this game, you will be presented with a faced card.  You are given the
opportunity to guess whether the next card will be of a higher or lower 
denomination than the currently faced card.  You also can choose to stop 
at any time, even after seeing the card.  If you choose to go on, you will 
be dealt another card.  If it fits the guess you made, you will double your
payout, and if not, you have lost it all.  When the same denomination is 
drawn, you win regardless of your guess.  You can continue this until you 
choose "Stop", lose, or reach a payout multiplier of 16x (4 consecutive 
correct guesses).  

Whatever the result, when you are done, you will be returned to the regular
Poker mode, to start anew.  You can play High & Low any time you earn any
payout in the Poker mode.

This is the portion of the game where the real money is made.  See
chapter 5 below about playing High & Low and making huge amounts of money.



=================================
  5 :: MAKING LOTS OF MONEY
=================================

Video poker alone isn't going to get you much.  If you never go for
double or nothing, you'll settle around the amount of money you started
with, occasionally winning a 1x, a 2x, and often losing.  Every once in
a while, you'll get a 10x payout or more, and if you're ridiculously 
lucky, you might get 100x back from a Royal Flush once in a blue moon.

Still, even 100x is only 10000 Coins, which isn't going to get you anywhere.

Wouldn't it be nice if there was a way to routinely rake in huge amounts
of Coins, such as 1600 from a simple pair, or 3200 from two pair?  Imagine
getting 4800 from a three-of-a-kind!  That's half as much as a Royal Flush,
and it comes up thousands and thousands of times more often.

Still, you are only allowed to gamble 100 Coins at a time, and even if you
were able to bet more, you'd have no guarantees of actually winning 
consistently over time at the simple Poker game.

The solution to all of this is to use the "High & Low" game, which is
ridiculously balanced to favor you--at an expected rate of payout of
5.5 times what you put in!  That means that over time, your pairs will
be worth 550 EACH--and you certainly get enough pairs to make that 
worthwhile.  

Playing the "High & Low" game feels a bit dangerous, especially when the
amounts get big, and the card isn't a nice friendly one such as a [Q] or
a [3], where it is extremely likely that the direction you pick will turn
up.  Still, in order to secure really fast, effective, and consistent
payouts, you must risk it all.

And here's the key to this entire guide:

**********************************************************
RISK IT ALL.  EVERY TIME.  NO MATTER WHAT CARD IS SHOWING.
**********************************************************

     NEVER ACCEPT ANYTHING SHORT OF A 16x PAYOUT.
     ============================================

Yes, you heard right, even on a full house already gone to 8x and a [7]
showing, I am saying you must go on.  The odds are in your favor every time,
even with the worst possible card faced, the dreaded [7].

It might feel frustrating to lose an 8x full house, but for every one you
lose, there will be even more 16x payouts that you would have otherwise
missed.

Remember, the odds are in your favor--always, every time, no matter what.

Here's the table of odds, assuming you pick logically, meaning LOW on
[K][Q][J][T][9][8], HIGH on [1][2][3][4][5][6], and whatever you like on
[7]--so long as it is not STOP!

[K] 100.00%
[Q]  92.31%
[J]  84.62%
[T]  76.92%
[9]  69.23%
[8]  61.54%
[7]  53.85%  <-- Yes, even this is in your favor over the long haul,
[6]  61.54%      which is what we're playing for.
[5]  69.23%
[4]  76.92%
[3]  84.62%
[2]  92.31%
[1] 100.00%

If you do not go on every time, all you're doing is slowing down your
gains.  It's irrelevant if you blow this 1600--you're playing for hundreds
of thousands, not a few measly Coins here and there.  In fact, I've done
some calculations below (see chapter 7 if you dare), and it turns out that
if you always go on, you will get a 16x payout about 1/3 of the time.  The
other 2/3 you will lose it all.  That's 5.5x on average, which is a
ridiculous expected payout for a gambling machine.  No real gambling machine
ever pays out above 1x on average, it would be suicide for the casino.
0.95x is a great payout.  This one pays out 5.5!  It would be a steal at
1.1, but now it's just ridiculous.  

You can make about 200000 Coins per hour if you follow this simple system,
and that's just with pairs and threes-of-a-kind.  In order to make 200000
Coins without "High & Low", you'd need to score 20 Royal Flushes without
losing.  And even one Royal Flush is so unlikely as to be irrelevant.
But--if you get one, remember--KEEP GOING, EVEN ON [7]!

I have personally used this system to rack up tons of Coins, and it never
fails.  You'd have to lose 16 times in a row between successes just to break
even on one single pair paid out through a 16x.  That doesn't happen often;
far more often you pull through another 1600 from another pair, and then
a 4800 from a three-of-a-kind.  Yes, it's frustrating to lose 8000 from a
x8 full house, but you'll get that 8000 right back in two minutes--far better 
to take the ODDS-ON bet to get to 16000.  And more often than not, those 8000
full houses will become 16000 full houses.  Even when a [7] is showing.

You're playing for the long haul, not the short term.  As such, it is your
goal to maximize expected payouts, just like a casino does.  A casino doesn't
mind the occasional player who hits the jackpot, since it's a certainty 
that for each jackpot, there are numerous losses going right into their
pockets.  And here, you get to be the casino--you get to experience what
it's like to have the odds in your favor.

If you still aren't convinced, read chapter 7 on the mathematics behind
"High & Low", or just follow my system for 15 minutes.  You'll see in
no time that it works.



========================
  6 :: CASHING OUT
========================

So you've made a lot of Coins, probabaly hundreds of thousands, playing
Poker and High & Low.  Now, the question remains--how do you get cold hard
G out of it?  You can only spend Coins on selected items at the casino
prize store, none of which are the famed AG-05 AGWS.  

Cashing out proves to be an extremely tedious process.  The quickest way
to do it is to go to the EVS save point on board the Elsa, which is directly
next to a UMN Silver Plate, where you can sell items for G.  Empty your
inventory of Med Kits, Ether Packs, Revives, and Cure-Alls, and go back to
the Casino using the Casino Passport.  Select "Exchange", and this time
select "Prize Exchange".  You'll be presented with the items in the table
below.  The first item, the Recovery Set, will be your source for G. 
Claim 99 Recovery Sets, for 9900 Coins by hitting the Circle button
99 times.  The easiest way to do this is not to count, but to determine
your finishing point, e.g. if you have 328740 Coins, you will jam on Circle
until you are down to 319740, 9900 less than you started with.  Then,
exit the casino and go back to the Silver Plate.  Sell off all your
Med Kits, Ether Packs, Revives, and Cure-Alls again, which should net you
990 for the Med Kits, 1980 for the Ether Packs, 2970 for the Revives, and
4950 for the Cure-Alls.  The total for all of that comes to 10890 G, for
and exchange rate of 9900 Coins to 10890 G, or nearly 1:1.

This takes time, though, since you constantly have to reload the Elsa,
then the shop, then the Elsa, then the menu, then the Casino, then the
Elsa, not to mention all the button jamming.  Overall, it takes about
1 minutes to transfer one set of 99 Recovery Sets, or about 1 minute
per 10000 G.  That's 300000 G, enough for the AG-05, transfered out in
about half an hour.  Still, it's tedious work, much less exciting than
playing Poker and High & Low.

If you're interested in Xenocard, you can cash out booster packs extremely
cheaply, at only 100 Coins each, and you don't even have to go through
the selling.  With hundreds and thousands of booster packs, you will easily
get every (non-promotional) card in the game, even rares, in sets of three,
allowing you to make any deck you want.  Later in the game, you can even
get several promotional cards from the Casino.  Finally, you can check out
some nice production sketches for next to nothing, considering how quickly
you can acquire Coins.

Just remember to buy a full set of Recovery Sets after you finish selling
them, so that you don't find yourself in a dungeon without Revives or
Cure-Alls that might be essential.

* The list of prizes

 Cost  Name                  What it does                               Avail. 
==============================================================================
  100  Recovery Set          1x Med Kit, Ether Pack, Revive, Cure-All     *
  150  Escape and Rest Set   1x Escape Pack, Bio Sphere                   *
10000  Golden Dice           Access- Fluctuating damage based on HP       1
15000  Bravesoul             Access- Strength+ when HP low                1
18000  Revive DX             Item- Revives with max HP                    1
12000  Stim DX               Item- PATK+50% for one fight                 1
 2000  Design Sketch 01      Shion 1                                      1
 2000  Design Sketch 02      Shion 2                                      1
 2000  Design Sketch 03      Shion 3                                      1
 2000  Design Sketch 04      chaos 1                                      1
 2000  Design Sketch 05      chaos 2                                      1
 2000  Design Sketch 06      chaos 3                                      1
 2000  Design Sketch 07      Jr. 1                                        1
 2000  Design Sketch 08      Jr. 2                                        1
 2000  Design Sketch 09      Jr. 3                                        1
 2000  Design Sketch 10      Jr. 4                                        1
 2000  Design Sketch 11      MOMO 1                                       1
 2000  Design Sketch 12      MOMO 2                                       1
 2000  Design Sketch 13      MOMO 3                                       1
 2000  Design Sketch 14      KOS-MOS 1                                    1
 2000  Design Sketch 15      KOS-MOS 2                                    1
 2000  Design Sketch 16      Ziggy 1                                      1
 2000  Design Sketch 17      Ziggy 2                                      1
 2000  Design Sketch 18      Ziggy 3                                      1
 2000  Design Sketch 19      Gaignun 1                                    1
 2000  Design Sketch 20      Gaignun 2                                    1
 2000  Design Sketch 21      Elsa                                         1
 2000  Design Sketch 22      AG-01                                        1
 2000  Design Sketch 23      Cockpit                                      1
 2000  Design Sketch 24      VX-9000                                      1
 2000  Design Sketch 25      AG-04                                        1
 2000  Design Sketch 26      VX-20000                                     1
 2000  Design Sketch 27      VX-4000                                      1
 2000  Design Sketch 28      AG-05                                        1
 2000  Design Sketch 29      Shion CG                                     1
 2000  Design Sketch 30      KOS-MOS CG                                   1
  400  Starter Set           Xenocard- Starter Deck                       *
  100  Card Pack #1          Xenocard- Booster Pack 1                     *
  100  Card Pack #2          Xenocard- Booster Pack 2                     *
 1000  PM Card F             Xenocard- AG-05 Promotional Cards            1^
 1000  PM Card G             Xenocard- Third Armament Promotional Cards   1^
 1000  PM Card H             Xenocard- Testament Promotional Cards        1^
 1000  PM Card I             Xenocard- AG-04 Promotional Cards            1^
 1000  PM Card J             Xenocard- Phase Transition Cannon Pro. Cds.  1^
 1000  PM Card K             Xenocard- Invoke Promotional Cards           1^
 1000  PM Card L             Xenocard- Destiny Promotional Cards          1^
 1000  PM Card M             Xenocard- Dammerung Promotional Cards        1^
 1000  PM Card N             Xenocard- So Weak! Promotional Cards         1^
 1000  PM Card O             Xenocard- Rhine Maiden Promotional Cards     1^
 1000  PM Card P             Xenocard- Unknown Armament Promotional Cds.  1^
 1000  PM Card Q             Xenocard- Proto Dora Promotional Cards       1^

Key:  (1) 1 time only purchase, (*) Unlimited purchase,
      (^) Only available after Song of Nephilim completion



=======================================
  7 :: THE MATHEMATICAL EVIDENCE
=======================================

*** NOTE:  This portion of the guide goes into extremely boring detail
           about the mathematics of the "High & Low" game.  Skip unless
           you have a fondness for goofy counting problems, or you just
           don't believe me when I say how great the payout is.

At last, the heavy part of this guide.  I've made the claim that the
"Hi & Low" machine is hugely weighted in favor of the player, with an
expected payout of about 5.5 times what you put in to it.  I've used this
fact to argue that you should always play on until you get the 16x 
multiplier, regardless of the [7]s and [8]s and [9]s along your way.  I owe 
it to the reader to present some evidence of this besides my own personal 
experience.

How, then, do we caluculate the expected payout of something as complicated
as a series of decisions like this?  

* Scratch Off Game

The answer is that there actually IS NO DECISION at all taking place in the
"Hi & Low" game!  A winning layout is ALWAYS a winning layout, and a losing
layout always loses, assuming the player chooses logically, according to
probability, whether the next card will be high or low.  For example, 
consider the layout:

[K] [6] [9] [4] [8] 

Assuming the player doesn't go against the odds, this will always win!  It's
like a lottery scratch-off game, in that the results are pre-determined,
and you are simply slowly revealing whether you have a winner or loser.
A sane player will always pick "Low" on the [K], "High" on the [6], "Low"
on the [9], and "High" on the [4].  Thus, the logical player always wins
with this layout.

[K] [6] [T] [J] [2]

Similarly, this layout should always lose.  There is no reason a sane player
would ever pick "High" on the [T], and thus the player will always lose to
the [J].  

Because of this, we can analyze all of the possible layouts and determine
how many winners there are and how many losers.

This is a slight oversimplification, however.  The truth is, that a [7] card
presents a dilemma.  Either "High" or "Low" present equal probabilities of
winning.  Thus, a layout like:

[K] [2] [7] [4] [9]

might be a winner, if the player picks "Low", or it might be a loser if the
player picks "High".  Thankfully, this does not present a real problem from
a mathematical sense.  Regardless of which option the player picks on the
[7], there are an equal number of winning and losing layouts.  We can 
simplify the mathematics by assuming the player always picks "High" on a
[7], but the math will work out the same regardless of what system you use
to pick your [7]s.  

* Sampling - With or Without Replacement?

There is one more simplification I will do in order to make the math 
immensely less difficult.  However, this simplification, unlike the [7]
issue, actually does slightly affect the results.

When a card is selected from a deck of cards, it is removed from that deck
and placed face up on the table.  If the [K] of Spades is picked, there is
no longer a [K] of Spades left in the deck, and so it cannot be picked 
again.  This concept is known as "Sampling Without Replacement".  This
makes any mathematical analysis of the problem ridiculously complicated,
since every card selected modifies the probabilities of every other card
in the deck.  For instance, when the [K] is showing as the first card,
the probability of the second card being a [K] is only 3/51, while any other
card has a probability of 4/51.  This is because there are only 3 [K]s left
in the deck, and 4 of every other card.

We can create a model, however, where the card that is selected is still
available in the deck to be selected.  This will not get us an EXACT 
mathematically sound analysis of the game, but it will provide us with
an extremely close approximation.  Since the whole point of this chapter
is to show that the "Hi & Low" game is weighted heavily in your favor,
and not to determine the exact probability to the ninth decimal place,
I will use this model, "Sampling With Replacement", to make the math
bearable.  Now, there is always a 1/13 chance of drawing a [K], regardless
of which cards are showing.

This simplification will provide us with a valid approximation as to the
expected payout of the "Hi & Low" machine without requiring a degree in
statistics.

* Counting

In order to determine the probability of a winning layout, we need to be
able to count two things:  The total number of layouts and the number of
winning layouts.  

Counting the total number of layouts in our "Sampling With Replacement"
model is easy:  There are five slots, which can contain any of 13 cards
each.  Thus, there are 13^5 total possible layouts.  (Some of these layouts
aren't really valid, such as [2] [2] [2] [2] [2], but these are very few
and are a result of our model being used instead of the actual game without
replacement.)

Total Layouts

13 * 13 * 13 * 13 * 13 = 371293

Now, all we need to do is to count the winning layouts.  This is a bit
more difficult, since a winning layout isn't readily visible through
simple mathematical methods.  However, something else that will give us
the same result in the end, would be to count the number of LOSING layouts.
This is MUCH easier to do, since we can determine the number of layouts
that start with a losing combination, such as [T] [J], and subtract those
all off.

We need to do this in four seperate steps, since a losing layout can occur
at any of the four decision points.  However, once a layout is a loser, 
there is no point in checking it again, it has already lost.  

So, starting at the beginning, we need to find out how many layouts are
losers after the first round.  Then, we can count the number of remaining
layouts, and check ONLY THOSE to see if they lose in further rounds.

* Subtract Losing Layouts

There are four decisions that need to be made successfully in order to
pay out.  We need to determine the chance of surviving all four decisions.
You can note from the tables below that even with the worst card, a 7,
showing, there is still a greater than 50% chance of surviving the round.

-----------------------------
ROUND 1:  [*] [F] [ ] [ ] [ ] 
-----------------------------

To explain the following table:
* The "Card" column indicates the faced card (represented by [*] above).
* The "#L" and "#W" column indicates the number of different cards that will 
  lose or win when flipped (represented by [F] above).
* The "#[L,W] Layouts" column indicates the total number of layouts that
  will win or lose this round, given that initially faced card.  This is 
  determined by multiplying the number of losers by 13^3, and the same
  for the losers, to represent any card in the blank slots to be revealed
  later (represented by [ ] above).
* The "Total Losers" column keeps track of a running total of losing layouts
  with each card faced.
* The "Win%" column shows the approximate chance of winning this round given
  the faced card.  This is ALWAYS GREATER THAN 50%, even with a [7]!

Card   #L  #W     #[L,W] Layouts  Total Losers    Win%
[K]     0  13     [    0, 28561]        0        100.00%
[Q]     1  12     [ 2197, 26364]     2197         92.31%
[J]     2  11     [ 4394, 24167]     6591         84.62%
[T]     3  10     [ 6591, 21970]    13182         76.92%
[9]     4   9     [ 8788, 19773]    21970         69.23%
[8]     5   8     [10985, 17576]    32955         61.54%
[7]     6   7     [13182, 15379]    46137         53.85%
[6]     5   8     [10985, 17576]    57122         61.54%
[5]     4   9     [ 8788, 19773]    65910         69.23%
[4]     3  10     [ 6591, 21970]    72501         76.92%
[3]     2  11     [ 4394, 24167]    76895         84.62%
[2]     1  12     [ 2197, 26364]    79092         92.31%
[1]     0  13     [    0, 28561]    79092        100.00%

That leaves 79092 layouts that lose on the first of four decisions.
Result:  292201 winning layouts, for a 78.70% chance of surviving round 1.

-----------------------------
ROUND 2:  [#] [*] [F] [ ] [ ] 
-----------------------------

Now, we have to examine the possible cards that are left for round 2.
What did we advance with?  We can analyze all possible winning combinations
from the previous round:

If the faced card is a...     ... we can advance with any of these.
[K]                                    KQJT987654321
[Q]                                     QJT987654321
[J]                                      JT987654321
[T]                                       T987654321
[9]                                        987654321
[8]                                         87654321
[7]                                    KQJT987
[6]                                    KQJT9876
[5]                                    KQJT98765
[4]                                    KQJT987654
[3]                                    KQJT9876543
[2]                                    KQJT98765432
[1]                                    KQJT987654321

Now, we can add up the number of occurences of each card to determine
the frequency of this card being used to start the next round.  As you can
see from the table, [8] and [7] are a bit more likely to be showing up here
than numbers at the extreme ends.

[K] 8,  [Q] 9,  [J] 10, [T] 11, [9] 12, [8] 13, 
[7] 13, [6] 12, [5] 11, [4] 10, [3] 9,  [2] 8, 
[1] 7

This time, there are only 3 cards left to flip.  We can calculate the number
of losing layouts with each card showing, but then we have to multiply by
the number of cases in which this card will be showing to get the total
number of times this combination occurs.  

The new "xOccur" column represents this.  Also, the "Total Losers" column
is now multiplied by "xOccur", to count all of the losers regardless of
what the first card is.

Card   #L  #W     #[L,W] Layouts  xOccur.  Total Losers    Win%
[K]     0  13     [   0, 2197]        8          0        100.00%
[Q]     1  12     [ 169, 2028]        9       1521         92.31%
[J]     2  11     [ 338, 1859]       10       4901         84.62%
[T]     3  10     [ 507, 1690]       11      10478         76.92%
[9]     4   9     [ 676, 1521]       12      18590         69.23%
[8]     5   8     [ 845, 1352]       13      29575         61.54%
[7]     6   7     [1014, 1183]       13      42757         53.85%
[6]     5   8     [ 845, 1352]       12      52897         61.54%
[5]     4   9     [ 676, 1521]       11      60333         69.23%
[4]     3  10     [ 507, 1690]       10      65403         76.92%
[3]     2  11     [ 338, 1859]        9      68445         84.62%
[2]     1  12     [ 169, 2028]        8      69797         92.31%
[1]     0  13     [   0, 2197]        7      69797        100.00%

That leaves 69797 layouts that lose on the second of four decision.
We had 292201 winning layouts from the first round, giving us a chance of
76.11% of surviving specifically round 2, and a 59.90% chance of making it
all the way to round 3.
Result:  222404 winning layouts, for 59.90% chance of surviving round 2.

-----------------------------
ROUND 3:  [#] [#] [*] [F] [ ] 
-----------------------------

For this round, we again have to determine the number of combinations that 
will start with each specific card.  This time, however, it's not as 
simple, since the third card likelihood is derived from the second card
likelihood (remember that certain cards are less likely to be showing since
we tend to lose with them, ending the game).

How often is a King showing for the third card?  Well, we know that a King
shows up 8 times out of 13 as a winner, and the other 5 times it ended our
game.  However, EVERY time a 7 shows up it wins--there is no case where
a 7 is a loser if you always pick according to the odds.  Because of this,
we're a lot more likely to be seeing 7s at this point than extreme numbers,
since often the extreme numbers ended our game.

We need to count how many combinations there are that have left us with
each card, and it's not so easy this time.  The number of combinations
from round 2 for cards that would make our card a winner are added up
to figure out the total number of combinations that would leave us with
this card faced.

K: Wins on K7654321, for 8+13+12+11+10+9+8+7 = 				 78.
Q: Wins on KQ7654321, for 8+9+13+12+11+10+9+8+7 = 			 87.
J: Wins on KQJ7654321, for 8+9+10+13+12+11+10+9+8+7 = 			 97.
T: Wins on KQJT7654321, for 8+9+10+11+13+12+11+10+9+8+7 =		108.
9: Wins on KQJT97654321, for 8+9+10+11+12+13+12+11+10+9+8+7 =		120.
8: Wins on KQJT987654321, for 8+9+10+11+12+13+13+12+11+10+9+8+7 =	133.
7: Wins on KQJT987654321, for 8+9+10+11+12+13+13+12+11+10+9+8+7 =	133.
6: Wins on KQJT98654321, for 8+9+10+11+12+13+12+11+10+9+8+7 =		120.
5: Wins on KQJT9854321, for 8+9+10+11+12+13+11+10+9+8+7 =		108.
4: Wins on KQJT984321, for 8+9+10+11+12+13+10+9+8+7 = 			 97.
3: Wins on KQJT98321, for 8+9+10+11+12+13+9+8+7 = 			 87.
2: Wins on KQJT9821, for 8+9+10+11+12+13+8+7 = 				 78.
1: Wins on KQJT981, for 8+9+10+11+12+13+7 =				 70.

This time, the math isn't so obvious, so to verify that this actually works,
I'll list out all 78 non-losing combinations that end with a king faced.

KKK K7K K6K K5K K4K K3K K2K K1K 
    Q7K Q6K Q5K Q4K Q3K Q2K Q1K
    J7K J6K J5K J4K J3K J2K J1K
    T7K T6K T5K T4K T3K T2K T1K
    97K 96K 95K 94K 93K 92K 91K
    87K 86K 85K 84K 83K 82K 81K
7KK 77K 
6KK 67K 66K
5KK 57K 56K 55K
4KK 47K 46K 45K 44K
3KK 37K 36K 35K 34K 33K
2KK 27K 26K 25K 24K 23K 22K
1KK 17K 16K 15K 14K 13K 12K 11K

Feel free to list out combinations for any other card, or just trust
my math above.

Now, to do the tables for round 3, since we know the number of appearances
for each card.

Card   #L  #W     #[L,W] Layouts  xOccur.  Total Losers    Win%
[K]     0  13     [  0, 169]         78          0        100.00%
[Q]     1  12     [ 13, 156]         87       1131         92.31%
[J]     2  11     [ 26, 143]         97       3653         84.62%
[T]     3  10     [ 39, 130]        108       7865         76.92%
[9]     4   9     [ 52, 117]        120      14105         69.23%
[8]     5   8     [ 65, 104]        133      22750         61.54%
[7]     6   7     [ 78,  91]        133      33124         53.85%
[6]     5   8     [ 65, 104]        120      40924         61.54%
[5]     4   9     [ 52, 117]        108      46540         69.23%
[4]     3  10     [ 39, 130]         97      50323         76.92%
[3]     2  11     [ 26, 143]         87      52585         84.62%
[2]     1  12     [ 13, 156]         78      53599         92.31%
[1]     0  13     [  0, 169]         70      53599        100.00%

That leaves 53599 layouts that lose on the third of four decisions.
We had 222404 winning layouts from the second round, giving us a chance of
75.90% of surviving specifically round 3, and a 45.46% chance of making it
all the way to round 4, the final round
Result:  168805 winning layouts, for 45.46% chance of surviving round 3.

-----------------------------
ROUND 4:  [#] [#] [#] [*] [F] 
-----------------------------

To calculate the number of combinations with each card faced for the final
round, we can use the same method we used for round 3, plugging in the
round 3 numbers in place of the round 2 numbers.

So, for example, the King calculation would look like:
K: Wins on K7654321, for 78+133+120+108+97+87+78+70 = 			 771.

Here's the table, with the "Wins on" line eliminated to save space:
K: 78+133+120+108+97+87+78+70 = 					 771.
Q: 78+87+133+120+108+97+87+78+70 =					 858.
J: 78+87+97+133+120+108+97+87+78+70 =					 955.
T: 78+87+97+108+133+120+108+97+87+78+70 =				1063.
9: 78+87+97+108+120+133+120+108+97+87+78+70 =				1183.
8: 78+87+97+108+120+133+133+120+108+97+87+78+70 =			1316.
7: 78+87+97+108+120+133+133+120+108+97+87+78+70 =			1316.
6: 78+87+97+108+120+133+120+108+97+87+78+70 =				1183.
5: 78+87+97+108+120+133+108+97+87+78+70 =				1063.
4: 78+87+97+108+120+133+97+87+78+70 =					 955.
3: 78+87+97+108+120+133+87+78+70 =					 858.
2: 78+87+97+108+120+133+78+70 = 					 771.
1: 78+87+97+108+120+133+70 =						 693.

Now, we can finally trim off the last round losers, leaving us with the
number of winning combinations.  (We've already trimmed all of the layouts
that lost before the last round.)

Card   #L  #W     #[L,W] Layouts  xOccur.  Total Losers    Win%
[K]     0  13     [ 0, 13]          771          0        100.00%
[Q]     1  12     [ 1, 12]          858        858         92.31%
[J]     2  11     [ 2, 11]          955       2768         84.62%
[T]     3  10     [ 3, 10]         1063       5957         76.92%
[9]     4   9     [ 4,  9]         1183      10689         69.23%
[8]     5   8     [ 5,  8]         1316      17269         61.54%
[7]     6   7     [ 6,  7]         1316      25165         53.85%
[6]     5   8     [ 5,  8]         1183      31080         61.54%
[5]     4   9     [ 4,  9]         1063      35332         69.23%
[4]     3  10     [ 3, 10]          955      38197         76.92%
[3]     2  11     [ 2, 11]          858      39913         84.62%
[2]     1  12     [ 1, 12]          771      40684         92.31%
[1]     0  13     [ 0, 13]          693      40684        100.00%

That leaves 40684 layouts that lose on the fourth of four decisions.
We had 168805 winning layouts from the third round, giving us a chance of
75.90% of surviving specifically round 4, and a 34.51% chance of making it
all the way through all four rounds and coming out a winner.
Result:  128121 winning layouts, for 34.51% chance of paying out.


* Conclusion
Assuming our sampling simplification is a reasonable approximation for the
actual probabilities of the "Hi & Low" portion of the Poker game, we see
that the approximate chances of paying out 16x is 34.51%.  That's very
near 1/3 of the time.  So, assuming you always play "Hi & Low" on every
winning poker hand, and always continue on to the end regardless of what
numbers show up, you will multiply your poker winnings by 16 approximately
one third of the time, and go home empty two thirds of the time.  Using
simple probability, the expected multiplied payout of "Hi & Low" is:

(16 * .3451) + (0 * .6549) = 5.5216.

That means over the long run you will win 5.5 times what you put in.
This is a HUGE bias in favor of you, the player.  In a real-life casino,
you will be lucky to get a machine that pays out a bit below 1.  Any
casino that paid out any multiplier over 1 would go broke in no time,
and if a casino could pay out the inverse of the "Hi & Low" game, (1/5.5216)
or 0.1811, they would rack up fortunes as fast as you can!  Of course,
nobody in their right mind would play on a machine such as that.  Thankfully
for you, the Durandal casino isn't in its right mind!



===================================
  8 :: COPYRIGHT INFORMATION
===================================

Copyright (c)  2003  James Doyle / "Kadamony"
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.2
or any later version published by the Free Software Foundation;
with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
A copy of the license is available at: http://www.gnu.org/licenses/fdl.txt