Mass Effect – Quasar Guide

=======================================================================
                             Mass Effect
                         Quasar Gambling Guide
                            by Sherwin Tam
=======================================================================


=================
TABLE OF CONTENTS
=================
1. Quick Summary
2. Rules
3. General Tips
4. Expected Value
5. The Numbers
  A. The No-Brainers:    17 - 20
  B. Do You Feel Lucky?  15 - 16
  C. The Sweet Spot:     13 - 14
  D. Reach for the Moon:  9 - 12
  E. Transitions:         6 -  8
  F. The Starting Five:   1 -  5
6. Disclaimer


================
1. QUICK SUMMARY
================
For those that just want to know what to do without all that explanation stuff,
here are my recommendations:

Number   Action
------   ---------
17-20    [Pay Out]
16       [Add 1-8]
13-15    [Add 4-7]
9-12     [Add 1-8]
6-8      [Add 4-7]
3-5      [Add 1-8]
1-2      [Add 4-7]


========
2. RULES
========
Quasar is a gambling game in Mass Effect that you can play in Flux, a club in
the Citadel Ward.  It plays similarly to the card game black jack:

*  After you pay 200 credits to play a round, you're given a random number from
   1 to 5.
*  You have the option to either add a random number from 4 to 7 by pressing X
   on the controller, or add a random number from 1 to 8 by pressing Y.
*  If the number is 14 or below, you must continue to add to the number.
*  Starting from 15, you can choose to "pay out" by pressing A to finish the
   round and receive credits:

   Number   Payout
   ------   ------
     20      400
     19      300
     18      250
     17      200
     16      100
     15       50

*  If you get to 21 or more, you "bust" (lose) and don't receive any payout.

The payouts here are for high stakes quasar; divide all credit amounts by 10 if
you're playing low stakes quasar.


===============
3. GENERAL TIPS
===============
*  Save your game before playing.  Sure, that's sorta cheating the system, but
   you won't care once you're down a thousand creds.  Load your last save, and
   presto, no debt.

*  Don't bother playing low stakes quasar, especially if you follow the above
   advice about saving.  Quasar's earnings aren't that great to begin with, so
   playing to earn a trickle of credits just isn't worth your time.

*  The recommendations here should give you the best chance at winning money,
   but of course they don't guarantee that you win every time, only that you
   should win more on average.  You won't make money at every sitting, and
   sometimes luck will just give you a bad streak.  That's just how it goes
   when you're gamblin'.

*  All the numbers here assume that you have an equal chance at getting any of
   the numbers in a given random range.  If the game is weighted somehow, all
   bets are off (natch), and shame on you, Bioware, for rigging your own
   single-player video game.


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4. EXPECTED VALUE
=================
To arrive at my recommendations, I calculated the expected value for each
number.  For those that don't know what "expected value" is, it's a math term
for random values where you take the average of each possible value times the
probability that you'll get that value.  For instance, if you roll a six-sided
die, you have a 1/6th chance of getting any side.  The expected value is:

(1 * 1/6) + (2 * 1/6) + (3* 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) = 3.5

Why is the expected value important?  Expected value represents the average
value you should receive when repeatedly generating a random number with the
same probabilities.  When applied to quasar, expected value represents the
average payout you should get when choosing what random number to add.  For
example, if you're sitting at 15 and choose to [Add 4-7] to the number, you
have an equal chance (1/4) of ending up with 19, 20, 21, or 22.  Thus, your
expected value using the payouts for those numbers is:

(300 * 1/4) + (400 * 1/4) + (0 * 1/4) + (0 * 1/4) = 175

That is, if you chose to [Add 4-7] whenever you had a 15 (and then paid out on
a 19 or 20), over many tries you should expect to get an average of 175
credits.

To find the best strategy, then, we need to figure out the expected value for
each action you can take at each number ([Add 4-7], [Add 1-8], or [Pay Out] in
some cases) and choose the action that gives the largest expected value, as
that choice represents your best chance at coming out ahead.

Note that for the calculations, I use profit for the expected value, not
payout.  When accounting for the initial cost to play, the profit for each
payout is:

Number   Profit
------   ------
  21+     -200
  20      +200
  19      +100
  18       +50
  17         0
  16      -100
  15      -150


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5. THE NUMBERS
==============
Calculations for lower numbers always use the highest expected profits of the
relevant numbers above them.

For the curious, the top five numbers in expected profit are:

Rank  Number   Expected Profit
----  ------   ---------------
 #1     20         +200.00
 #2     19         +100.00
 #3     13          +87.50
 #4      7          +51.15
 #5     18          +50.00

The bottom five numbers in expected profit are:

Rank  Number   Expected Profit
----  ------   ---------------
#16     10          +21.67
#17      9          +18.13
#18     17            0.00
#19     15          -25.00
#20     16          -56.25


-------------------------
A. The No-Brainers: 17-20
-------------------------
The easiest numbers to decide on are the ones with payouts that don't involve
you losing money.  You should always [Pay Out] when you reach 17 or higher, as
your chances of busting are very high if you continue, and you don't lose
credits for stopping.  [Add 4-7] is obviously bad, as you'll bust no matter
what, but your chances are too low to [Add 1-8] and expect much better, even at
the break-even of 17.

                      EXPECTED PROFIT
Number  [Add 4-7]  [Add 1-8]  [Pay Out]  Recommended Action
------  ---------  ---------  ---------  ------------------
  20     -200.00    -200.00    +200.00       [Pay Out]
  19     -200.00    -150.00    +100.00       [Pay Out]
  18     -200.00    -112.50     +50.00       [Pay Out]
  17     -200.00     -81.25       0.00       [Pay Out]


---------------------------
B. Do You Feel Lucky? 15-16
---------------------------
After the positive payouts, we drop like a rock to the two worst numbers you
can fall on.  15 and 16 are the only two numbers with a negative best expected
profit.  They're both bad in that they're very close to profitability, but also
very close to busting, and the money you'll lose busting is more than you can
usually expect if you don't.  Despite that, it's better in both cases to take
your chances, because the chance you won't bust is better than what the house
is giving you if you chicken out.

                      EXPECTED PROFIT
Number  [Add 4-7]  [Add 1-8]  [Pay Out]  Recommended Action
------  ---------  ---------  ---------  ------------------
  16     -100.00    -56.25     -100.00       [Add 1-8]
  15      -25.00    -38.28     -150.00       [Add 4-7]


------------------------
C. The Sweet Spot: 13-14
------------------------
After the carnage of 15-16, we get to a good pair of numbers outside of the
straight payouts of 17-20.  13 guarantees that you won't lose money for the
round, as you can only get a 17-20 if you [Add 4-7].  14 gives you a good
chance of getting a positive profit, although the chance at busting brings down
the expected profit a bunch.  Make sure you don't choose to [Add 1-8], as you
open yourself to the pain of stumbling on 15 or 16, or just plain busting more.

                EXPECTED PROFIT
Number  [Add 4-7]  [Add 1-8]  Recommended Action
------  ---------  ---------  ------------------
  14     +37.50     -16.41        [Add 4-7]
  13     +87.50     +13.28        [Add 4-7]


---------------------------
D. Reach for the Moon: 9-12
---------------------------
For 9-12, the strategy for adding really shifts to trying to get to the sweet
spot of 13-14 or skipping directly to 17-20 without hitting 15-16.  Choosing
[Add 1-8] gives you a bigger range to avoid the bad numbers; 10-11 especially
have a 50% chance to get 15-16 if you choose [Add 4-7] instead, and the low
payouts at 17 and 18 result in negative expected profit with the wrong choice.

                EXPECTED PROFIT
Number  [Add 4-7]  [Add 1-8]  Recommended Action
------  ---------  ---------  ------------------
  12     +23.44     +49.22        [Add 1-8]
  11      -7.81     +30.37        [Add 1-8]
  10     -10.94     +21.67        [Add 1-8]
   9     +10.94     +18.13        [Add 1-8]


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E. Transitions: 6-8
-------------------
Below 9, you aren't able to reach the good payouts at all, so the focus changes
to getting to one of the better numbers in the middle range.  7 in particular
is a good number to hit, as [Add 4-7] gives you a number in the range of
11-14, all of which have a high expected profit.  The profit at 6 is also good,
while 8 dips because of the 25% chance to end up with a 15.

                EXPECTED PROFIT
Number  [Add 4-7]  [Add 1-8]  Recommended Action
------  ---------  ---------  ------------------
   8     +37.30     +20.39        [Add 4-7]
   7     +51.15     +32.09        [Add 4-7]
   6     +47.19     +41.60        [Add 4-7]


-------------------------
F. The Starting Five: 1-5
-------------------------
You start with a random number from 1-5, so you don't get much sway this far
down the totem pole.  However, there's still some clear differences in expected
profit for some of the starting values.  Of note are the relatively high
expected profits around 12-13, which bump up the profits for [Add 1-8] to 4
and 5.  After that, 3 is pretty close either way, and 1-2 lowers the random
range to give bigger sway to the high expected profits from 5-7.

                EXPECTED PROFIT
Number  [Add 4-7]  [Add 1-8]  Recommended Action
------  ---------  ---------  ------------------
   5     +29.85     +42.82        [Add 1-8]
   4     +26.87     +37.23        [Add 1-8]
   3     +32.06     +35.73        [Add 1-8]
   2     +38.44     +36.40        [Add 4-7]
   1     +44.62     +38.50        [Add 4-7]


=============
6. DISCLAIMER
=============
This guide is made by Sherwin Tam, copyright 2007.  Please contact me at
sherwintam (at) yahoo (dot) com if you see any glaring errors, and please
don't use this without my permission.