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Optimal Strategy for Mass Effect's Quasar game

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Summary

On this page I show how to optimally play the gambling mini-game Quasar (from BioWare's Mass Effect game), and I state what the expected returns are when it is played optimally.

Spoiler Warning

If you haven't played Mass Effect yet and you want to try to figure out how to play Quasar for yourself, then stop reading now.

Rules of Quasar

Quasar is a bit like blackjack: you need to get your total as close as possible to 20 without going over it. You start on a random total in the range 1 to 5. If your total goes over 20, you lose (i.e., get 0 payout). Each turn, you must pick one of three options:

1. Take the payout and end the game.
   • If total = 20, payout = 40;
   • if total = 19, payout = 30;
   • if total = 18, payout = 25;
   • if total = 17, payout = 20;
   • if total = 16, payout = 10;
   • if total = 15, payout = 5;
   • otherwise, payout = 0.
2. Add a random number in the range 4 to 7 to the total.
3. Add a random number in the range 1 to 8 to the total.

It seems pretty obvious that if your total is about 18 or more, you should take the payout. Beyond that the optimal strategy isn't clear at first.

Summary of optimal strategy

Here is the optimal strategy:

• Whenever the total is 17 or more, take the payout.
• Whenever the total is 3, 4, 5, 9, 10, 11, 12, or 16, choose option c. above (add a random number in the range 1 to 8).
• Otherwise (whenever the total is 1, 2, 6, 7, 8, 13, 14, or 15), choose option b. above.

To see this strategy in the form of a table, download the details PDF document, described below.

Here is the expected payout for each of the 5 possible starting totals:

• If starting total = 1, expected payout = 24.46;
• if starting total = 2, expected payout = 23.84;
• if starting total = 3, expected payout = 23.57;
• if starting total = 4, expected payout = 23.72;
• if starting total = 5, expected payout = 24.28.

(These results apply to high stakes Quasar too; just multiply all the payouts by 10.)

Since the game costs 20 to play, Quasar is a profitable game. Whether it is worth your time to repeatedly play Quasar is another matter: I estimate that, playing high stakes Quasar, it would take about an hour to make a profit of 10,000.

Details

I worked this out in Mathematica. You can download a PDF document showing how I worked it out. The PDF document contains more detail on the results, and it also gives the results when either option b. or option c. (above) are excluded from the game.

Please email me if you have any comments or questions.

By Andrew Moylan (email).