What Are the Odds to “Draw 2?” Part 3

From last time we have that with

Probability Part 3 Equations 1

The change in odds when your opponent plays a special card and thereby draw two cards is

Probability Part 3 Equations 2

If this difference is positive, the odds go up.  If this difference is negative, the odds go down.  Let’s expand this formula and see where it can be simplified

Probability Part 3 Equations 3

Notice that the fraction shown in the first set of brackets must be positive.  We can set that aside for now since what we’re really interested in is when this formula is equal to zero.

Probability Part 3 Equations 4

Notice that the fraction in the left hand brackets must be positive.  Again we can set that aside for since what we’re really interested in is when this formula is equal to zero.

This leaves us with the formula and the information we need.  When a “draw 2 cards” special is played, the odds that this player holds another are…

When Probability Part 3 Equations 5 < 0, the odds decrease.

When Probability Part 3 Equations 5 = 0, the remain unchanged.

When Probability Part 3 Equations 5 > 0, the odds increase.

Hopefully, all this math will put a useful tool in your designer’s toolbox–and all arose from an off-handed comment I made about probability.

What do you think of “draw 2 cards” cards?  Have you incorporated them into your designs?  What did you learned from the experience? Do they improve a design or weaken it?  Share with your fellow readers in the comments below.  And if you’re enjoying what you’re reading, create an account with WordPress and follow this blog.  If you keep reading, I’ll keep writing.

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