Pirate Gold (Treasure Hunt)
Simple Pairs

Pirate Gold is often recommended for children, but it's a fun, fast-paced game for anyone who has a minute to fill, regardless of age! You deal two rows of five cards each, and then keep covering pairs of cards having the same rank. You win if you can use up the entire deck of cards (you will end up with five pairs left showing), or the game can end in a loss if there are no more pairs to cover. Simple Pairs is played similarly, but with nine piles instead of ten.

Exact Win Rates

Rather than estimating the win rate of this game by playing many simulated deals, I was able to compute the exact odds of winning! Besides the normal 10 piles, I also computed the win rate when using 9 piles to play Simple Pairs, as well as 6, 8, or 12.

In order to avoid rounding, the exact win rate for Pirate Gold can be expressed as a fraction:

     3,384,988,980,058,254,648,013,079,595,325,921
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     5,957,455,641,325,123,725,555,208,208,390,625
    

The exact win rate for Simple Pairs, expressed as a fraction:

     6,672,005,774,126,943,561,852,689,117,778,833
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    27,355,663,659,145,976,290,814,731,569,140,625
    

Including Jokers

I like to include two jokers as a 14th rank. The following table shows the win rates when including Jokers:

Including jokers reduces the win rate, although not as much as decreasing the number of piles.

Two Decks

Solitaire.io previously described a variant of Pirate Gold that uses two decks of cards. This drops the win rate a bit more than you might expect, down to 24.5%, or just 3.4% for Simple Pairs.

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