Simulations revealed that for an unbiased program the AGT should be equal to 3.96 and the ATSV to -32.29 over a large number of games. Fortunately this is easily done via simulation. Note that for the ATSV to be independent of the player, we assume that a player who concedes a game must expose all unseen cards in a random order (although the player can choose which unseen card to expose first, he cannot avoid the fact each unseen card occurs with equal probability). If we compute the TSV whenever a new card is exposed we can calculate the average TSV (ATSV) statistic for a single game. The reason for taking the negative is to ensure that higher values indicate more chances of winning just like the AGT. In the above example, seven Queens and two Jacks would contribute to the sum. Hence I defined the total square variation (TSV), obtained by taking the negative sum of squares of the count of adjacent ranks. For instance if there are seven Queens but only two Jacks in play problems can occur even with one or more empty columns. Note that the AGT is independent of the player so it is easy to simulate the probability distribution of the AGT by running a large number of trials (that is, dealing a large number of rows).įrom my experience, I noted that a player can also get into trouble if the overall distribution of cards is poor. If the GT is low for a number of rounds, the player may get into trouble. In this way we can calculate the average GT (AGT). We can do a similar calculation whenever a new row of ten cards is dealt (and pretending it is the start of a new game). Once the first ten cards are dealt we can calculate the guaranteed turns (GT), that is the minimum number of cards a player can be sure of exposing before being forced to deal another row. Typical scatterplot for Spider solitaire (o = win, x = loss).
(the AGT and ATSV statistics are defined below) where blue circles and red crosses indicate wins and losses respectively.
The idea is to estimate what value these test statistics would take in a perfectly fair, unbiased game and then compare them to the values recorded in a game we suspect might be biased. Test statisticsįor each game played we wish to record a set of statistics that reflect the luck of the cards, so higher values indicate more chances of winning. Since there are kings in a total of cards, the chance of a single one of the exposed cards being a king is The expected number of exposed kings is therefore If after a large number of games we find the number of kings exposed is closer to on average then we will have reason to believe the program is biased. For instance, we know that there are 10 cards exposed in the starting position. If at any point in the game there are cards unseen, each card should have a chance of appearing as the next card turned over (for sake of argument we will ignore the equivalence of cards with identical suit and rank). Ideally, a Spider program should simulate a game played manually using physical playing cards and assuming perfect shuffling. By experimenting with Brown's strategies, I am indeed able to achieve He also points out his play is not perfect and an expert player could do even better, perhaps Popular belief suggests that very few games can be won under these conditions,īut Steve Brown ( California State University, Long Beach) gives some detailed strategies in his excellentīook Spider solitaire winning strategies and reports a win rate of 48.7% over 306 (declining a game with a poor initial deal), and that he or she is playing to win without regard to score, time taken "a Spider program is biased") is likely to be true or not.įor purposes of this article we will assume the player is playing with no "undo", "restart", or "mulligans" This can also serve as a good exercise of how one can use data observed in the real world and statistical techniques to test whether an hypothesis (e.g. However, with some elementary statistical techniques, it should be possible to validate or Of course users can also be on tilt and play below More specifically, ifĪ program detects the player has a high win rate, then it will "rig the cards" on subsequent games toĪrtificially reduce the win rate.
#Tarantula solitaire plus software
Users have been known to complain about various software programs being biased. Spider solitaire is played with two standard decks of cards.
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