Annotated output from the automatic solitaire playing program. This uses a pretty simple strategy, which seems to win about one time in thirty, and gets partial wins sufficient to lose only about $1.68 per game over the long haul. [Output from various runs of many games. "exp value" is the average number of cards raised up (i.e., the ones you get $5 for). If the average were ever 10.40, we would break even for that set of runs. Unfortunately, as you can see, averages over fairly large sets of games tend to be about 10.06 +- 0.15 so at least with the present strategy it looks unlikely that one could even break even in a long set of games.] For this run, numgames and exp value are 32768 10.129150390625 For this run, numgames and exp value are 32768 10.155731201171875 For this run, numgames and exp value are 32768 10.046051025390625 For this run, numgames and exp value are 32768 10.07061767578125 [100 repetitive, boring lines deleted] For this run, numgames and exp value are 32768 10.0517578125 For this run, numgames and exp value are 32768 10.061248779296875 For this run, numgames and exp value are 32768 10.093719482421875 For this run, numgames and exp value are 32768 10.1175537109375 For this run, numgames and exp value are 32768 10.097442626953125 For this run, numgames and exp value are 32768 10.058441162109375 For this run, numgames and exp value are 32768 10.0125732421875 For this run, numgames and exp value are 32768 9.897796630859375 For this run, numgames and exp value are 32768 10.047515869140625 For this run, numgames and exp value are 32768 10.073883056640625 total games played: 3618364 Average number of cards raised up is 10.0644, that is, this strategy tends to lose $1.67732793 per game. In the following table, the number in the second column is the number of games among those 3,618,364 in which I was able to raise n cards for the $5, where n is the number in the first column. Thus for example in 20,568 of the games (0.6%) I never found an Ace. Observe that in about half the games, I was only able to raise 7 or fewer cards up. 0 20568 1 71967 2 158243 3 246657 4 314696 5 350063 6 344655 7 321322 8 283372 9 243280 10 202712 11 168035 12 136813 13 112636 14 90555 15 73704 16 59979 17 49245 18 39939 19 33204 20 26807 21 22369 22 18486 23 15138 24 12439 25 10660 26 8973 27 7257 28 6133 29 5380 30 4643 31 4070 32 3524 33 3235 34 2710 35 2297 36 1990 37 1776 38 1482 39 1310 40 1103 41 1025 42 838 43 790 44 543 45 618 46 322 47 455 48 219 49 298 There are no entries next to 50 or 51 since it is impossible to be left with precisely 1 or 2 cards to be raised up. (I'm sure that virtually all the cases counted in the last few lines could have been won by a human willing to move cards around. But this would only increase the average number of cards raised by a few 0.001's -- possibly decreasing average loss by about a penny. Next to '52' would be the total of all the remaining games -- those in which all cards were raised to their suit pile, and the maximum $260 is won. Stupidly, I did not record this number but if I did the subtractions correctly, this happened in 129829 of the 3618364 games (which is 3.58806% of the games: one out of every 27.87 games). Could I break even with some cleverness? Let's suppose I managed to completely win all the games in which the computer got more than half of the cards raised. That would mean winning about half-again more games (181847 total, out of 3618364 games: just over 5% (one in 20) fully won). In that case I would still lose $1,015,918, i.e. about 28 cents per game. If I could also bring the 8973 26-cards-moved-up games to the full-win column, I finally clear a profit ($150,572 -- about 4 cents per game). Of course it would be far more helpful to move up just one or two additional cards whenever the computer manages to move a dozen or so, but in my experience there are not many opportunities for human intervention in those cases. I conclude it is possible but perhaps unlikely to design a program which will play the game with an expected net profit, and that even a very good program cannot expect to win as many as one game in ten. But these are simply estimates!