Dween
Joined: Jan 24, 2010
• Posts: 339
March 10th, 2011 at 12:20:00 PM permalink
Here is my final analysis of the Money Cards on Card Sharks. Each mini-system ran 1,000,000 times. Here is what each term represents:
50% Always bet half the bankroll, rounded up to nearest \$50 Always bet 75% of the bankroll, rounded up to nearest \$50 Always bet the whole bankroll Bet fraction of bankroll: WrongCards÷RightCards Bet fraction of bankroll: WrongCards÷RightCards, plus \$50 Bet fraction of bankroll: RightCardsInclTies÷TotalCards Bet fraction of bankroll: RightCardsInclTies÷TotalCards, plus \$50 Bet fraction of bankroll: (RightCardsInclTies+4)÷TotalCards Number of times player busts out Average amount won Average amount won, disregarding busts Best score for algorithm Average win * Bust % Never change cards Anytime a card comes up that's between 5 and J, change it Anytime a card comes up that's between 6 and 10, change it Change 1st card on line if 7-9, change 2nd if 6-10, change last if 5-J

RightCards is how many cards left in the deck would result in a correct call.
WrongCards is how many cards left in the deck would result in incorrect call.
RightCardsInclTies is how many cards left in deck would result in a correct OR push call.
TotalCards is how many cards are left in the deck.
Wager 50% 75% 100% Hilo Frac HLFrac+50 Btie/Tot Btie/Tot+50 Btie/Tot,+4
Change None None None None None None None None
Busts 45 11010 643234 4172 29452 10479 66990 70607
Avg Win 1911 3026 4768 3350 3650 3713 4024 4152
Avg(nobust) 1911 3059 13366 3364 3761 3752 4313 4468
Max win 5650 13650 32000 30400 31000 30500 32000 32000
Risk 1911 2992 1701 3336 3543 3674 3755 3859
Change Any 5-J Any 5-J Any 5-J Any 5-J Any 5-J Any 5-J Any 5-J Any 5-J
Busts 23 5522 546110 3931 26312 8822 53407 80165
Avg Win 2320 3997 6824 4961 5377 5404 5846 6128
Avg(nobust) 2320 4019 15036 4981 5523 5452 6176 6662
Max win 5650 13650 32000 31600 32000 32000 32000 32000
Risk 2320 3974 3097 4942 5236 5357 5534 5636
Change Any 6-10 Any 6-10 Any 6-10 Any 6-10 Any 6-10 Any 6-10 Any 6-10 Any 6-10
Busts 7 4692 538156 3979 28303 9397 54793 78774
Avg Win 2360 4087 7042 4999 5449 5469 5952 6216
Avg(nobust) 2360 4106 15248 5019 5608 5521 6297 6747
Max win 5650 13650 32000 31600 32000 31650 32000 32000
Risk 2360 4068 3252 4979 5295 5418 5625 5726
Change 7, 6, 5 7, 6, 5 7, 6, 5 7, 6, 5 7, 6, 5 7, 6, 5 7, 6, 5 7, 6, 5
Busts 7 4644 534124 4077 27968 9387 55220 80642
Avg Win 2371 4118 7129 5057 5520 5526 6046 6272
Avg(nobust) 2371 4137 15304 5077 5679 5578 6399 6822
Max win 5650 13650 32000 32000 32000 31650 32000 32000
Risk 2371 4099 3321 5036 5366 5474 5712 5766

* The strategies tend to improve moving down and to the right (save for the 100% method, which is high-risk).
* The "Bet 100%" method busts over half the time, so even though it has a higher average, the RISK value is lower.
* "Bet 50%" almost never busts, but has a low average, and you'll never win more than \$5,650.
* If you keep your bet consistent with the probability of making a correct call, busting out stays at or below 1%.
* The "best" method, which is to the "Btie/Tot,+4", and changing with the above described "7,6,5" rule, works out with the highest average win, \$6,272, but has an 8% change of busting.

Longer explanation of "Btie/Tot, +4"...

The idea behind this strategy is to pretend your card is one rank better, and bet based on the odds of your call being right.
Say you have a 10 as the first card. That means a call of 2 through 10 would be correct or push... that's 35 cards. (Btie)
The total number of cards unseen is 51. (Tot)
The amount bet would be: (35+4/51), or 39/51, or just over 75% of the bankroll. Since we're rounding up, this would be all \$200 on the first card. Rounding down, we might have less busts and a lower average.

If there is a different strategy to changing cards that you think might do better, let me know. I can only go by my own ideas at this point, and the 7,6,5 strategy seems like a decent enough idea. It seems to do better than changing the first 6-10 seen.

Same goes for betting strategy. Betting with the odds works well, but adding \$50 or pretending you have a better card gives a push to the average win, but carries a higher risk.

OneAngryDwarf, I hope this answers your original question. This was a question I've always wanted to answer for myself, and I am glad I had a push to do it.
-Dween!
slyther
Joined: Feb 1, 2010