March 10th, 2011 at 12:20:00 PM
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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:

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.

* 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.

50% | Always bet half the bankroll, rounded up to nearest $50 |
---|---|

75% | Always bet 75% of the bankroll, rounded up to nearest $50 |

100% | Always bet the whole bankroll |

HiLo Frac | Bet fraction of bankroll: WrongCards÷RightCards |

HLFrac+50 | Bet fraction of bankroll: WrongCards÷RightCards, plus $50 |

Btie/Tot | Bet fraction of bankroll: RightCardsInclTies÷TotalCards |

Btie/Tot+50 | Bet fraction of bankroll: RightCardsInclTies÷TotalCards, plus $50 |

Btie/Tot, +4 | Bet fraction of bankroll: (RightCardsInclTies+4)÷TotalCards |

Busts | Number of times player busts out |

Avg Win | Average amount won |

Avg(nobust) | Average amount won, disregarding busts |

Max win | Best score for algorithm |

Risk | Average win * Bust % |

Change: None | Never change cards |

Change: Any 5-J | Anytime a card comes up that's between 5 and J, change it |

Change: Any 6-10 | Anytime a card comes up that's between 6 and 10, change it |

Change: 7,6,5 | 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!

March 10th, 2011 at 2:29:36 PM
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Very cool Dween! Now if only someone could figure out how to play "Pay The Rent" on TPIR! :)

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