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Needing help with statistics to ensure proper ranking order of card sets

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lance.hoag
lance.hoag's picture
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Joined: 03/21/2012

Hello all,
Not being very mathy, I could use some help to ensure that the statistics of a card game prototype is in proper order. Specifically, the card game is a a little like Haggis/Tichu, with role-drafting and associated special abilities (but with a fun theme incorporated). So there is a climbing/trick-taking aspect of which I need to ensure that the "Sets" hierarchy is accurately ordered.

Here are the specifics:
1. 5 suits (100 cards + 15 wilds = 115 total cards in a deck)
2. each suit consists of 20 cards numbered 1-10 (2 copies of each card)
3. 15 wild cards, breaking down to 3 per suit, however, all wilds are suit-less and number-less:
a)full wild---number and suit
b)number-only wild...suit cannot be changed,
...must be played with another card of which the number is being modified and suit remains the same.
c)suit-only wild....number cannot be wild,
...must be played with another card of which the suit is being modified and the number remains the same.
4. 10 cards are drawn into a hand (2-4 players for now)

Sets to be collected/played are:
1) 1 pair
2) 2 pair
3) 3 ofakind--needs at least 1 wild
4) 4 ofakind--needs at least 2 wilds
5) Straight of at least 5 single cards, (1,2,3,4,5)
6) Sequence of at least 2 consecutive Pairs (2,2,3,3,4,4...)
7) Sequence of at least 2 consecutive 3 ofakinds (2,2,2,3,3,3...) --needs at least 2 wilds
8) Sequence of at least 2 consecutive 4 ofakinds (2,2,2,2,3,3,3,3)--needs at least 4 wilds

With generous application of wilds, sets of more than 4 ofakinds are possible (5 ofakind and higher), but I am drawing the line at 4, just to keep it simpler. I can always allow set greater than 4 ofakind to be Bombs (Tichu/Haggis) later if it looks beneficial.

All sets must be of the same suit (excluding suit-less wild cards, and Sequences of Pairs)...as the suits represent creatures for which Sets of evidence is being collected...think Mystery Rummy.

I suspect that this ordering might be close to that above, but to be the next great hotness in light card games to sweep the planet, this needs to accurate and not just a guess. The math seems straight forward until I mix in the partial wild cards. If I had a number that represented the probability of drawing a hand of each of these Sets could also base the scoring/reward according to the actual probabilities, rather than just the ordering.

Thanks to everyone for reading this long post and considering my mathy problem. Acknowledgements in the rules for all those who contribute.

Traz
Traz's picture
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Joined: 04/06/2009
dude..........

I'lll be the first to admit that I am no math guy. I'll also be the first one to tell you that probabilities mean jack-squat here. Regardless of the math involved, if you've ever played MTG you know regardless of what the odds are, you are still at the mercy of the draw no matter what.

Do yourself a favor, and just playtest the thing. It looks to me like the only leeway you've given yourself is to cut wildcards or drop the # of cards in your suits.

Or add....

Just playtest it until you are happy with it. I doubt you'll be happy with just the math.

TLEberle
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Joined: 08/10/2008
Wait a minute, you don't need

Wait a minute, you don't need statistics. You can't jump ship from one flavor of hand to another midstream. If the round is two pairs, you can't play three of a kind to change things up.

What sort of math are you looking for? The likelihood that in a hand of Cards you'd be able to build HandType? I'm not sure that with the number of wild cards you've included that you'll be able to do anything other than use the Monte Carlo method to find out.

I like the idea of role selection as part of a Tichu game, I'm interested, but I don't think the math is the problem.

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