..because I'm too busy to figure it out myself.

With cards distributed at 18-18-18-2, what is the probability that you'll have a set with three?  ..with four?

I stole this but it answers your question.

The possibility of a wild shifts the odds far more, such that the chance is actually 42.28% that three randomly selected cards will form a set. (12.37% of the time it will be a set of three the same; 29.60% of the time it will be a set of one of each; and 0.32% of the time it will include both wilds and thus could be either type.

The odds of four cards including a set are 81.70%. However, if someone has three cards that did not form a set (for instance, you're pretty sure they'd have cashed in a set if they could've), and they draw a fourth card, the odds that the fourth card gives them a set are only 68.29%. Five cards, of course, always include a set.

If you're wondering whether someone else's cards might include a set, you can sometimes get more precise odds by considering your own cards, particularly whether you are holding any wilds. If you're looking at one wild (or remember that one wild has been cashed in since the last time the deck was shuffled), the odds that someone else with 3 cards has a set are 38.06%. Someone with 4 cards is 79.87% likely to have a set. If you know that the other person has neither wild, the odds he has a set with 3 cards are 33.41%; the odds he has a set if he has 4 cards are 77.80%.

Semi-related, in Risk you get to see the cards at turn in right?  But not before correct?

I think in Risk you get to see the cards before, but you get different amounts for the image on the card.  Some people play that you get units in the territories on the cards, since cards help randomly distribute territories.  If you didn't get to see the cards, how would you know if you had a set with 3 cards?

Yertle wrote:

Semi-related, in Risk you get to see the cards at turn in right?  But not before correct?

Correct.  In the original game (which is basically the only one I know), cards needed to be hidden because there was a somewhat optional rule that if you held one of the territories on the card, it was worth additional armies.  But you did have to show because there was no program to keep you honest.

In WG games you never get to see opponent's discards.. Neither are you able to know for sure how many cards are remaining in the deck (except by inference).  In moderately fogged games you may not know who's been taken out ..etc.

Edward Nygma wrote:

If you're wondering whether someone else's cards might include a set, you can sometimes get more precise odds by considering your own cards, particularly whether you are holding any wilds. If you're looking at one wild (or remember that one wild has been cashed in since the last time the deck was shuffled), the odds that someone else with 3 cards has a set are 38.06%. Someone with 4 cards is 79.87% likely to have a set. If you know that the other person has neither wild, the odds he has a set with 3 cards are 33.41%; the odds he has a set if he has 4 cards are 77.80%.

A corollary of this should be that if you have not seen a wild, the probability that your opponent holds a set increases as the deck gets smaller.

The reason I asked is because I was just playing a game where I had the opportunity to run the board leaving one remaining player who held 3 cards. I knew that if that player could cash, I would be toast, but if they couldn't I would easily win on the following turn because of bonuses.  I suspected that the probability he could cash was somewhere around 50+%, which was close considering I had not seen any wilds up to that point in the game.  It was a game with five players and I figured it was smart play to bring it down to a coin flip ..so I went for it.

Edward Nygma wrote:

  If you didn't get to see the cards, how would you know if you had a set with 3 cards?

I was curious if other people were able to see the cards turned in.

I still think it would be slightly cool if we could see Number of Cards turned in and possibly even what cards were turned in (if Fog/Rules allowed), although the Card Deck # would need to show too.

Ah yes, everybody does get to see the cards when turned in, so you can do a little card counting I suppose. 

On WG do we shuffle the cards back in immediately, or is there a discard pile?

There was discussion of that back here:
http://www.wargear.net/forum/showthread/107p1/Flash_Player_feature_requests
No idea whether it was ever implemented.

Edward Nygma wrote:

Ah yes, everybody does get to see the cards when turned in, so you can do a little card counting I suppose. 

On WG do we shuffle the cards back in immediately, or is there a discard pile?

It's more like having a discard pile. Once the deck's last card is drawn, a new deck full of 18/18/18/2 (or whatever) appears.

So, the information gets a little hard to sort out when there are cards floating around from more than one deck. Regardless, more accurate probabilities can be calculated by combing the log/history.

I second what Hugh said.