you have set of 5 cards: CAAAB

what to do, trade AAA or ABC?

Interesting question. I just trade any, but I would need Tom to tell if the card drawing system takes into account the already used cards.

Do a Rain Man and count cards to see which is better :)

Toto wrote:

but I would need Tom to tell if the card drawing system takes into account the already used cards.

I'm not tom, but yes there is a "virtual deck" according to the Card Distribution settings.  Once that deck runs out a completely new one is created to be drawn from.  At least that's the way its been described.

I have wondered in this situation what the distribution of cards turned in was- and have considered asking for that information to be displayed somewhere - but in the end I don't think it matters that much.  

Amidon37 wrote:

I have wondered in this situation what the distribution of cards turned in was- and have considered asking for that information to be displayed somewhere - but in the end I don't think it matters that much.  

I think it would be cool too, and I think it was requested as an enhancement once, not sure it's on the list though.

I trade ABC.  Here's why:  In the absence of information, I assume equal numbers of all three types in the deck.  So if I have AAABC, the deck is missing 3 A's, 1 B and 1 C.  If I get another A, I'm in good shape.  If I don't, I'll get another B or C.  Let's assume B without loss of generality.  Now there are 2 less B's, and 1 less C.  Again an A gives me a complete set, but if I don't get it, I'm more likely to get a C than a B.  In other words, all things being equal you're more likely to get a BC than a BB or CC, so keeping an A will serve you better than a B or a C.  Of course this could be modified if you had already traded some sets in, and thus new more about the deck.

I thought there was no advantage, but I think I may have been wrong. In the absence of knowledge of the availability of other cards, and assuming an even beginning distribution, there seems to be an advantage to cashing ABC over AAA.

Take the example where you hold AAABC and you began with a deck of 12 cards: AAAABBBBCCCC.

If you cash AAA, the probability of getting a set on the next round is ~14% (holding BC, you need an A with remaining cards ABBBCCC)

If you cash ABC, the probability of getting a set on the next round is ~14% (holding AA, you need an A with remaining cards ABBBCCC)

So far, they look even..

but if you don't hit on the first draw, you will hold either BBC/CCB after cashing AAA, or AAB/AAC after cashing ABC.

Holding BBC (the first case) the deck will have ABBCCC remaining, which gives you a 50% probability of hitting a set on that round.

..and holding AAB (the second case), the deck will also have ABBCCC, but you will now have a ~67% probability of hitting a set.

Yertle wrote:

Toto wrote:

but I would need Tom to tell if the card drawing system takes into account the already used cards.

I'm not tom, but yes there is a "virtual deck" according to the Card Distribution settings.  Once that deck runs out a completely new one is created to be drawn from.  At least that's the way its been described.

This is accurate. An array is initialized to hold the values of the distribution settings. As each card is drawn, one of the array values is decremented. On the last card (when the total of the values is 1), when the drawcard function is called, the array is reset to its distribution settings.

My original code has been changed to accomodate a non-18,18,18,2 distribution, but my guess is that it is still functionally equivalent to this.