iambabyd
Joined: Feb 28, 2011
• Posts: 29
February 28th, 2011 at 3:00:03 PM permalink
For those not familiar with Big 2, it is a card game played with 2, 3, or 4 players. Each player is dealt 13 cards. Instead of traditional 2,3...K,A ranking, it is 3,4..A,2. Suits are spades, hearts, clubs, diamonds in high to low order. The object of the game is to get rid of all your cards before the other players do. The first player can play a singleton, pair, three of a kind, or a five card hand (straight, flush, full house, four of a kind with a singleton, straight flush, royal flush). The next player counterclockwise must follow the lead (single can only be played on single, etc). The player can choose to pass or if they cannot beat the card played, they must pass. The turn ends when all other players cannot or choose to not beat the card played, then the last player who played a card can choose to lead whatever they want.

The question about the game has to do with when 2 or 3 players are playing. We deal out 13 to everybody and the other cards remain dead. My question is -

Is it an advantage or disadvantage to be dealt more cards than another player? If it was broken down 13-13-14, 13-13-15, etc, what is the percentage advantage/disadvantage?

My initial hunch is that there is a small advantage to having a few more but with quickly diminishing returns.

Thanks,
Michael
Founder and Editor-in-Chief, GamblersGrind.com and HoopsHabit.com.
iambabyd
Joined: Feb 28, 2011
• Posts: 29
March 3rd, 2011 at 8:22:20 AM permalink
Perhaps somebody has a good link for resources on big 2. Unfortunately I think the math involved with this problem is ridiculously difficult to figure out because of all the strategy involved and how it's not really one hand vs. another specific hand.
Founder and Editor-in-Chief, GamblersGrind.com and HoopsHabit.com.
cardshark
Joined: Nov 30, 2009
• Posts: 239
March 4th, 2011 at 9:29:41 AM permalink
My hunch also says the more cards the higher the advantage, however, I disagree with the "quickly diminishing returns". Take, for example, an extreme 51 vs 1 card distribution. The 51 card hand should win every time, even if the other player's only card is a 2 of spades. One always winning strategy in that case would be to play all cards as pairs, and the remaining singleton is the last play you go out on. I think you could also come up with an unbeatable strategy for 50 and 49 cards.

The more cards you have, the easier it is to make those powerful 5 cards hands and the harder it is for your opponents to play on them.

I'd be curious to see if my intuition is right.