Cactus Game Design Message Boards

Quote from: jmhartz on August 02, 2011, 12:54:55 PM

I think a FTM is a 11 card advantage.  If you have a 50 card deck with hopper, go first, and get the perfect FTM, after you play Mayhem you will have 7 cards in territory, 1 in discard, and 6 in hand (14 total), and your opponent will have 6 in hand, 0 in discard, and 0 in territory (6 total).  But your opponent also drew 3 when you didn't, so they should have been +3 on you, and instead you are +8 on them, thus an 11 card advantage, IMHO.

And the percentage chance of a FTM with 50 card deck with Hopper is 19.05%, so about 1 out of every 5 games.

Interesting factoid:  If both players have 50 card decks with Hopper and Mayhem, the odds that one player (but not both!) gets a FTM is 30.84%.  If you estimate that a player with a FTM (and their opponent does not get a FTM) wins 95% of the time (and this might even be conservative!), then when two 50 card decks with Hopper/Mayhem are paired against each other, the odds that the game is already decided before it starts is 29.30%.  <-- This is a good of a reason as any as to why Mayhem should be banned - if a game is decided almost 1/3 of the time before it is started because of one card.

Can I ask what math you used to get those percentages? I'm just curious as to why I've got a 21% chance of FTM, and you've got a 19% one.

Prof A answered for me on my FTM percentages.  As for the odds that one player (but not both) gets a FTM, that would be 2*odds that one person gets FTM*odds that the other person does not get FTM = 2*19.05%*80.95% = 30.84%. 

In about 1/3 of all games between two decks of 50 cards with Hopper and Mayhem, exactly one player gets a FTM.  QED

What is FTM???

If you consider that you may draw other cards that allow you to draw, your chance at a FTM is above 19.05%

If you consider that you may draw other cards that allow you to draw, your chance at a FTM is above 19.05%

Interesting point. I think its still valid to assume that it doesn't happen, or if it does, the consequence is less severe, since drawing extra cards lessens your chances of being able to put most of your hand on the table.