Joined: Mar '08
Location: Australia
Age: 45 (M)
Posts: 1158

can anyone help that can work out our new game,we love omaha and manilla or seven up,so we made omahnilla,all cards under 7 taken out of deck like manilla,but you get delt 4 cards like omaha.thing is in manilla a flush beats a fullhouse cause its harder to get,yet in our game does that still apply cause you get delt four cards in your hand.you can only use 2 of your 4 cards in a hand like omaha to win.does it switch to fullhouse being better or stays the same.we do gamble on this game,its insanely fun,but risky.who got maths skills to do it..

Joined: Feb '08
Location: United Kingdom
Age: 32 (M)
Posts: 1885

Never heard of manilla either but I think I understand. The ratio of cards with the same value to cards with the same suit is a lot higher in manilla so three of a kind and a full house become more likely compared to a flush.

But before I can help with the maths I need to be clear what cards are left. I assume we have 7 8 9 10 J Q K A of each suit making a total of 32 cards.

Joined: Feb '08
Location: United Kingdom
Age: 32 (M)
Posts: 1885

Well the maths seems pretty complicated to me but I'll give it a try. It would be helpful if other people could double check my maths.

First of all; to work out the chances of hitting a flush. You need to have at least two hole cards of the same suit since you have to use two in your hand. I believe we need to work out the odds of being dealt two suited cards, three suited cards and all four suited since it would effect your outs in the deck although I'm not sure. I may be overcomplicating it.

Chances of two suited cards: 7/31 X 25/30 X 24/29 = 0.15573 + 25/31 X 7/30 X 24/29 = 0.15573 + 25/31 X 24/30 X 7/29 = 0.15573 = 0.46719

Chances of hitting a flush with those two suited cards: 6/28 X 5/27 X 4/26 X 8 = 0.0488 (I believe this sum includes all flush possibilities in one including boards where all five cards are of the same suit but I may be wrong. My theory is that as long as three are the same the rest are irrelevant and those three can be in one of 8 positions)

Chances of three suited cards: 7/31 X 6/30 X 25/29 = 0.03893 + 7/31 X 25/30 X 6/29 = 0.03893 + 25/31 X 7/30 X 6/29 = 0.03893 = 0.11679

Chances of hitting a flush with three suited cards: 5/28 X 4/27 X 3/26 X 8 = 0.0244

Chances of four suited cards 7/31 X 6/30 X 5/29 = 0.00779

Chances of hitting a flush with four suited cards: 4/28 X 3/27 X 2/26 X 8 = 0.0098

So if I'm right, which I'm having some doubts about, the chances of hitting a flush in this game is

0.46719 X 0.0488 = 0.0228 + 0.11679 X 0.0244 = 0.0029 + 0.00779 X 0.0098 = 0.00008

about 2.578%

That took me so long to work out and I'm not sure if I'm even right so I'll leave the calculation of full house odds for now.