Joined: Nov 25, 2016
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November 25th, 2016 at 3:16:54 AM permalink
Happy Holidays guys!

I have a question that I can't seem to find the answer (math) to anywhere.

When the dealer gets 4 of a kind and 3 of a kind, I've seen places play them 2 different ways; play the highest pair in front and the other being play a pair from the 3 of a kind in the front.

What is the math between the difference? Like how much does each win, and a general answer of why is this rule so split?

Thank you for any help you guys provide!
Joined: Mar 29, 2010
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November 25th, 2016 at 4:09:50 AM permalink
A full house is going to win the 5 card hand 99.8% of the time. A four-of-a-kind will win 99.9% of the time. So you only gain about 0.1% by upgrading your 5 card hand from a full house to a four-of-a-kind.

On the other hand, a pair of twos will win the two card hand about 80% of the time. A pair of threes is about 82%, fours 84%, etc. So upgrading your 2 card pair by a rank increases your probability of success by about 2%. Upgrading from a pair of twos to a pair of aces improves your hand by a whopping 20%.

Clearly, the success of this hand is most sensitive to the rank of the pair in the two card hand. The best strategy is to play the highest pair in front.
Joined: May 21, 2013
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November 25th, 2016 at 6:33:31 AM permalink
I have found the "highest 2 csrd hand " to be true in general about House way, not just this hand.

For example, last week house had 4 aces and pair queens. No hesitation, they split the aces. And pushed me with trips....heeheehee. Not that I disagree with what.they did. Sure push, almost sure house win. House plays to push.

Not uncommon, hand with both straight and lflush. House will always play to maximize 2 card hand, even if that's the straight in back.
If the House lost every hand, they wouldn't deal the game.
Joined: May 19, 2016
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November 25th, 2016 at 10:46:23 AM permalink
Quote: beachbumbabs

Not uncommon, hand with both straight and lflush. House will always play to maximize 2 card hand, even if that's the straight in back.


I may be the only reader who didn't understand what you said, but you lost me here.

It almost seems you are saying the House Way would break up the straight (or flush) to get a high 2-card hand.

But, the House Way tends to favor keeping the strongest strong hand. I believe House Way would almost without exception keep the straight (or flush) to insure ties rather than losses versus the players.

Am I wrong in how I read your post?

(I once thought I was wrong, but I was mistaken...)
Joined: Nov 2, 2009
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November 25th, 2016 at 11:08:13 AM permalink
Lucky -

Babs is not saying they'll break a straight or flush to get a better 2 card hand. She's saying if there's the possibility of both a straight or flush, they'll go for the best 2 card even if it leaves them with a straight rather than the flush.

For example:
Ac Kh 9c 8c 7d 6c 5c
They'll put the AK on top leaving the straight rather than the K7/flush.

Note: the casino is not playing to maximize wins but to minimize losses. Yeah, it's a very subtle difference.
I invented a few casino games. Info: 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁

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