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Can you help with the mathematics of this?

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  1. mabedi mabedi is offline

    Richmond Hill
    Canada

    Posts: 242
    Joined: Apr 06

    Oct 13th, 2008 (10/13/2008 10:46pm)

    I would appreciate it if someone could help me out with the mathematics behind this? You are three-handed with A6 on the button. What are the chances that small and/or big blind have a better hand than you?

    Much appreciated, thanks.
  2. thome52 thome52 is offline

    Mankato, MN
    United States

    Posts: 81
    Joined: Nov 07

    Oct 14th, 2008 (10/14/2008 2:31am) in reply to mabedi

    50% of them having a better hand - 50% they have a worse hand

    Pretty basic to me
  3. ntanygd760 ntanygd760 is offline

    Fort Drum, NY
    United States

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    Oct 14th, 2008 (10/14/2008 3:31am) in reply to thome52

    do you mean the chances of them having a hand to call your shove, or just A6 winning against 2 random hands.
     
  4. dgillis dgillis is offline Moderator

    CA
    United States

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    Oct 14th, 2008 (10/14/2008 9:30am) in reply to mabedi

    4 aces in the deck, you have one of them, odds that they have one 3:50 (52 cards in deck but you have two of them)... so yea theoretically your proabably slightly ahead, problem is your only a slight fav over a large number of the hands that they have, also with the draws\pp's your going to be behind alot of hands.. overall not a very strong hand. Your behind any suited connector and obv any PP. At this point I think you have to play those people and your table image more so than your cards. fyi the card calc puts you at 36% to 29% for each of the other players. 6% chance of tie.
     
  5. lordxixor101 lordxixor101 is offline

    Westland, MI
    United States

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    Oct 14th, 2008 (10/14/2008 11:36am) in reply to mabedi

    Well, I won't get into the probablilities of winning the hand, only the probablility that you are starting with the best (note, some of this I'm stealing from wikipedia).

    There are 52 first cards you can be dealt, 51 second cards you can be dealt (can't be dealth pocket A of spades for example). So, there are 1,326 potential starting hands. Hands that are better than you, include all pocket pairs 22-AA, and A7-AK.

    There are 6 combinations for paired hands, so (13*6)= 78 paired possibliites
    There are 16 combinations for unpaired hands (7*16)= 112 non paired possibilities.

    So 190 combinations beat you. There are 9 that tie you.

    So, roughly, you are ahead of a random hand ((1326-190)/1326) or 85.67% of the time. To be ahead of 2 random hands then, it's approximately 73% of the time.

    Now, this ignores that certain combinations of hands are now impossible (since you have a 6 and an A). However, it also ignores that there are less possibilities.

    So, this isn't a perfect answer, but I think it's close enough for discussion here.
  6. mabedi mabedi is offline

    Richmond Hill
    Canada

    Posts: 242
    Joined: Apr 06

    Oct 14th, 2008 (10/14/2008 12:50pm) in reply to ntanygd760

    yeah, that's what I meant. Thanks for the responses guys, very helpful indeed.
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