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Facing 1/6 pot bet on river - do we split MDF?

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  • Facing 1/6 pot bet on river - do we split MDF?

    No Limit Hold'em $0.02/$0.05
    6 players

    Stacks:
    UTG - Hero (
    $6.88)
    MP - MP ($2.74)
    CO - CO (
    $6.21)
    BTN - BTN (
    $2.53)
    SB - SB (
    $9.45)
    BB - BB (
    $5.34)

    Preflop: (
    $0.07, 6 players) Hero is UTG with ??
    Hero raises to $0.15, MP calls $0.15, 2 folds, SB calls $0.13, BB calls $0.10

    Flop:
    Qd3s8h ($0.60, 4 players - SB: $9.30, BB: $5.19, Hero: $6.73, MP: $2.59)
    SB checks, BB checks, Hero checks, MP checks

    Turn:
    2c ($0.60, 4 players - SB: $9.30, BB: $5.19, Hero: $6.73, MP: $2.59)
    SB checks, BB checks, Hero checks, MP checks

    River:
    Kh ($0.60, 4 players - SB: $9.30, BB: $5.19, Hero: $6.73, MP: $2.59)
    SB bets $0.10, BB folds, Hero ??


    So here SB is risking $0.10 to win $0.70 so this only needs to get folds 14% of the time to be profitable. So the remaining 3 players, including myself, need to have a combined (right?) MDF of 86% to stop this being immediately profitable.

    So my thinking was when it's on the BB there are still 2 players left to act behind him (for a total of 3) so his MDF should be 86 / 3 = 29%. So he can happily fold 71% of his range and not be exploited.

    When it gets to me UTG there is now just 1 person left to act behind me (for a total of 2) so my MDF is now 86 / 2 = 43%. So I can fold 57% of my range without being exploited but should be defending with the other 43%.

    If I fold and it gets to the final in MP does he now assume the full burden of the 83% MDF needed?

    There are clearly some flaws here. For starters, BB has to worry about the 2 players behind overcalling/raising so he should actually be defending tighter than 29%. Secondly, if I have to find 43% of my range to call with there is going to be some fairly awful hands in there - would these need to be a raise?

    Am I thinking along the right lines here or have I got this completely wrong?


  • #2
    My understanding is the sum of the defense frequency of the 3 players needs to equal 83%. The MDF is not split equally though. The allocation gets progressively more as the player is more in position but does not exceed the 83%.

    In this instance, BB might defend 14% of their range, Hero might defend with 28%, and MP defend with 41% of their range.

    Also, the fact that we have checks around for 2 streets would throw MDF out for the hand. One of the ways MDF doesn't apply is when you get great pot odds on the round before. Think Btn vs BB. BTN min raises and BB defends. There are 4.5bb in the pot, BB checks and BTN bets 2bb. MDF is 69% however BB doesn't have to defend 69% of their range.

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