Calculating the ODDS when playins suited connector. Pls some math geek help !

    • silent21
      Joined: 08.08.2008 Posts: 1,556
      A recent thread about using the 5/10 rule to call preflop raises with PPs and suited connectors got me thinking about the kind of implied odds required to call preflop raises with SCs; people tend to arbitrarily use things like the 5/10 rule, even though I've never seen any mathematical description of the kind of odds you need to call these raises. I'm going to attempt to solve that problem (but I still need some help!).

      I'll list the conclusions first, and leave the tl;dr math for the bottom for those of you that want to peruse it. I also encourage math-head-types to check my math to make sure I didn't mess anything up.

      There are two kinds of hands you can flop with SCs: Good made hands (most of which can be made by calling with ATC, which of course we don't do) and draws. First, made hands, stolen off some page I googled:

      Odds of flopping...
      Flush: 0.84%
      Two pair: 2%
      Trips: 1.35%
      Full house: 0.09%
      Quads: 0.01%
      Straight: 1.31%
      Total: 5.6% (1 in 18 times, 17:1)

      However, most of the time you will be flopping draws instead of big hands with SCs, and that's where things get complicated. Let's separate this into two categories: combo draws and regular draws.


      Odds of flopping...
      20 outer (OESD + FD + pair): 0.077%
      17 outer (Gutshot + FD + pair): 0.153%
      15 outer (OESD + flush draw): 1.424%
      14 outer (Pair + flush draw): 1.450%
      13 outer (Pair + straight draw): 1.147%
      12 outer (Gutshot + flush draw): 2.664%
      Total: 6.9% (1 in 14 times, 13:1)

      These draws are all hands that can be played profitably after the flop; either you are a favorite against an overpair, or getting AI on the flop is +EV when you take some fold equity (and thus taking down dead money) into account.

      Combining these big draws with good made hands, you'll have a relatively "big hand" on the flop 12.5% of the time, or 1 in 8 (very close to how often you will flop a set with an overpair). However, since a set is a near-invincible hand and you still have to improve with these draws, you can't say that you also need about 7:1 odds to call with a suited connector. Your average equity on the flop with these made hands and combo draws against an overpair is 66% (the made hands go from 75%-99%; the combo draws range from 45%-65%); compare this with sets, where your equity is generally 90+%.


      Odds of flopping...
      9 outer (flush draw): 5.2%
      8 outer (straight draw): 8.0%
      Total: 13.2% (1 in 7.5 times, 6.5:1)

      These are your standard draws; when you flop a hand with which you can continue, it will most frequently be one of these. These draws improve to a flush or straight on the river about 1 time in 3.


      - you have a 5.6% (1 in 18, 17:1 chance) of flopping a good made hand
      - you have a ~7% (1 in 14, 13:1) chance of flopping a strong (12+ outs) combo draw
      - you have a ~13% chance (1 in 7.5, 6.5:1) chance of flopping a standard OESD or FD

      Adding these all together, you will flop a hand you can continue with on the flop 25% of the time (1 in 4). However, only half of the time will these hands be immediately profitable (i.e. +EV to shove it in); the other half, you'll have your standard old OESD or FD which requires playing some poker.

      So, a question from me to all you math-heads: How do you combine these preflop odds with the odds of hitting your hand postflop to figure out the implied odds required to call with SCs preflop?
  • 2 replies
    • gavinonymous
      Joined: 18.12.2008 Posts: 1,146
      Strange, I was thinking about the same thing today. I play NL SH. I also find calling with SC's is a lot different than set value, because you hardly hit a made hand, more likely a draw. I tried a few things in equilator to give preflop equity vs different number of opponents to see when it was ok to call limpers.

      i gave a limping range first about 25%

      89s vs 1 opponent 40%/60%
      89s vs 2 opponents 27%/36%/36%
      89s vs 3 opponents 23%/25.5%/25.5%/25.5%

      TJs is a fair bit better at 45%, 30.5%, and 25% vs. 1,2 or 3 opponents, almost even money preflop. 34s is slightly worse than 89s but not so bad.

      Against someone raising say 14% and callers around the same range.

      89s vs 1 opp = 35%
      89s vs 2 opp = 25%
      89s vs 3 opp = 22%

      Not sure if this is a better way to calculate when you can call for pot odds. I think sometimes it's better to raise SC's in position isolate players, get initiative and fold equity with a hand that plays well postflop.
    • silent21
      Joined: 08.08.2008 Posts: 1,556
      i dont think you calculation is usable. you are using preflop equity which is calculated after 5 card but the flop is from 3. we should use the odds for flopping something (2pair, draw, trips etc) and then evaluate our hand equity against different ranges.

      and yes i agree with the isolation with SCs, probably against ANY limper.