Fixed Limit ~ Pot Odds to Call With any 2 Cards Preflop

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[emmasdad]

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Thanks for the thoughts emmasdad ... what your saying makes sense. I was also considering the question further myself today ... I think to feel comfortable playing a "Bingo" hand ... you'd have to have odds to call at least = to the odds of flopping 2 pair or better.

Needless to say I checked these odds ... pretty steep indeed. I can't see any reason ever to call a Bingo hand playing Fixed Limit 6~Max. (It was around 50~1 to flop 2 pair) ... no Bingo hand is going to stand up in a pot with 3 or 4 other callers, even if you catch a pair of of it. If you don't catch 2 pair or better on the flop, it becomes very difficult to defend that hand. You're calling instead of raising ... and if you're betting and raising ... you shouldn't be. Basically it's always a fold on the flop ... even when you hit ... and it's a big waste of money to wait for lightning to strike.

Thanks again!

[oddmanout]

I was trying to do this myself for HU limit play, however it is not simple.

The immediate pot odds for the SB to call the BB are 1/4. With this in mind, all hands should be played which is obviously wrong.

However, you can estimate that a player will make a bet with roughly Pp% of hands preflop, Pf% of hands on flop, Pt of hands on turn and Pr of hands on river and so, as a rough estimate, the implied pot-odds for this situation will be:
average cost = SB+Pp+Pf+(Pt+Pr)*2
average pot with only calls= [ 2*(1+Pp+Pf)+4*(Pt+Pr) ]

i.e. implied pot-odds of 0.5+Pp+Pf+(Pt+Pr)*2 / [ 2*(1+Pp+Pf)+4*(Pt+Pr) ]

Of course, Pp,Pf,Pt,Pr can be obtained statistically with PT or other stats programs, but if we estimate these at 15% for a tight player and 30% for an agressive player, we have implied pot-odds of:
0.5+0.15+0.15+(0.15+0.15)*2 / [ 2*(1+0.15+0.15)+4*(0.15+0.15) ] = 37% for a tight player
and
0.5+.3+.3+(.3+.3)*2 / 2*(1+.3+.3)+4*(.3+.3) ] = 41% for an aggressive player

Therefore, as a first-approximation, from HU SB position, it worth playing hands with winning chances of more than 37% against a tight player and hands with winning chances of more than 41% against an aggressive player.

I don't know if my figures are correct, but it seems to suggest that it is worth playing more hands than I would naturally play from SB position (e.g. 28s,35s,48o against tight players, and 2Jo,94s,69o against aggressive players).

If you can see a flaw in my maths, please let me know before I throw all my money away. Of course this is a first-approximation - many winning hands will be thrown away before the river and many pots will be stolen due to the late position. There is no substitute for hand-based EV statistics against your opponent (although this takes time to gather and is sometimes not available).

A few of my calculations for the heads-up winning chances of each hand:
2h3h Chances to river: 0.35 (1548029.28/4467820)
2h3s Chances to river: 0.31 (1387581.73/4467820)
2h4h Chances to river: 0.35 (1585441.67/4467820)
2h4s Chances to river: 0.32 (1427188.11/4467820)
2h5h Chances to river: 0.36 (1630286.07/4467820)
2h5s Chances to river: 0.33 (1474744.95/4467820)
2h6h Chances to river: 0.36 (1622111.32/4467820)
2h6s Chances to river: 0.33 (1465232.49/4467820)
2h7h Chances to river: 0.37 (1642891.60/4467820)
2h7s Chances to river: 0.33 (1486843.56/4467820)
2h8h Chances to river: 0.39 (1735064.19/4467820)
2h8s Chances to river: 0.35 (1584448.71/4467820)
2h9h Chances to river: 0.41 (1828681.35/4467820)
2h9s Chances to river: 0.38 (1683439.78/4467820)
2hTh Chances to river: 0.43 (1934865.94/4467820)
2hTs Chances to river: 0.40 (1795846.59/4467820)
2hJh Chances to river: 0.46 (2045590.83/4467820)
2hJs Chances to river: 0.43 (1912572.05/4467820)
2hQh Chances to river: 0.49 (2167480.97/4467820)
2hQs Chances to river: 0.46 (2041091.81/4467820)
2hKh Chances to river: 0.51 (2300497.50/4467820)
2hKs Chances to river: 0.49 (2181358.78/4467820)
3h4h Chances to river: 0.37 (1665411.85/4467820)
3h4s Chances to river: 0.34 (1512883.29/4467820)
3h5h Chances to river: 0.38 (1711547.30/4467820)
3h5s Chances to river: 0.35 (1561867.97/4467820)
3h6h Chances to river: 0.38 (1704251.10/4467820)
3h6s Chances to river: 0.35 (1553290.35/4467820)
3h7h Chances to river: 0.39 (1725674.84/4467820)
3h7s Chances to river: 0.35 (1575572.29/4467820)
3h8h Chances to river: 0.39 (1761820.79/4467820)
3h8s Chances to river: 0.36 (1613514.32/4467820)
3h9h Chances to river: 0.42 (1866253.55/4467820)
3h9s Chances to river: 0.39 (1724110.73/4467820)
3hTh Chances to river: 0.44 (1972656.64/4467820)
3hTs Chances to river: 0.41 (1836765.17/4467820)
3hJh Chances to river: 0.47 (2083454.99/4467820)
3hJs Chances to river: 0.44 (1953583.11/4467820)
3hQh Chances to river: 0.49 (2205263.81/4467820)
3hQs Chances to river: 0.47 (2082030.08/4467820)
3hKh Chances to river: 0.52 (2338044.91/4467820)
3hKs Chances to river: 0.50 (2222059.80/4467820)
4h5h Chances to river: 0.40 (1789376.00/4467820)
4h5s Chances to river: 0.37 (1645291.94/4467820)
4h6h Chances to river: 0.40 (1783778.78/4467820)
4h6s Chances to river: 0.37 (1638540.25/4467820)
4h7h Chances to river: 0.40 (1805782.51/4467820)
4h7s Chances to river: 0.37 (1661445.59/4467820)
4h8h Chances to river: 0.41 (1842551.99/4467820)
4h8s Chances to river: 0.38 (1700038.20/4467820)
4h9h Chances to river: 0.42 (1892949.30/4467820)
4h9s Chances to river: 0.39 (1753096.27/4467820)
4hTh Chances to river: 0.45 (2009892.15/4467820)
4hTs Chances to river: 0.42 (1877061.20/4467820)
4hJh Chances to river: 0.47 (2120783.96/4467820)
4hJs Chances to river: 0.45 (1993991.36/4467820)
4hQh Chances to river: 0.50 (2242535.17/4467820)
4hQs Chances to river: 0.48 (2122389.00/4467820)
4hKh Chances to river: 0.53 (2375108.39/4467820)
4hKs Chances to river: 0.51 (2262208.78/4467820)
5h6h Chances to river: 0.42 (1863476.75/4467820)
5h6s Chances to river: 0.39 (1723984.80/4467820)
5h7h Chances to river: 0.42 (1886631.25/4467820)
5h7s Chances to river: 0.39 (1748131.13/4467820)
5h8h Chances to river: 0.43 (1924141.13/4467820)
5h8s Chances to river: 0.40 (1787520.38/4467820)
5h9h Chances to river: 0.44 (1975247.13/4467820)
5h9s Chances to river: 0.41 (1841319.12/4467820)
5hTh Chances to river: 0.46 (2040499.83/4467820)
5hTs Chances to river: 0.43 (1910249.75/4467820)
5hJh Chances to river: 0.48 (2161549.24/4467820)
5hJs Chances to river: 0.46 (2038078.09/4467820)
5hQh Chances to river: 0.51 (2283270.16/4467820)
5hQs Chances to river: 0.48 (2166452.15/4467820)
5hKh Chances to river: 0.54 (2415666.44/4467820)
5hKs Chances to river: 0.52 (2306091.36/4467820)
6h7h Chances to river: 0.44 (1961868.68/4467820)
6h7s Chances to river: 0.41 (1828284.33/4467820)
6h8h Chances to river: 0.45 (1999545.47/4467820)
6h8s Chances to river: 0.42 (1867861.98/4467820)
6h9h Chances to river: 0.46 (2051046.02/4467820)
6h9s Chances to river: 0.43 (1922077.82/4467820)
6hTh Chances to river: 0.47 (2117085.03/4467820)
6hTs Chances to river: 0.45 (1991825.60/4467820)
6hJh Chances to river: 0.49 (2189310.72/4467820)
6hJs Chances to river: 0.46 (2067679.77/4467820)
6hQh Chances to river: 0.52 (2320940.55/4467820)
6hQs Chances to river: 0.49 (2206679.40/4467820)
6hKh Chances to river: 0.55 (2453602.85/4467820)
6hKs Chances to river: 0.53 (2346608.95/4467820)

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