by oddmanout » Wed Dec 06, 2006 4:50 am
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)