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Old 12-19-2005, 02:26 AM
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Default Re: Pl 25 middle set

Your post got me thinking, so I did the math of an all in with a NAKED middle set (no other nut features):

Math of Top Set vs Middle Set Heads Up:

If they have top set, you have:

10% chance of winning (assume a backdoor as well as 1 out [img]/images/graemlins/smile.gif[/img])
90% chance of losing

If they don't have top set, but another common all in hand like a double draw, flush + low draw, straight + low draw, wrap draw, etc:

60% equity for you
40% equity for them

Assume S% of the time they have top set, the rest of the time they don't. We need to find the break even point.

0 = 60(100-S) - 40(100-S) - 90S + 10S

6000-60S - 4000 + 40S - 90S + 10S = 0

2000 - 100S = 0

S = 20%

Thus, if they have top set more than 20% of the time, you're losing money in the long run by playing this way. Against a tight or solid player, you're definitely losing money in this spot. (Obviously pot odds can factor in but if you're facing a stack committing pot (re)raise from a good player, these are the numbers). I won't even consider bottom set here as most decent players throw it away to action or won't aggressively reraise it.

Of course, if you're up against fishy or overly aggressive players, getting all in is the right course of action, but again not ridiculously profitable. Against a 70/30 (just a flush draw, or just a low draw) you stil need them to have top set less than 33% of the time just to break even. The fact that they may have bottom set does add some equity and against weaker players it's a clear all in.
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