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I found a good chunk of free time, and here's what I did with it:
Starting with grb's
very likely scenario, I specified Hero's next card and randomly dealt out 4th street cards to the other players.
For reference, here are the hands on third (Hero is chasing a 7 low, two 8 lows and a pair of tens high):
Seat 1: 3[img]/images/graemlins/spade.gif[/img] 5[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/diamond.gif[/img]
Seat 2: 2[img]/images/graemlins/club.gif[/img] 6[img]/images/graemlins/spade.gif[/img] 8[img]/images/graemlins/heart.gif[/img]
Seat 3: 7[img]/images/graemlins/club.gif[/img] 8[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/club.gif[/img]
Seat 4: T[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/spade.gif[/img] T[img]/images/graemlins/heart.gif[/img]
Hero: 6[img]/images/graemlins/heart.gif[/img] 7[img]/images/graemlins/spade.gif[/img] 6[img]/images/graemlins/diamond.gif[/img]
(The bring-in has been dropped)
There were 5 sets of random cards dealt to villains. The next 4 cards off the top were:
1) A[img]/images/graemlins/spade.gif[/img], T[img]/images/graemlins/diamond.gif[/img], Q[img]/images/graemlins/club.gif[/img], 9[img]/images/graemlins/club.gif[/img]
2) J[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/club.gif[/img], J[img]/images/graemlins/spade.gif[/img], Q[img]/images/graemlins/diamond.gif[/img]
3) 2[img]/images/graemlins/spade.gif[/img], 4[img]/images/graemlins/diamond.gif[/img], J[img]/images/graemlins/spade.gif[/img], K[img]/images/graemlins/heart.gif[/img]
4) T[img]/images/graemlins/spade.gif[/img], A[img]/images/graemlins/spade.gif[/img], 4[img]/images/graemlins/heart.gif[/img], 5[img]/images/graemlins/diamond.gif[/img]
5) K[img]/images/graemlins/club.gif[/img], T[img]/images/graemlins/diamond.gif[/img], 9[img]/images/graemlins/club.gif[/img], 3[img]/images/graemlins/club.gif[/img]
Hero picks up a brick (K[img]/images/graemlins/spade.gif[/img])
Equity values:
.134,
.175,
.120,
.193,
.206.
Hero picks up an eight (8[img]/images/graemlins/diamond.gif[/img])
Equity values:
.135,
.241,
.153,
.182,
.258.
Hero picks up a seven (7[img]/images/graemlins/heart.gif[/img])
Equity values:
.084,
.193,
.143,
.196,
.241.
Hero picks up a six (6[img]/images/graemlins/club.gif[/img])
Equity values:
.361,
.480,
.361,
.467,
.563.
Hero picks up a five (5[img]/images/graemlins/heart.gif[/img])
Equity values:
.162,
.281,
.174,
.244,
.293.
Hero picks up a non-ace low (3[img]/images/graemlins/diamond.gif[/img])
Equity values:
.146,
.257,
.159,
.205,
.292.
Hero picks up an ace (A[img]/images/graemlins/diamond.gif[/img])
Equity values:
.153,
.274,
.172,
.203,
.294.
So what's the point of it all?
There are 16 cards nine or bigger that are still live. If hero gets one of these, he has no reason to continue past 4th.
There are 2 eights, and picking up one of these cards doesn't usually help hero enough for him to continue. The times that continuing is good are when all villains pick up bricks.
There are 2 sevens, and they don't help hero very much.
There is 1 six, and it's the magic money card for hero.
There are 3 fives, and this does give hero enough help to continue.
There are 10 non-ace lows remaining. Hero should continue with his hand as long as the seven doesn't also improve.
There are 3 aces, and they behave pretty much like the non-ace lows. Hero should continue if the seven doesn't improve.
In all, there are 20 cards that Hero can see where he will usually not play on. There are 4 money cards that make hero's hand worth playing. And there are 13 cards where hero needs to look around and see what's going on around him. Overall, since hero is getting very nice pot odds to peel for just the money cards (8:1), it looks like hero can pull out profit from this hand.
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Thanks for putting the time into doing those simulations. I know its a lot of work. However, I must say I'm not quite convinced. My main problem with your analysis is that its based on 5 random deals, which is simply not enough deals to base such a sweeping analysis on. Scenario #2, in particular, seems to be the dream 4th street (everyone bricks) that most puts you at possible 4th street scenarios equty >.25. Your simulation of 5 seems to imply that such a dream deal would occur 20% of the time.
I also question your analysis of the 13 cards that require you to survey the field to proceed. If you could run simulations to determine the liklihood that a favorable field would present itself in those 13 other times, and then use those to determine which of the 13 are "bricks" and which are "hits" -- your argument might have more strength.
But these are still very interesting simulations, and I appreciate the time you put into making them.
-grb