[BeerMoney]

I want to get a post going where we have useful probability calculations as well as some useful sims. In the sims in the back of 7CSFAP they don't make too many assumptions about dead and live cards.

Some probabilities.
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Let's say you have trips on 4th street, the chances of filling up or better: (ALL LIVE CARDS) Assume you've seen 13 cards.
P(Filling up) = 1 - P(not filling up)
= 1 - (35/39)*(32/38)*(29/37)= .4077
Odds: 1.45:1 against.

This actually seems high. (Can someone verify.)
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P(Hitting flush with 4 to a flush on fourth street given 2 of your suit are out from a total of 13 seen cards)= 1 - P(Not hitting flush) = 1 - (32/39)*(31/38)*(30/36) = .4421

Odds : 1.26 : 1

P(Hitting full house with two pair on 4th street, using the two pair you have on fourth street.) Assume all pair cards are live:

P(Filling up or better) = 1 - P(Not filling up)
(Assume 12 seen cards)
= 1 - (36/40)*(35/39)*(34/38) = .2773
Odds : 2.6 : 1

** I would say the prob. of filling would be a little higher since you could go running trips, and that isn't accounted for in my calculation.

Maybe add : 3/39*2/38 = .004 to the above prob. (Negligible.)

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Some sims.

[a [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/diamond.gif[/img] 2 [img]/images/graemlins/heart.gif[/img] Vs q [img]/images/graemlins/club.gif[/img] q [img]/images/graemlins/diamond.gif[/img] 5 [img]/images/graemlins/heart.gif[/img]] / DEAD CARDS: J [img]/images/graemlins/spade.gif[/img] 4 [img]/images/graemlins/diamond.gif[/img] 6 [img]/images/graemlins/club.gif[/img] 7 [img]/images/graemlins/heart.gif[/img] t [img]/images/graemlins/diamond.gif[/img] 8 [img]/images/graemlins/spade.gif[/img]
7-card Stud Hi: 500000 sampled outcomes
cards win %win lose %lose tie %tie EV
As 2d 2h 221268 44.25 278728 55.75 4 0.00 0.443
Qc Qd 5h 278728 55.75 221268 44.25 4 0.00 0.557
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Same race, except there is a dead ace..

[a [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/diamond.gif[/img] 2 [img]/images/graemlins/heart.gif[/img] Vs q [img]/images/graemlins/club.gif[/img] q [img]/images/graemlins/diamond.gif[/img] 5 [img]/images/graemlins/heart.gif[/img]] / DEAD CARDS: A [img]/images/graemlins/diamond.gif[/img] 4 [img]/images/graemlins/diamond.gif[/img] 6 [img]/images/graemlins/club.gif[/img] 7 [img]/images/graemlins/heart.gif[/img] t [img]/images/graemlins/diamond.gif[/img] 8 [img]/images/graemlins/spade.gif[/img]

cards win %win lose %lose tie %tie EV
As 2d 2h 198133 39.63 301862 60.37 5 0.00 0.396
Qc Qd 5h 301862 60.37 198133 39.63 5 0.00 0.604


Effective odds:

For 3/6 party: Assume a full table.
$4 ante, assume completed bet, dead $1 bring in, and assume action goes bet-call, bet-call, etc..
$3 on 3rd, fourth st, $6 on 5th, 6th, 7th..

You are paying $24 to win $4+$1+$24 = $29 Effective odds are $29: $24. Which means you would like chances of winning to be > 24/(24+29) = 45%. (Here I am assuming you play about equally as well as your opponent.)

Please point out any flaws, and add some other sims and probs. to this thread.