Flop a straight with AQ when two tens are held out?

[Mike Kelley]

PokerStars No-Limit Hold'em, $0.50 BB (7 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

SB ($64.90)
BB ($49)
Hero ($71.35)
MP1 ($54.25)
MP2 ($51.30)
CO ($26.65)
Button ($42.35)

Preflop: Hero is UTG with T[img]/images/graemlins/spade.gif[/img], T[img]/images/graemlins/club.gif[/img].
<font color="#CC3333">Hero raises to $2</font>, <font color="#666666">4 folds</font>, SB calls $1.75, <font color="#666666">1 fold</font>.

Flop: ($4.50) K[img]/images/graemlins/heart.gif[/img], T[img]/images/graemlins/diamond.gif[/img], J[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, <font color="#CC3333">Hero bets $4</font>, <font color="#CC3333">SB raises to $11</font>, <font color="#CC3333">Hero raises to $67</font>, SB calls $51.90 (All-In).

Turn: ($130.30) 7[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players, 1 all-in)</font>

River: ($130.30) 4[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players, 1 all-in)</font>

Final Pot: $130.31

Results in white below: <font color="#FFFFFF">
SB has Qd Ah (straight, ace high).
Hero has Ts Tc (three of a kind, tens).
Outcome: SB wins $130.30. Hero wins $4.09. </font>


Anyone know how to calculate the odds of him flopping a straight with AQ when I hold two of the tens?

[BruceZ]

[ QUOTE ]
Anyone know how to calculate the odds of him flopping a straight with AQ when I hold two of the tens?

[/ QUOTE ]

2*4*4/C(48,3) =~ 0.185% or 539.5-to-1

That is, 2 possible Ts that can flop, times 4 possible Js, times 4 possible Ks, divided by the total number of possible flops C(48,3) = 48!/(48-3)!/3! = 48*47*46/(3*2*1).

OR if you prefer fractions to combinations:

2/48 * 4/47 * 4/46 * 6 =~ 0.185% or 539.5-to-1

That is, compute the probability of flopping a T (2/48), followed by a J (4/47), followed by a K (4/46). This gives the probability of flopping T-J-K in exactly that order, so we multiply by 6 since there are 3! = 3*2*1 = 6 orders that the T,J,K can flop.

[Mike Kelley]

.185% I think you meant.

Thanks for the explanation. I'll remember that for future reference.

[BruceZ]

[ QUOTE ]
.185% I think you meant.

[/ QUOTE ]

Right, sorry. I fixed the typo.