LVH Semifinal round, last hand

[KenSmith]

This is the hand that prevented me from reaching the Hilton finals in the April qualifier for MD2.

I'm in second place going into the hand, betting from second position behind the leader. Two players advance to the finals. Betting is $100 to $2500 and surrender is allowed.

The dealer has a 2 up.

A $11150 Bet $1000 Doubled ($2000 in action) Final hand = Stiff
Me $8660 Bet $2500 Cards T 2
C $5750 Bet $2500 Cards T 9
D $8000 Bet $2500 Cards A 5
E $6550 Bet $2500 Cards BJ

I was certainly pleased to see nobody behind me take second low. However, second low became meaningless once Player E had the blackjack, taking him to $10,300 assuming he accepts it without doubling.

There was some debate after the round whether I made the right choice here. At the table, I had little doubt that I needed to double, but in the ensuing discussion I began to second-guess the decision. Looking at it now, I don't understand what the dilemma was. Doubling looks like the only reasonable play. IIRC, the conversation revolved around the perils of giving up a low, but the low is long-gone already. FWIW, I busted the double-down.

If I don't double, I give the dealer-bust outcome to player D, who will certainly double behind me. Looks pretty cut and dry to me.

 

[tirle_bj]

let's try to understand

Let's consider Ken's double option.

First of all he doesn't have to bust. (9/13)
Now as always we have to find out the best reaction for each of the opponents based on Ken's actual card.

Ken gets "stiff" hand - A, 2, 3, 4 (4/13)

Player C should double since even if A will lose, his single win won't be enough.
Now he may bust (11/13) or make a hand (2/13).

Player D
a) C busts: D needs to win the hand when dealer doesn't bust. Because if dealer busts, even double will put him behind Ken and A. So he must hit 'til 18 (hard or soft) P18=P19=P20=P21=15.0%
b) C makes a hand: D must double (actually for less to have low against Ken) and win when dealer makes the hand.

Player E
The only time when he needs double is when C gets 20 or 21 and D gets 18 or more on double.

As we can see Ken always advances with stiff hand when dealer busts and never advances when dealer makes a hand.
P = 4/13 x 35.7% ~11%

Now Ken makes a hand after double (5/13).
It's easy to make sure that the reaction of C, D and E should be the same.
Now we have for Ken:
P adv. > P win (some push cases are OK for Ken)
P win = 23.6% (when Ken makes the hand)
So, total we have slightly more than 33.6% to Advance.

Ken Stands:

C still doubles
D doubles
E accepts BJ

P adv. = 0! If dealer busts A and D advance, if Dealer makes a hand E and eather A or D advance.

Ken hits 'til 18(he must beat the dealer by points) P18=P19=P20=P21= 11.15%
C still doubles
D doubles
E accepts BJ

Dealer has to make a hand, Ken has to win, D has to lose or push.
(D17 x 44.6 x 9/13) + (D18 x 33.45 x 10/13) + (D19 x 22.3 x 11/13) +
+ (D20 x 11.15 x 12/13) = 11.3%

Finally:
Double 33.6%
Hit 11.3%
Stand 0.0%

Tirle & K*