Bidding dilemma

Playing on BBO against the robots at matchpoints, you pick up:



:sp: AKQxxxxxx

:ht: -

:dm: Tx

:cl: AK



Q1. How many spades would you bid if you had to decide right now?

Spoiler:

You open 2:cl:, partner bids 2:dm:, you bid 2:sp: and partner rebids 3:dm: which isn't the 8+ points and decent diamonds hand.



Q2. How many spades would you bid if you had to decide right now?

Spoiler:

So you rebid spades and ask for keycards. Partner has none.



Q3. How many spades will you bid since you have to decide right now?



Make your decisions before opening the next spoiler, which truly spoils...

Spoiler:

I just want to make 6, so:



P[A] = 1/3

P[KQ] = 1/9

P[K, no Q, A with LHO] = 2/9 x 1/2 = 1/9

That's at least 5/9, and I haven't even bothered to contemplate KJ with the Q in front. So I went ace-asking.



When the ace doesn't turn up, my chances are down to about 2/9 so I call it quits and sign off in 5.



Of course, dummy shows up with :dm: KJxxxx and on the run of spades RHO tosses away :dm: Qx preventing me from guessing and letting me make 6 for a 39%.

Bidding dilemma