Estimating suit length

[Cyberyeti]

A question that's been bugging me for a while and I'm not sure how to approach the solution.

 

RHO is playing something fairly normal for America.

 

a) 2+ card club

b) 3+ card club

 

You hold

 

1) 5 clubs

2) 6 clubs

 

How much does your holding actually impact the frequency of opener holding less than 4 clubs.

[wanoff]

Combinations maths will tell you. I can remember using a ZX81 to work out the suit splits but would need to google how to do it now.

Intuitively I'd say that even if you had as few as one club, compared with a void, the chance of RHO having a club suit is reduced. So obviously going from 5 to 6 will also reduce the chance.

[Cyberyeti]

Combinations maths will tell you. I can remember using a ZX81 to work out the suit splits but would need to google how to do it now.

Intuitively I'd say that even if you had as few as one club, compared with a void, the chance of RHO having a club suit is reduced. So obviously going from 5 to 6 will also reduce the chance.

I don't think it's anything like that simple, the point being it's not "how many hands have 3 clubs rather than 4", but it's "how many of those hands are actually opened 1♣ rather than 1♦ or 1N", it may not be sensibly analytically solvable and require a sim.

 

I didn't say so in the original post, my reason for asking was to get more of a feel whether to overcall 1N or pass with 1N overcall type strength and clubs when a short club is opened as this will often allow me to X 1N after a 1♣-1?-1N auction showing the hand fairly precisely.