Here’s a deal from the Wednesday teams night at Piedmont. The discussion invoked almost physical violence. In an uncontested auction South gets to declare 6. West leads a small . What’s the best approach?
Two paths: take the safety play in ( King and then small towards the Ten), or, if the lead smells like a singleton play trumps from top.
Do the statistics perhaps provide an answer? Any 4-1 trump split occurs 28.26% of the time, but you can only tackle four trumps in West, that leaves 14.13%. Compare that to the splitting exactly 1-5, which is close to 7.27%. So it looks like we’ve got a winner, safety play beats singleton 2-1.
Bayes Theorem (credits to Geoff for explaining me):
P( singleton | lead) = ( P( singleton) * P( lead | singleton) ) / P( lead)
Read this as:
The odds the being a singleton given a lead are equal to the odds for a singleton , multiplied by the odds for a lead given a singleton, divided by the odds for a lead.
We’ll assume West always leads a singleton if he has one, so:
P( lead | singleton) = 1
P( singleton) = 0.0727
P( lead) = 0.0727 + 1/3 * 0.9273
That last part means that in 1/3 of the remaining space will be the lead chosen. We’ll ignore a broken trump holding as lead option.
This all calculates to more than 19%. So compared to the safety play, this is the superior path.
Well, this was pretty much an eye opener for me, very counter intuitive.
At our table Geoff (East) decided his hand looked like a weak two in . After South’s take out double I took maximum advantage of the vulnerability and put up a massive wall by jumping to 6. Let them figure out if and what slam they have at the 6-level! North took her plus and doubled. When the defence slipped up by not leading trumps twice, we got away for -500. Not a bad deal if you get your odds right.
1 thought on “Approach”
Just wondering (and being picky)
I think the chances on the spade lead should be closer to 1/3. Wouldn’t it be correct to take into account the chance of a club singleton that isn’t lead? This would lead to:
0.0727+1/3*(0.9273-0.1414)=0.335 and a subsequent chance of a spade singleton of 21.7%
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