On request for Richard. Note that this is still (and always will be) a draft. It is not a complete reviewed document, or anything and should never be used for any purpose other than Richard seeing my code etc

It was done purely as an interest exercise when I maybe should have been doing other things, with constant distractions, and also some anxiety about posting anything like this without it being properly checked and written up etc

Please bear with me - editing a few times to add results. It would take too long for me to format into friendly form so am just pasting Lua code (constraints) which I used with Bdeal (Beling) and the raw results with or without the 3S psych/misbid/mistake/whatever etc

Important note. It is a crude sim looking simply at defeating the contract or not and not making any assessment on number of tricks won/lost for matchpoint considerations etc I have a very simple approach to bridge, especially defence against a slam. I have in the past tried to work out a more sophisitcated distribution of the outcomes and how that distribution changes with different leads and the different bids. Its not much more code but could be provided if necessary. As I said it was a very simple sim

Results show mean number of tricks for declarer with each card led, with a 95% CI (I think it may be 1.96 SEs its not clear - I think the funny An symbol is +/-) but the Standard deviation and number of hands is also listed etc

As you can see without the 3S bid the 95% CIs do not overlap and the Ace (for me) is clearly the best lead in terms of average tricks and chance of defetaing the slam

With the 3S bid the difference in mean estimates is smaller and the 95% CIs do overlap. For me that doesn't affect thinking that the Ace is still a slightly superior lead etc

I'm not sure of the bdeal version but it was built on 27/11/18 (Australian date style)

Run on an HP Spectre 360X using Windows 10 etc on a sunny Friday morning somewhere in Australia

They are very basic scripts and assumptions. For example minium point ranges for E and W and assumption of 6+ hearts for W and 4+ hearts for E and (when used) the splinter being 0 or 1 tricks. I didn't put any other constraints on hand shapes - eg assumptions on Jacoby or number of losers in each hand etc

I didn't put any assumptions on controls etc. To make it more sophisticated I could have put in some loser and control assumptions that would lead to a 6H bid etc The configuration section has the North hand and requests bdeal to generate enough hands to get 1000 that fit the constraints.

The stats section calculates means and CIs for number of tricks and chance of declarer making slam for each possible card led

Note the funny copyright symbol is in the rendered HTML. It should be the letter c in parenthesies, ( c ) © "©"

--------------------------------------------------------------------------------------------------

--LUA Script for Bdeal v17.10.0 (Piotr Beling.

http://bcalc.w8.pl/) without the 3S bid (my interpretation of point ranges etc)

--Written and run by the possum on 2nd Oct 2020

conf = {

N="at743.3.j962.j87",

num = 1000

}

function filter()

return W:hcp()>13 and W:hearts()>5 and E:hcp()>12 and E:hearts()>3

--and W:spades()<2

end

function stats()

for c in N:cards() do -- for each card c in the hand N:

local t = tricks(W, "H", c) -- tricks to take by E-W

count("E-W tricks after " .. tostring( c ), t)

count("chance to defeat after " .. tostring( c ), t < 12)

end

end

E-W tricks after C7: 12064 / 1000 = 12.064 Ań 0.0485418 (95% conf.) min: 10 max: 13 sdev: 0.782243

E-W tricks after C8: 12064 / 1000 = 12.064 Ań 0.0485418 (95% conf.) min: 10 max: 13 sdev: 0.782243

E-W tricks after CJ: 12070 / 1000 = 12.07 Ań 0.0486684 (95% conf.) min: 10 max: 13 sdev: 0.784283

E-W tricks after D2: 12066 / 1000 = 12.066 Ań 0.0479729 (95% conf.) min: 9 max: 13 sdev: 0.773074

E-W tricks after D6: 12067 / 1000 = 12.067 Ań 0.0479274 (95% conf.) min: 9 max: 13 sdev: 0.772341

E-W tricks after D9: 12073 / 1000 = 12.073 Ań 0.0480542 (95% conf.) min: 9 max: 13 sdev: 0.774384

E-W tricks after DJ: 12079 / 1000 = 12.079 Ań 0.0481777 (95% conf.) min: 9 max: 13 sdev: 0.776376

E-W tricks after H3: 12085 / 1000 = 12.085 Ań 0.0460116 (95% conf.) min: 10 max: 13 sdev: 0.741468

E-W tricks after S3: 12275 / 1000 = 12.275 Ań 0.0462453 (95% conf.) min: 10 max: 13 sdev: 0.745235

E-W tricks after S4: 12275 / 1000 = 12.275 Ań 0.0462453 (95% conf.) min: 10 max: 13 sdev: 0.745235

E-W tricks after S7: 12275 / 1000 = 12.275 Ań 0.0462453 (95% conf.) min: 10 max: 13 sdev: 0.745235

E-W tricks after SA: 11714 / 1000 = 11.714 Ań 0.0383639 (95% conf.) min: 10 max: 13 sdev: 0.618226

E-W tricks after ST: 12276 / 1000 = 12.276 Ań 0.0461807 (95% conf.) min: 10 max: 13 sdev: 0.744194

chance to defeat after C7: 232 / 1000 = 0.232 Ań 0.0261938 (95% conf.) min: 0 max: 1 sdev: 0.422109

chance to defeat after C8: 232 / 1000 = 0.232 Ań 0.0261938 (95% conf.) min: 0 max: 1 sdev: 0.422109

chance to defeat after CJ: 231 / 1000 = 0.231 Ań 0.0261543 (95% conf.) min: 0 max: 1 sdev: 0.421472

chance to defeat after D2: 229 / 1000 = 0.229 Ań 0.0260747 (95% conf.) min: 0 max: 1 sdev: 0.420189

chance to defeat after D6: 228 / 1000 = 0.228 Ań 0.0260346 (95% conf.) min: 0 max: 1 sdev: 0.419543

chance to defeat after D9: 225 / 1000 = 0.225 Ań 0.0259129 (95% conf.) min: 0 max: 1 sdev: 0.417582

chance to defeat after DJ: 224 / 1000 = 0.224 Ań 0.025872 (95% conf.) min: 0 max: 1 sdev: 0.416922

chance to defeat after H3: 214 / 1000 = 0.214 Ań 0.0254503 (95% conf.) min: 0 max: 1 sdev: 0.410127

chance to defeat after S3: 156 / 1000 = 0.156 Ań 0.0225169 (95% conf.) min: 0 max: 1 sdev: 0.362855

chance to defeat after S4: 156 / 1000 = 0.156 Ań 0.0225169 (95% conf.) min: 0 max: 1 sdev: 0.362855

chance to defeat after S7: 156 / 1000 = 0.156 Ań 0.0225169 (95% conf.) min: 0 max: 1 sdev: 0.362855

chance to defeat after SA: 319 / 1000 = 0.319 Ań 0.028923 (95% conf.) min: 0 max: 1 sdev: 0.466089

chance to defeat after ST: 155 / 1000 = 0.155 Ań 0.0224579 (95% conf.) min: 0 max: 1 sdev: 0.361905

Number of hands dealt: 696262. CPU time usage [sec]: 6.21 (x8 threads).

----------------------------------------------------------------------------------------------------

Notes

Without the 3S bid the Ace is the only lead with a mean number of tricks less than 12 (approx 11.75) 95% CI approx +/- 0.04-0.05 tricks

Chance of defeating the slam is approximately 32% with the Ace but only of the order of 22-23% with any other suit. CI +/- approx 2-3%

Clearly you would never lead a small spade - I could have excluded them from the sim

---------------------------------------------------------------------------------

--LUA Script for Bdeal 17.10.0 (Piotr Beling.

http://bcalc.w8.pl/) with the 3S bid (my interpretation of point ranges etc)

--Written and run by the possum on 2nd Oct 2020

conf = {

N="at743.3.j962.j87",

num = 1000

}

function filter()

return W:hcp()>13 and W:hearts()>5 and E:hcp()>12 and E:hearts()>3

and W:spades()<2

end

function stats()

for c in N:cards() do -- for each card c in the hand N:

local t = tricks(W, "H", c) -- tricks to take by E-W

count("E-W tricks after " .. tostring( c ), t)

count("chance to defeat after " .. tostring( c ), t < 12)

end

end

E-W tricks after C7: 12265 / 1000 = 12.265 An 0.0499058 (95% conf.) min: 10 max: 13 sdev: 0.804223

E-W tricks after C8: 12265 / 1000 = 12.265 An 0.0499058 (95% conf.) min: 10 max: 13 sdev: 0.804223

E-W tricks after CJ: 12276 / 1000 = 12.276 An 0.0496369 (95% conf.) min: 10 max: 13 sdev: 0.79989

E-W tricks after D2: 12270 / 1000 = 12.27 An 0.0486684 (95% conf.) min: 10 max: 13 sdev: 0.784283

E-W tricks after D6: 12270 / 1000 = 12.27 An 0.0486684 (95% conf.) min: 10 max: 13 sdev: 0.784283

E-W tricks after D9: 12276 / 1000 = 12.276 An 0.0486179 (95% conf.) min: 9 max: 13 sdev: 0.783469

E-W tricks after DJ: 12282 / 1000 = 12.282 An 0.0485645 (95% conf.) min: 9 max: 13 sdev: 0.782608

E-W tricks after H3: 12289 / 1000 = 12.289 An 0.0466641 (95% conf.) min: 10 max: 13 sdev: 0.751983

E-W tricks after S3: 12494 / 1000 = 12.494 An 0.0385521 (95% conf.) min: 10 max: 13 sdev: 0.62126

E-W tricks after S4: 12494 / 1000 = 12.494 An 0.0385521 (95% conf.) min: 10 max: 13 sdev: 0.62126

E-W tricks after S7: 12494 / 1000 = 12.494 An 0.0385521 (95% conf.) min: 10 max: 13 sdev: 0.62126

E-W tricks after SA: 11951 / 1000 = 11.951 An 0.0407203 (95% conf.) min: 10 max: 13 sdev: 0.6562

E-W tricks after ST: 12495 / 1000 = 12.495 An 0.0384526 (95% conf.) min: 10 max: 13 sdev: 0.619657

chance to defeat after C7: 186 / 1000 = 0.186 An 0.0241459 (95% conf.) min: 0 max: 1 sdev: 0.389107

chance to defeat after C8: 186 / 1000 = 0.186 An 0.0241459 (95% conf.) min: 0 max: 1 sdev: 0.389107

chance to defeat after CJ: 182 / 1000 = 0.182 An 0.0239435 (95% conf.) min: 0 max: 1 sdev: 0.385845

chance to defeat after D2: 175 / 1000 = 0.175 An 0.0235787 (95% conf.) min: 0 max: 1 sdev: 0.379967

chance to defeat after D6: 175 / 1000 = 0.175 An 0.0235787 (95% conf.) min: 0 max: 1 sdev: 0.379967

chance to defeat after D9: 172 / 1000 = 0.172 An 0.0234182 (95% conf.) min: 0 max: 1 sdev: 0.37738

chance to defeat after DJ: 170 / 1000 = 0.17 An 0.0233098 (95% conf.) min: 0 max: 1 sdev: 0.375633

chance to defeat after H3: 156 / 1000 = 0.156 An 0.0225169 (95% conf.) min: 0 max: 1 sdev: 0.362855

chance to defeat after S3: 62 / 1000 = 0.062 An 0.0149648 (95% conf.) min: 0 max: 1 sdev: 0.241156

chance to defeat after S4: 62 / 1000 = 0.062 An 0.0149648 (95% conf.) min: 0 max: 1 sdev: 0.241156

chance to defeat after S7: 62 / 1000 = 0.062 An 0.0149648 (95% conf.) min: 0 max: 1 sdev: 0.241156

chance to defeat after SA: 213 / 1000 = 0.213 An 0.0254069 (95% conf.) min: 0 max: 1 sdev: 0.409428

chance to defeat after ST: 61 / 1000 = 0.061 An 0.0148516 (95% conf.) min: 0 max: 1 sdev: 0.23933

Number of hands dealt: 2044012. CPU time usage [sec]: 7.66 (x8 threads).

--------------------------------------------------------------------------------

Notes

With the 3S bid the Ace is the only lead with a mean number of tricks less than 12 (approx 11.95) but the 95% CIs overlap +/- approximately 0.05 tricks

Chance of defeating the slam is approximately 21% with the Ace but only of the order of 17-18% with any other suit. But the CIs overlap, they are +/- approx 2-3%

Note however the standard deviation for the Ace lead is now much larger etc. However the standard deviations for all other leads are very large too I could keep adding notes forever

Clearly you would never lead a small spade. I could have editted them out