[thorvald]

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Against 3N partner started with ♦5, and dummy played low.


I know the robots don't follow the rule of 3rd hand high, but here I was not able to find a situation, where playing the 6 could be right

But playing the 6 wasn't right with this layout

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[pescetom]

If you held KQ4 it doesn't cost, but thats still no reason to risk.

[smerriman]

thorvald, on 2023-June-24, 06:53, said:

but here I was not able to find a situation, where playing the 6 could be right

It's not about finding situations where playing 6 was right, it's about how many situations playing 6 wasn't wrong.

By my calculations:

- a 10 deal simulation will tell GIB to play low 9.2% of the time
- a 20 deal simulation will tell GIB to play low 2.5% of the time
- a 30 deal simulation will tell GIB to play low 0.7% of the time
- a 40 deal simulation will tell GIB to play low 0.2% of the time

We don't know how exactly how many deals BBO has configured GIB to simulate, but according to barmar it is "a few dozen" for advanced robots, so playing low will be rare but still within the realms of possibility, even if there weren't any bugs in the intended algorithm. (And of course, with basic bots it would be considerably less rare).

[thorvald]

I see your point about the difference between being right and not being wrong :-)

I am not sure I can follow your simulations

If you make a 40 deal simulation and it is not wrong in one of those deals it should be 2.5%, but I guess 1 simulation will give a percentage to each card, and then just add up and create the average.

But with the 40 boards simulation, what is the percentage for the 3 other cards, and after the percentages are calculated is it then just a random function used to select the card?

[smerriman]

I used resampling. I got GIB to deal about 3000 hands that it thought were possible:

a) 71.0% of them had ace, ten, low all equal double dummy
b) 9.6% had low worse than ten
c) 12.9% had low and ten equal, and ace better (partially due to its annoying habit of leading low from xxx against no trumps).
d) 6.4% had low and ten equal, and ace worse

Low was never better than the ten (well, I lie; in 2 of the hands, it found a psych with South having 6 hearts and outside of the NT range when low was better than the ten, but I excluded these to make the calculations simpler).

If you deal N hands, and there are A, B, C, D from each of the four cases above, then:

- if B=0 and C=D, it will think all four cards are equal, so play low 50% of the time
- if B=0 and C<D, it will rule out the ace but the others are equal, so play low 2/3 of the time
- otherwise it won't play low

I thus looped over all A+C+D=N, and added choose(N,A)*choose(N-A,C) * 0.710^A * 0.129^C * 0.064^D * (C==D ? 0.5 : 2/3) to get the above numbers.

I didn't calculate how often it would play ace and ten, which would require separating out case b) into more subcases.