Posted 2012-January-31, 22:04

The problem seems to be the robots play bridge differently than you do, with different goals.

IF you try the two hearts before the spade finesse (assuming the lucky Qx) is doesn't happen, you will go down several extra tricks (lose diamonds, and a few hearts). I also think you overlooked the possibility that diamonds might be divided 4-4 (since you see the ew hands, you don't consider this possibility perhaps). The robots figure net gain (average number of points) for one line versus the other. Cashing the heart king increases, on average, the number of undertricks while (at 50 or 100 points per) while not cashing it stops some of the bleeding. In addition, after a successful spade finesse, you rack up a couple of spade tricks, plus if the queen drops that is just extra. In addition, cashing the heart ak leads to disaster if the heart queen does not fall and diamonds are 4-4.

So let;s imagine this from a small sample of 100 deals. On these deals, the spade finesse will work 50% of the time. The heart queen will fall doubleton 16 times (8 times when the finesse wins, eight times when it does not). Further, we will ignore things like blocked diamond suit, but we will include the possibility of 4-4 diamonds, and 5-3 and 6-2 diamonds. We know diamonds are not 8-0, and lets assume we know they are not 7-1, so diamonds will split 4-4, 45 times, where you always make with the spade finesse (they win 3 diamonds and the spade) and split 5-3 or 6-2 the other 55 times. (the numbers below may clearly be wrong estimates, I am doing this for illustration purposes, the big difference is the robots don't know about 5-3 diamonds, so they take into account possibility of 4-4 where the finesse is not instant death).

So what has the robot's simulations done for us?

BY PLAYing the spade finesse without the cashing heart AK, they make 9 tricks on half the 55 times the diamonds are not 44, the other 1/2 the time, they make at least 10 tricks (3♠+2♥+1♦+4♣), with chances for additional tricks if the queen falls, or if spades split nicely. Let's estimate that in the robot simulations, the spade suit divided 3-3 or the queen dropped doubleton about 1/3 of the time the spade finesse won, this gives the robots line of success...

WHEN spade finesse wins, robot will 10 tricks (50 * 2/3 x 430 = 33 x 430 = 14,190 points)

when spade finesse wins, and heart queen falls or spades friendly (17 * 460 = 7,820 points)

WHEN spade finesse failed but diamonds were 4-4 (50 x .45% = x 400 = 9,000 points)

WHEN spade finesse failed, and diamonds 5-3 (50 * .48% x -50 = 24.5 x -50 = -2450 points)

when spade finesse failed, and diamonds 6-2 (1.5 -100 = -150 points)

33 hands at = 14,190

17 hands at = 7,820

22.5 hands at + 9,000

26 hands at -1225

1.5 hands at - 150

100 hands = 33930 points = 339.3 points/hand on average (note the big bump for 4-4 diamond split you will not see below, and less negative results when heart queen does not fall.

Cashing the heart AK before taking the spade finesse will gain 9 tricks right way 16 times, I assume for this comparison that the robots will forgo the finesse in this case, but this might be wrong, but for the calculations lets say yes.... so cashing the hearts

Cashing hearts 16 x 400 = 6400 points (the 16 out of 100 times the heart queen is doubleton, we are working on heart queen not singleton, so odds might be slightly higher now that the queen is doubleton, since void and singleton heart queen are no longer possible.

half the time cashing heart fails, the spade finesse will win (100-16 = 84/2 = 42 * 430 = 18,060), we could throw in a tiny bit more for lucky spades, but heart queen falling has already failed, so I will add a bonus 42*30%*30 for an extra trick, raising this by 378 points to 18,438

when the spade finesse fails, you always go down, at least two (3D, 1h, 1S), and sometimes 3 or more (couple hearts, 4 or more diamonds).

Lets say down just two when diamonds are 4-4 and down three other times (can be more, a 5th diamond, or a 2nd heart).

So, of the 42 times the finesse loses, you are down two 45% of the time (diamonds 4-4, or 42*.45 * -100 = 19 * -100 = -1900 points

The other 23 time you are down three (23 x -150 = -3450 points)

Total for the 100 hands,

16 at = 6,400

42 at =18.438

19 at - 1,900

23 at -150

100 = 19,488 = +195 points/hand for play heart queen then hook....

One would think you gained some chances cashing the heart AK before taking the spade finesse on you line play. HEART Ace-king drops the queen doubleton 16% of the time removing need for finesse, and then finesse wins 1/2 of the remaining time (for .5 x 84% = 42%) for a total of 58%. The robot looks at it differently. if the spade finesse fails, you still make if diamonds are 3-3 (35% of the time), as long as you don't cash the AK of hearts setting up the setting trick for the defenders. So they see 50% (with overtricks) + 1/2 of the 4-4 diamond splits (and since 8=0 and 0=8 are no longer possible, they figure the odds of 4=4 around 40%, i figured them a little higher, above since 7-1 you make anyway). So 50% + 1/2 40% = 70%.

So the robot, over the course of a very long match (infinite) would gain 144.3 or 4 imps on average to your play. Who is right, and who is wrong. NOT sure. In a short match, I surely don't want to go down in this game. So combining all the chances to go plus makes a lot of sense. On the other hand, you can see the 5-3 diamond split, so you know you are down, at the table, I, like the robot, can not see how diamonds split. And even if they are 5-3, is it worth the risk for an extra down one? Cashing the top three clubs and the heart AK before taking the spade finesse risk down two when diamonds are 5-3 instead of down one a lot more frequently than one might expect (you need both qx of hearts and 3-3 clubs, that is 16% x 35.5% = about 5%. So your risk -100 on the 5-3 split (not to mention going down when diamonds are 4-4) 95% of the time. Even if we ignore the 44 diamond split, your line gains 10 imps 5% of the time, but loses 2 imps 95% of the time. In the long run, even assuming no 4-4 diamond split, you line seems to be too costly (net gain on 100 hands, 50 imps making five times, minus 190 not making 95 times (costing 2 imps each time down). So put me down for thinking the robots played this one correctly (I would not cash akq of clubs like gib did, so gib actually messed it up I think).

--Ben--