TRUMPING WITH THE RIGHT BOWER

[irishwolf]

You are in Seat 2, the score is 2 to 3 your side down by 1 point. Your partner picks up the QC . The AD is led by S1 and you hold JC & two low doubletons: .

You must decide to trump the AD or slough another suit? You can't create a void by playing 2nd hand low* (see note below).

* Note: Technically speaking, 2nd hand low implies when a King or low card is played, and you can create a void.

[Mxx]

I trump in and watch what my partner plays to see if I can hit their void with my second card.

Maybe if I knew my partner well and could trust they would lead trump after taking the first trick, might be worth throwing off. I would still guess it's not a winning play though.

[irishwolf]

Hmmm!

One comment in 4 days.

Where are the experts on this play?

IRISH

[jblowery]

I'd definitely trump the ace. At least a 50% chance my partner has the left.

[sdu754]

It is always a good idea to Trump your opponent's Ace. Your partner could have a Diamond, and you are saving them from having to Trump in to take the trick, leaving them with a better hand.

I would Trump in. You are showing your partner where the Bower is, and you have little chance of taking any other Trick. The right is only worth one trick, and worst case scenario your partner sloughs off a card. Whatever they slough off, you lead the opposite suit.

[Catch10110]

That's how i'd play it too. Trump and lead whatever partner doesn't throw. If they follow suit, I'm gonna lead red; it's my cleanest suit.

[jspectre]

With an ace being led and no ability to create a void, this is an automatic trump situation.

[raydog]

I spent a lot of time simulating and analyzing this, and finally have some results to share.

First let me say that if I came across this situation in live play, and had 10 sec. to decide, I would play the R. My reasoning is that, looking at the 7 cards I have seen, I know there are 5D + 4H + 3S remaining which my partner in S4 may hold, so they don't have a great chance of trumping in. And while playing the R is a bit of overkill (and I don't get to use it to take out other trump from the opponents' hands), the upside is that my partner will know where it is, which is generally a great piece of information for the declarer as they plan their play.

Second, let me specify the limits of my analysis (my simulator program) and why these results should be interpreted with a reasonable amount of skepticism (just how much is up to you to decide).

My program makes assumptions about:
1) when S4 calls trump? [this is the primary assumption; ultimately, when S4 has only 1 trump in hand (2 after they pick up the QC), my program is rather selective. I won't go into the details - there is a related post which deals more specifically with this, which I will analyze next. Suffice to say they don't call very often];
2) what does S4 discard? [this is not too hard, and I think I have it close to optimized. The primary considerations are getting void in a suit (preferably a green suit), and keeping any Aces. There are of course exceptions and specific borderline situations, but I trust my program on this];
3) when does S1 lead the AD? [once again, I think I have this optimized. S1 will lead the AD except when a) they have 3+ diamonds (unless that is their only non-trump suit); b) they have the AH, and that suit is equal in length or shorter than the D suit*; c) they have the AS, and that suit is shorter than the D suit]
4) how the hand is played in general (I tried to find the best play in a few common situations, as you will see below)

* this is a minor programming issue. Suits are analyzed in order, and H comes before D. So A singleton (doubleton) H won't be usurped by a singleton (doubleton) H. With A-9H and A-KD, better to lead the AD, but this entails a lot of programming for a very rare and marginally significant situation).

Clearly a big caveat. But I did discover some interesting things, and I think my results look reasonable and defendable.

I gave S1 the AD, gave S2 the JC + Q-10S + Q-10H, and set the QC as the turned card; all other cards were random. I also looked at 2 different scenarios: if S4 ended up with 2 trump or 3+ trump [perhaps a meaningless exercise, since S2 can't know how many trump their partner has, and so can't use that information in their decision making process, but it was interesting to compare the results].

Out of curiosity, I first looked at what suits S4 was void in, WHEN S4 declared AND S1 led the AD (about 18.4% of the hands).

When S4 had 3 trump (~16.0% of cases), they were void in:
S 63%
H 63%
D 39%
so 65% of cases they were void in 2 suits

When S4 had 2 trump (~2.4% of cases), they were void in:
S 54%
D 52%
H 26%
so 32% of cases they were void in 2 suits

Interesting how it shifts, but I'm not going to delve into that (though I do think I can explain the shift). This may explain some differences in play in the 2 cases later on [which, again, is academic, since S2 doesn't now how many trump S4 has, and S4 MOST LIKELY has 3 trump, as my simulator currently plays].

Let's say S2 trumps the 1st trick with the R. Now they have to decide what to lead on the 2nd trick.

If S4 has 3+ trump, what should S2 lead if S4 discards a:

D: lead 10H: (17,113 / 67,939 / 12,883) [sweep / 1 pt / euchred] EV = +0.78
lead 10S: (16,494 / 69,584 / 11,857) EV = +0.81 [fewer sweeps, but fewer euchres]
better to lead 10S, but difference not significant

H: lead 10H: (2,754 / 28,610 / 5,516) EV = +0.63 [fewer sweeps, but fewer euchres]
lead 10S: (3,136 / 27,610 / 6,109) EV = 0.59
better to lead 10H, but difference not significant

S: lead 10H: (3,237 / 18,854 / 3,381) EV = +0.73
lead 10S: (2,770 / 19,668 / 3,034) EV = +0.75 [fewer sweeps, but fewer euchres]
better to lead 10S, but difference not significant

If S4 has 2 trump, what should S2 lead if S4 discards a:

D: lead 10H: (1,182 / 9,616 / 809) EV = +0.89
lead 10S: (1,095 / 9,650 / 862) EV = +0.87
better to lead 10H, but difference not significant

H: lead 10H: (205 / 5,645 / 3,638) EV = -0.13
lead 10S: (252 / 4,707 / 4,529) EV = -0.41
better to lead 10H

S: lead 10H: (173 / 2,419 / 505) EV = +0.57
lead 10S: (108 / 2,165 / 824) EV = +0.24
better to lead 10S

There are some differences here, but not surprising, given that the suit(s) S4 is likely to be void in vary depending on how many trump they have. You can do the math to verify, but the end result is that, if S2 plays the R after S1's AD lead [18.4% of hands], and then leads either the 9 (H or S) on the 2nd trick, the EV is about 0.72. That's the headline number to remember.
____________________________________________

But what if S2 plays off on the first trick? Is it better to dump the 10H or the 10S?

Remember, the starting point is that S4 declared C trump, and S1 led the AD. If S2 plays off on the 1st trick, and anything but a D is led on the 2nd trick, S2's choice is clear. So we are only looking at cases where S1 wins the first trick with their AD, and then re-leads a D [there may be further considerations on the 3rd trick, but I didn't delve that far).

S2 discards the 10H, trick 1; D led by S1, trick 2; S4 has 3+ trump:

play R: (0 / 44,450 / 15,035) EV = +0.24
play QH: (0 / 49,453 / 10,032) EV = +0.49

S2 discards the 10S, trick 1; D led by S1, trick 2; S4 has 3+ trump:

play R: (0 / 44,482 / 15,015) EV = +0.24
play QS: (0 / 49,839 / 9,657) EV = +0.51

When S4 has 3+ trump, better for S2 to throw off the same suit and get void

S2 discards the 10H, trick 1; D led by S1, trick 2; S4 has 2 trump:

play R: (0 / 6,078/ 1,299) EV = +0.47
play QH: (0 / 5,025 / 2,352) EV = +0.04

S2 discards the 10S, trick 1; D led by S1, trick 2; S4 has 2 trump:

play R: (0 / 6,251 / 1,389) EV = +0.45
play QS: (0 / 5,272 / 2,368) EV = +0.07

When S4 has 2 trump, better for S2 to trump with R

Overall, since S4 is far more likely to have 3+ trump, if S2 plays off on the first trick, best to do the same on the 2nd trick, if they have the chance.

But in most instances, S2 will simply be following suit on the 2nd trick (after throwing off on the 1st trick). If we follow the above protocol (i.e., throwing off the same suit IF a S1 wins the 1st trick AND a D is re-lead), and otherwise following suit, the overall result is:

(10,138 / 151,589 / 23,031) EV = 0.68

This is lower than the 0.72 EV of trumping with the R on the 1st trick, so I stand by that play. BUT, the difference is small, so in the end, it all depends on how well you know your partner's and your opponents' play.

[irishwolf]

First thanks Ray for running this analysis trumping with Right from S2 an Ace led by S1 and he cannot create a void. The concluding results being that when S4 on R1 (QC up) has y two (2) trump it better to trump with the Right and if S4 has 3 trumps better to discard.

My comments but still digesting you post, and this is first blush:

1) With regular partner this is a Convention that S2 should only use the Right if he CANNOT create a void and does not have an Off suit Ace. If he has 2 dooubletons with an Ace also do Not trump in as you have a helping hand. Thus when S2 does trump in with the Right - S4 know knows he is on his own to win two tricks and should anyway for he is the one who called trump, unless Blocking and he expects to get euchred. I need to review these euchre rates when I get time because if he has two trumps + an ace it requires a strong coordinated Defense effort to get euchred.

2) Not trumping an Ace led by S1 presents a lot issues when S2 is void and S4 only has two Trumps. I WISH WE COULD SEPARATE OUT THE ANALYSIS FOR WHEN S4 HAS TWO TRUMPS WITH AN ACE. Reason is there are hands if S4 only has the 9C or 10C as the other trump card with NO Ace, S4 should always pass unless donating with nothing in Next??

I am assuming that you forced S4 to make trump with any Two (that's a question and important for the Posted results??

I suggest that Dealer should always (almost unless holding Jacks in opposite color) should call trump with any two trumps + an off suit ace. This leads me to the next issue I have:

3) You made a statement: "Overall, since S4 is far more likely to have 3+ trump" I don't know how to read that statement. Look at the probability of 5c1 & 5c2 for the 5 unknown trumps. 5c1 = 42% and 5c2 = 33%.

However, my rationale is ordering with two trumps + an Ace for S4 (otherwise that is suicide call if he has just 9C/QC or 10C/QC no ace) - 5c1 9C, 10C, KC AC & JS 42% BUT MUST HAVE ONE OF THE TWO ACES UNKNOWN = ~50% ! Thus 50% x 42% = ~21% the Dealer should have two trumps + an Ace & 6.5% will have two Aces (unless he passes with 2 aces).

Now let's look at those combos with 5c2 = (3+ trump QC UP) – 9C/10C; 9C /KC; 9C/AC; 9C/JS and 10C/KC; 10C/AC; 10C/JS and KC/AC, KC/JS & AC/JS. 10 combos make up the 33% but with QC/KC/JS AND QC/AC/JS MIGHT BE LONER ATTEMPTS DEPENDING ON THOSE OTHER TWO CARDS. So we have to reduce the 33% by a factor of, perhaps, 5% down to 27%. Of course with 2 trumps with or with or without an ace.

Now compare the holdings that S4 has with two trumps 21% and 27%. So 48% of the time S4 orders up the QC 21/48 two trumps vs 27/48 has 3 trumps. I don't call that FAR MORE LIKELY TO HAVE 3 THAN 2? And if S4 has 3 + QC trumps he most likely has the Left and is going alone. Thus 6/48 = 12.5% more likely has 3 than 2. Do you agree?

HOWEVER, WITH 5C1 = 42% - WITH AND WITHOUT AN ACE, I HAVE NO CLUE WHAT YOUR SIMULATOR DOES?

4) And if the convention is used it gives a wider range to call than having 3 total trumps using the Convention!

5) One more comment is that by NOT trumping in with the Right you are False carding your partner into believing your have created a VOID. Never false card like this is my Motto! And if you slough you have nothing of value to lead back to your partner. Get your trick even though you prefer not to use the Right like this - you have few options.

i am out until next week - traveling.

IRISH

Thanks for running this.

[raydog]

I realize now my results are presented a bit obscurely, but Irish's comments will help me clarify the important bits.

I neglected to simply do a head-to-head comparison of which card to play, once i figured out how to play the 2nd trick. So I shall present that now.

S4 has 2 trump: [24,080 hands meet criteria out of 1,000,000 played]
1) play R, then lead 10H: (1487 / 17,646 / 4947) EV = +0.45
2) slough 10H (then either follow suit, trick 2, or slough KH if D led): (36 / 18,277 / 5767) EV = +0.28

better to trump with R

S4 has 3+ trump: [160,711 hand meet criteria of 1,000,000 played]
1) play R, then lead 10H: (23,027 / 116,034 / 21,650) EV = +0.74
2) slough 10H (then either follow suit, trick 2, or slough KH if D led): (10,161 / 133,380/ 17,170) EV = +0.74

a toss-up (unless you are going for just one point and need to avoid being euchred)

So in the end, since S2 doesn't know how many trump partner in S4 has, it's better to play the R - in case S4 only has 2 trump.
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As for S4's hand, Irish correctly says that it depends a lot on what hands S4 calls with when holding only 2 trump. Which was also one of my caveats. Right now, that is a small minority of hands, but it still does drive the result - that the R should be played by S2 - so perhaps modifying this (i.e., having S4 call more often with just 2 trump) won't change the overall conclusion.

I won't bore you with ALL the rules my program uses to decide whether S4 should call with just 2 trump, but here is sampling:
1) With R+1, S4 might go alone, declare with partner or pass. With R+1 and 2 aces (3-suited), will go alone; with R+1 (K or lower) and all other suits blocked [max 1 pt if opponents call, R2], will pass; else will call;
2) with A+1 and and 2 off-suit Aces, will call if the A trump is turned, but pass if the A trump is in hand;
3) with any 2 trump + an off-suit green ace + 2-suited, will call.

That last scenario, is as close as I get to Irish's "call with any 2 trump + off-suit A". I plan on testing more aggressive calls by S4 (like 2 trump + off-suit A - mindful of what other suits are blocked [this is largely a defensive play to optimize EV, even if negative]), but I will address that when responding to the next post.
_______________________________

A couple of final notes.
1) I corrected my previous post, where I repeated mentioned playing the 9H or 9S. I meant the 10H or 10S (cards S2 actually has). I did simulate this correctly in my analysis - I screwed it up a few time, but got errors, and corrected!
2) I appreciate Irish's 2 conventional plays: the rule for trumping with the R from S2 (and generally how to deal with an A lead), and the notion of S4 declaring with 2 trump + off-suit A. I will test these scenarios to see if I should include in my program, but they look quite promising.

[irishwolf]

Ray, you concluded for this post when S4 has 3 trump:

"S4 has 3+ trump: [160,711 hand meet criteria of 1,000,000 played]
1) play R, then lead 10H: (23,027 / 116,034 / 21,650) EV = +0.74
2) slough 10H (then either follow suit, trick 2, or slough KH if D led): (10,161 / 133,380/ 17,170) EV = +0.74

a toss-up (unless you are going for just one point and need to avoid being euchred)

So in the end, since S2 doesn't know how many trump partner in S4 has, it's better to play the R - in case S4 only has 2 trump."

This to me, a little bit of a surprise as to the tie. However, that said, much easier to understand that with the two trumps scenario because it's a clear decision to order the Queen up with any two size trumps. And since S2 has no idea (repeating also what you said) what the Dealer holds having a lower euchre rate sways the decision to playing the Right as qualified above.

Further, it's justified that S4 have any two trumps + an off suit ace for S2 to trump as well even though it appears your program is WAY, more likely disqualify a lot of 2 trump holdings than I would in real play. Why - your program for 1,000,000 hands only 24,080 qualifies and that is only 2.4% by my calculations of having 2 trumps and 1 ace. And we do not need to delve into the restrictions as I can see what what your program is doing. Personally, I think the program might be too restrictive with some holdings on some holdings for S4 (if those were laid out for analysis, IMO). But that's okay,IMO.

The take away from the original post is that S2 should trump with the Right which I already knew but posted here on OE so others might also improve their play. It appears those who replyed to the post already suspected playing the Right was better in this situation. Also, S2 having an Ace or creating a void will change what S2 should do as he now has something of value and not obstruct his partner.

Thanks again for running the scenario Ray.

IRISH