The A-K-10-9 loner (4/19/02)
Another euchre scholar (3/5/04)
Another lesson in “next” (4/16/04)
B There (9/4/09)
B Woods’ loner (6/7/02)
Bid euchre 102 (1/12/07)
Book review: Joseph D. Andrews’ (2/4,11/05)
Book review: Fred Benjamin’s (4/13/07)
Book review: Richard Buchko’s (4/3/09)
Call it a “safety” (6/18/04)
“Carrying” your partner (11/19/04)
Champ’s ace (5/2/08)
Cheaters and obstructors (11/21/03)
Desperation loner in “next” (10/19/07)
“Dirty” deals (5/7/04)
Discarding the card ordered (9/5/03)
Discarding trump, part 1 (5/1/09)
Discarding trump, part 2 (6/5/09)
Don’t argue with success (7/3/09)
(Don’t lead the suit turned down) (9/17/04)
Don’t trump your partner’s ace! (7/12/02)
“Double suited,” part 1 (6/28/02)
“Double suited,” part 2 (7/5/02)
Down in the boondocks (8/30/02)
“Dumb and Dumber” (3/29/02)
Dumb luck (6/20/03)
The “end play,” part 1 (11/08/02)
The “end play,” part 2 (11/15/02)
Euchre ’n’ etiquette (5/23/03)
The “euchre hand”: Pass (1/2/04)
Euchre marching song (4/7/06)
Euchre on line (3/22/02)
Exposing your hand (9/19/03)
Exposing your hand: The penalty (10/3/03)
False carded & sucked in (8/2/02)
The finesse (5/9/03)
Five-handed euchre (4/4/08)
Going alone with 8 points (2/6/09)
“Green,” “next,” and idiocy (10/17/03)
Helping your partner sort his hand (5/4/07)
Holding aces (revisited) (6/6/03)
Holiday quiz (12/2/05)
“Honor on an honor” (8/1/08)
Hot bot (4/25/03)
How to get euchred going alone (1/7/05)
If you need the math . . . (8/9/02)
International “Eurchre Meetup” (7/18/03)
It’s “bower,” not “bauer” (11/7/03)
Journey to the past (2/3/06)
The jury is still out (11/5/04)
Lead low trump on “next” (10/4/02)
Lead trump, damn it! (2/28/03)
Lead trump only once on “next” (4/2/04)
Leading (6/6/08)
Leading away from an ace (2/14/03)
Leading before the discard (5/17/02)
Leading through a loner (2/1/08)
Leading to a loner: A two-ace convention (1/4/08)
Leading to the right bower (8/1/03)
Leading trump on defense (10/1/04)
Leading with three aces (3/7/08)
Lesson in “next” (12/19/03)
“Let the puppy in!” (8/23/02)
The marginal hand (1/31/03)
“Method” euchre (10/11/02)
The McLaughlin Group (10/14/05)
Money games (7/4/08)

The ace of hearts is led; the dealer’s partner is unable to trump, and the dealer takes the trick with the 10 of clubs. And now the question: Does he lead back his ace or king of clubs – to draw trump? Or does he lead the 9 of diamonds – to give his partner a shot, and perhaps to establish his own king? (I forbid him to lead the king of diamonds!)

This hand is not at all unusual. It is similar to a lot of other marginal trump calls. A cabal of euchre players – including a professional mathematician – spent several months on this question, and what follows is what we came up with.

For starters, the probability that the 9 of diamonds will draw the ace of diamonds is approximately, and not more than, three-fourths, which is the approximate probability that the ace is not in the pack. I say “approximate[ly],” and “not more than,” because of (1) the possibilities that the dealer’s partner or the third hand sloughed the ace of diamonds on the first trick, and (2) the possibility that the ace is not the lone diamond in the hand in which it is held, if any, and its use on the second trick would be futile or wasteful (i.e., someone trumped, or second or fourth hand takes the trick with the queen of diamonds).

The probability that the dealer’s partner holds the ace of diamonds is thus approximately, and not more than, one-fourth. But the probability that he will use it is less because of the possibility that the player on the dealer’s left will trump the 9 of diamonds.

And the probability that the player on the dealer’s left will trump the 9 of diamonds is not easy to calculate because it depends not only on his being void in diamonds, and on how many trump he has (if he has any), but on the rank of the trump he has (if any). Since only a 9 led, he might be smart to play second hand low and hold a lone trump on the chance his partner has the ace of diamonds; and he would be foolish to unguard a left bower in this situation. This all is based on an underlying assumption that each player plays his hand the best way possible for his team.

Now to the question of the probability that a trump lead will draw a bower:

The probability that both bowers are in the pack is 3/18 times 2/17 = just a little less than 2 per cent. Thus the probability that a bower is held by an opponent or partner is about 98 per cent. I would say that it is no more than 98 per cent because the club was not ordered.

The probability that a bower will be played on the dealer’s trump lead is 3 or 4 per cent less because of the possibility his partner has three trump with both bowers, or the left bower guarded by one smaller trump. And the probabilities that it will be used by partner or opponent, of course, are less than one-third of the remaining 94 per cent and about two-thirds of that, respectively, or about 25 per cent and 63 per cent, respectively (“approximately” again, of course, because by the time the trick gets to the fourth player, the jig is up; he knows what to do. The reason the dealer’s partner is less likely to trump than an opponent is, of course, that the dealer has led the ace of clubs; and his partner will not lay the left bower on that if he has it guarded).

But other variables that must be considered are (1) whether both bowers are out (probability about five-sixths), (2) whether both will fall on the dealer’s trump lead if both are out, and (3) the relative positional strengths (opponent gets to play last), etc. etc.

All of which makes one wonder whether the empirical approach might be more efficient than mathematical analysis – i.e., play a statistically significant sample of hands twice (once each way) and see what happens.

Harvey Lapp, webmaster of Euchre Central (and “Ask Harv” fame), posited:

“My friend Henry and I tried a few duplicate style samples of the hand. As with any common hand in euchre, we found that almost anything is possible. Sometimes the maker won and sometimes he got euchred. We tried leading trump and throwing off, but there seems to be no definite answer. I would simply guess that you have a 55 to 60 per cent chance of making a point with the hand, with the play siding in favor of leading the 9 of diamonds.”

“I can see the potential for this problem to grow in complexity very rapidly. And I don’t think we can get a definitive answer soon.”

But what is the probability each opponent will hold an unguarded bower? If the probability is infinitesimal (definition: Significantly less than 5 per cent), then my conclusion is either (a) lead the 9 of diamonds, or (b) it doesn’t make any difference.

I would have liked to have withheld calculation of the probabilities of the dealer’s partner’s holding as long as possible, but ultimately we could not. E.g., the probability that his partner has a bower is almost 4/15, but a little less, since he didn’t order (I do not factor in the knowledge that the lead opponent holds or held the ace of hearts because only an idiot opponent will lead a bower in this situation). The probability the dealer’s partner has the ace of diamonds is about the same – less than 4/15 because he didn’t order, but a little closer to 4/15 because it was not led.

I e-mailed these thoughts to Dr. Math just to get his juices flowing, and he got definitive. He replied:

“With that exercise complete, the probability that both opponents hold unguarded bowers (“simultaneous unguarded bowers”) is fairly easy: There are two classes of pairs of opponents’ hands – right bower or left bower in West’s hand. Assume West has the right. The rest of West’s hand is formed by drawing three cards from eight (since none can be a trump). This makes C(8,3) such hands. Then East’s hand is formed by drawing three cards from a deck lacking both trumps and West’s other three cards. This makes C(5,3) hands. So we have C(8,3)C(5,3) pairs of hands with the unguarded right in West’s hand and unguarded left in East’s. Since we have divided the totality of pairs of hands with unguarded bowers into two equally sized classes, the number of such pairs is 2C(8,3)C(5,3). The total number of pairs of any kind is C(15,4)C(11,4), so the probability of simultaneous unguarded bowers is 2C(8,3)C(5,3)/[C(15,4)C(11,4)] = 0.0025.

“Or one-fourth of 1 per cent. Definitely infinitesimal.”

And we were back on the precipices of intuition and subliminal perception, as in, “Did the guy on my right raise his left eyebrow, or did I just imagine that?”

Because even though a trump lead would establish high trump in the dealer’s hand 57 per cent of the time, it would do nothing to establish his king of diamonds; and it would guarantee him only two tricks – the one he already had taken with the 10 of clubs on the first lead, and the one he eventually would take with the king of clubs. And it could jerk an unguarded left bower or other lone trump from his partner that his partner could have trumped the 9 of diamonds with.

The quest went on. And it brought the kicker from Dr. Math:

As Dr. Math indicated, the question whether to lead the nine of diamonds or a club defies precise mathematical analysis. So while I was corresponding with Dr. Math and Harvey Lapp and others, I was also conducting empirical research – playing hand after hand, both ways, time and again, to see what happened (this was before I discovered Gerry Blue’s Euchre Laboratory. I did it with a real deck of cards, on the kitchen table).

And here are the results: I played 30 samples, each way (60 hands in all) – once with a 9 of diamonds lead, once with a club lead. Playing it “right,” I had 26 winners; I was euchred only four times. Of the 26 winners, however, five depended on leading the 9 of diamonds, and four depended on leading trump (on the other 17 it did not matter). Not real conclusive. We are still looking for volunteers to “go to the ball park” (i.e., the Euchre Lab!) and play 100 hands (twice each; 200 all day).

Now let’s do some really simple math: If you played those 30 hands only one way (i.e., leading the 9 of diamonds or the club), you’d be four or five short of 26 winners (depending on which lead you chose). So, you’d have at least 21 winners, maybe 22. Let’s call it 21-and-a-half.

Almost three-fourths of the time (21.5 divided by 30 equals 71.7 per cent) you’ll be glad you picked up the club for a two-suited shot at a point or two. That's significantly even better than the 55 to 60 per cent success rate predicted by Harvey Lapp and friend. Even if you are euchred 28.3 per cent of the time (8-1/2 out of 30), you are points ahead even if you score only one point every time you are not euchred. And sometimes you will score two.

In the midst of this extended query, I submitted the hand to Joe Andrews for publication in his MSN Zone monthly euchre column. Joe published it (July, 2001), but he missed the bus: He didn’t even get to the ball park! No chance to get in! Joe said you should not pick up the club!

That is absolutely incorrect. The dealer must pick up the club. Picking it up makes him two-suited with three trump. Mathematical analysis and experience both indicate that you will score (which means also, not get euchred) more than 70 per cent of the time if you pick up the club.

And if that’s not enough, there is another, perhaps even more compelling reason to pick it up. If you don’t, you are a sitting duck in “next,” and likely for a loner.

It is important to recognize the power of the deal (Joe seems not to understand this). The dealer’s position in trump is more secure than any other player’s: No one else felt secure enough to order the dealer up on this hand. The danger of finding both bowers on your left lurks, yes; but that’s another good reason not to lead trump: Make the opponent use one of his bowers on your nine of diamonds if you can.

[second of two parts]

Natty Bumppo, author,
The Columbus Book of Euchre

Borf Books http://www.borfents.com
Box 413
Brownsville KY 42210

(270) 597-2187 [copyright 2002] [next]

John Ellis, author of Euchre: The
Grandpa Lou Way, thinks that be-
ing “double suited” means having two
cards in one suit.

Well, I don’t think so – unless your opponents have six or seven points and could go out on a loner – or you see your left-hand opponent, who never has managed to hold a poker face, drooling and panting, waiting for you to turn down the heart. Or maybe you are getting your butt kicked 9 to 2, and you have to try something outrageous just to shift the momentum (but if that’s the case, why not go alone with that Q-10 of clubs?!).

Ron made a pretty good pitch, and he’s a good player (58 per cent winning percentage on Yahoo!, with the big boys, last time I looked); but I took his proposition to Gerry Blue’s Euchre Laboratory to test it. I played Ron’s scenario 100 times – playing the opponents’ cards optimally but without taking advantage of the X-ray vision the Euchre Lab gives you (and I threw out the hands on which an opponent obviously would have ordered up the club). These were the results:

But also he stopped nine loners held by the opponents, including two hands on which he scored two points – those were 6-point turnarounds! Ron was euchred on the other seven stoppers, saving his team 2 points on each hand.

Also he stopped one lone hand his partner would have made: That one cost his team 3 points.

In sum, Ron scored a net of -23 points in the 100 hands (that’s minus 23, or an average of nearly a fourth of a point lost every time he picked up that 10 of clubs).

Those nine opponents’ loners stopped out of 100 hands still give Ron a pretty good argument for picking up, however, when his opponents have 6 or 7 points – it’s the Bloomington corollary (see pages 13 and 35, The Columbus Book of Euchre [2nd ed.; pp. 13 and 34, 1st ed.]). And they might give him a good argument for picking up when his team has a big lead to protect – like 8 to 1 or 9 to 2 or 3 – that’s the Bubinski (pp. 13, 34-35, 2nd ed.).

I made one other interesting observation, on which I did not take notes: A few of the euchres (I did not count them) depended on a bold opening trump lead by the left-hand opponent – something he should rarely do. This observation either gives Ron’s weak pickup a little better odds, or lets some of the air out of my recommendation not to lead trump against the opponents. But there weren’t enough euchres depending on bold trump leads to give that recommendation a flat tire. Another study may be needed.

There was one potential euchre that depended on the left hand opponent’s leading a lone ace of trump from a holding of ace of clubs, ace-king of hearts and queen-nine of spades. Such a lead normally would be so stupid that I just did not let him do it; any other lead would have given Ron a point, and I gave him the point. ("Oh?" you say. "I would have led the ace of clubs!"? Go on. Lead it. That’s stupid. That’s my story, and I’m stickin’ to it.)

[first of two parts]

Natty Bumppo, author,
The Columbus Book of Euchre

Borf Books http://www.borfents.com
Box 413
Brownsville KY 42210

(270) 597-2187 [copyright 2002] [next]

Natty Bumppo, author,
The Columbus Book of Euchre

Borf Books http://www.borfents.com
Box 413
Brownsville KY 42210

(270) 597-2187 [copyright 2002] [next]

The logo on the Yahoo! group Euchre
Science is not the standard “perfect”
hand you see on so many euchre web
sites, but consists of ace and jack of
diamonds, 10 of clubs, and queen and
10 of hearts.

It is subtler than most hands heading euchre web sites. Gerry doesn’t tell us what was turned, but if we assume it was a heart lower than the right bower, I’d say:

At first hand I pass and wait for a chance to call next (or to euchre the dealer if he picks up).

At second hand I order into my partner’s hand only if we have 8 points or 9 (let him pick it up, for a loner, if we have less; I have “next” covered). If the opponents have a substantial lead, I order and go alone. If the score is close or we have a comfortable lead, I pass.

At third hand I keep my mouth shut: Too good an opportunity to euchre the dealer if he picks up; too likely I’ll get euchred or queer my partner’s “next” call if I order.

As dealer, I pick up and go alone (unless we have 8 or 9 points).

Second round (hearts down):

At first hand, I call next (diamonds) and lead the 10 of clubs. If my partner does not have the ace or a good king of clubs to cash, or a left bower to ruff with sometime in the hand (or another ace or good king off suit that avoids getting trumped), I hope my left hand opponent takes a trick to give me an end play with my right-ace. I am playing for one point, and no more. I need help; I don’t want to bleed my partner’s unguarded left bower if that’s all he has (and, with hearts down, he is more likely to have it than the opponents are), and I am not about to give the opponents an opportunity to go alone in black.

At second or third hand I pass: Too easy to get euchred, too good a chance to euchre the opponents.

Fourth hand is moot: Hearts would not be down.

Those were my “off the cuff” remarks in anwer to Gerry’s question, without application of probability theory or trial and error, based on “Double’s” principle: No time for analysis. But I stood ready to defend all of it. Those were my stories, and I was st-stickin’ to ’em!

But there did come fierce argument from Ryan (“Lead the Right Bower, Damn It!”) Romanik, who stated in regard to my suggestion to lead the 10 of clubs if going “next” in diamonds:

“Disagreed. Right bower lead is ‘best by test.’ If the club is going to find your partner’s ace, it will do it better after all unprotected trump are out of your opponents’ hands. Besides, although you fear the unprotected left in your partner’s hand, remember that since you hold only two trump, the probability that his left is protected soars.

“Furthermore: If your goal is your partner’s ruffing your lead with an unprotected left, you’re better off leading a heart, in my opinion. Four hearts are gone (queen and 10 in your hand, one turned down, and the jack ain’t a heart).”

The problem with Ryan’s reply is that, although he said “best by test,” he did not put it to the test. I did. This hand does not lend itself easily to mathematical analysis; so I took it to Gerry Blue’s Euchre Laboratory and gave it 100 revolutions times three: Once each with a 10 of clubs lead, once each with a heart lead (the queen and 10 are equal in the same hand, since the jack – wherever it may be – is the left bower), and once each with a “Lead the Right, Damn It!” lead. That’s 300 hands played (100 times 3; count ’em) all day (actually it took several days!). And I threw out all hands – “reset the scenario” – on which it would make sense for the dealer to pick up the heart that was turned.

The results:

First of all, on more than two-thirds of the hands (69 out of the 100) it did not make any difference what was led: All three ways the maker’s team scored either one point or two points or was euchred.

The broader results: The club lead made a net of 51 points; the heart lead, a net of 45, and the right bower (damn it!), a net of 29 points.

The club lead made 1 point 69 times, made 2 points 11 times, and got euchred 20 times: 69 plus 22 minus 40 = 51.

The heart lead made 1 point 63 times, made 2 points 14 times, and got euchred 23 times: 63 plus 28 minus 46 = 45.

The right bower lead (damn it!) made 1 point 59 times, made 2 points 13 times, and got euchred 28 times: 59 plus 26 minus 56 = 29.

I think it is interesting to note that the offensive totals – i.e., 1-point and 2-point scores combined – were equal for the club lead and the heart lead: 91 points. To me this says that when the heart lead worked, it generally worked better. But it didn’t work as often – 80 to 77 in favor of the club or, to put it the other way, the heart lead got euchred three more times. Even without these results from 100 samples, the reason I lead the club instead of the heart is that it gives my partner two chances: To take it with the ace or king of clubs, or to trump it. I don’t expect the heart lead to survive all three other hands; and since the dealer turned down a heart, I consider him the most likely player to be able to trump it; and he’s sitting in a position to overtrump my partner, or to hold back a trump if my partner plays a bigger trump than the dealer holds.

And I am not at all impressed by leading from a right-ace trump tenace when that is all the trump you have, and you have no aces outside. The right bower lead, like the heart lead, scored more 2-point marches than the club lead did. But it scored only 72 times or, to put it the other way, it got euchred a lot more. “There was a little girl, who had a little curl, right in the middle of her forehead . . . .” This seems to be a trump combination begging to be reserved for end play.

OK, I’ve played enough hands at the Euchre Lab! Lead the 10 of clubs, damn it! That’s my story, and I’m stickin’ to it!

Natty Bumppo, author,
The Columbus Book of Euchre

P.S. If it had been a diamond turned down, on second round:

At first or fourth hand, hearts alone.

At second or third hand, hearts with help.

Black down?

Hearts, any of the four hands. Alone if we really need it, from any of the four positions – depends on the score.

That’s my story, and I’m st-stickin’ to it!

Borf Books http://www.borfents.com
Box 413
Brownsville KY 42210

(270) 597-2187 [copyright 2002] [next]

In a question posed in a poll on Yahoo!’s
EuchreScience group, B Woods and his
partner, the dealer, trailed 8 to 6. The dealer
turned down a small club, and B called hearts
trump alone.

Now what to do?

The poll results:

0% B should lead the king of hearts
83% B should lead the king of spades
17% B should lead the ten of spades
37% B should not have gone alone
25% B’s partner should shoot him

I voted for leading the ten of spades. I had the advantage (or misfortune) of having played this hand with B Woods, as his partner, and watching him get euchred by leading the king of spades, costing us the game. Before I get to the reasoning behind my vote (yes, there is more than pure emotion), let’s take a look at the other answers.

Having suffered the euchre and the loss with B, I cannot fault the respondents who voted that B should not have gone alone and voted that his partner should shoot him – particularly the latter.

But I don’t really fault B’s going alone. It was a fair chance to win in a heartbeat against the opponents’ 8-to-6 lead. If B’s right bower had dropped the left and ace of trump – or just either one of them – the king and ten of spades would have looked pretty good, particularly in light of B’s right-hand opponent’s having elected not to go “next” with spades.

And it was a reasonable shot at just a point, to keep the third hand from going out in diamonds or spades.

As it happened, B’s lead of the king of spades drew the ace from the opponent on his left; that opponent then led the ace of trump to his partner’s left bower (taking B’s king of trump down with it), and the partner on B’s right then took the euchring trick with the queen of spades (over B’s ten).

There are other ways the disaster could have occurred: For example, the jack of spades would have worked as well as the queen; or the opponent who cashed the ace of spades might have had the jack or queen of spades himself to lead back (or even the nine to be trumped by his partner); or he could have had the left bower to lead, taking B’s king of trump, and then, with or without his partner’s help, cashed diamonds or clubs; or he could have led a club or a diamond to his partner’s trump and the partner could have led the nine of spades back to the first opponent’s trump, etc.

The point is, B had to know he was in trouble when neither the left bower nor the ace of hearts fell to his right bower. At that juncture he had to forget about the loner and concentrate on saving a point (he could still get lucky, but he had to keep his eyes on the prize – the game, and staying in it).

If he had led the king of hearts, he would have had to drop both the left and the ace on one trick, or hope the opponents had only one and not the other, and hope they would lead spades – twice, if they have the ace of spades. If B dropped only one of the two bigger trump with his king of hearts, there would be a fair chance the guy who played it had the other, and no spades, or the ace of spades, or that his partner had the ace of spades, etc. Scratch king of hearts (no one voted for that).

I think B maximizes his chance of saving a point by leading the ten of spades. That forces the ace of spades if it’s unguarded, or guarded only by the nine, making B’s king good if the taker eventually has to lead the nine or his partner winds up with the fourth trick and nothing but a spade to lead. And if the opponent on B’s left is void in spades, he might forget “second hand low” and waste his ace of trump on the ten of spades in his eagerness merely to stop the loner (B’s call could have been a “lone bluff”: See page 47, The Columbus Book of Euchre (2nd ed. The left-hand opponent should be shot, of course, if he plays the left bower on B’s ten of spades).

If the ace takes B’s ten of spades and the opponent leads the ace of trump (as happened), B’s king of spades might have saved the day (if the left bower was led, though, school was out, of course – as it would be if the opponent took the ten of spades with the jack or queen and had the ace to lead back). If the opponent leads another suit his partner cannot trump, B prevails with his king of trump.

The king of spades lead works if both opponents have spades without the ace. The mathematical probability of that is only 8/18, or 44 per cent, but realistic odds are closer to 50-50 given the right-hand opponent’s election not to go “next.”

The king of spades has a fair chance to work if it forces an opponent to trump – but that works only if the opponents have only one trump, or have both but no opportunity to draw or overtrump B’s king of hearts, or have to lead the nine of spades back to B’s ten.

All I am saying is, leading the ten of spades is more likely to set up the king as a winner than the king is to set up the ten. The ten is almost as likely as the king to force a trump. And the ten will not suggest that you have another spade to any but a sophisticated opponent; so it gives a fair chance of getting spades led back.

I think the king of hearts is the second most reasonable lead, on the hope the left and ace are in partner’s hand or the deck, or that someone will eventually have to lead to the king of spades. It is a lot to hope for the spades to take two tricks even if you get the trump out first (i.e., it was a “long shot” loner in the first place), and it is just too much to hope that both the kings of hearts and spades are good when you have not seen the left or ace of trump or a single spade after two tricks.

But I am going to let Gerry Blue, the EuchreScience webmaster and inventor of the Euchre Laboratory – where this hand is set up for you and you can play it out – have the last word. He voted for the king of spades lead, and would again. He voted also that B should not have gone alone.

Gerry agreed that there was a reasonable shot at one point, “especially with help. Pretty decent shot at two points with help. That would have tied up the game, and then while the opponents are distracted by your berating B for not going alone, he’s stealing the deal.”

Gerry added:

“I toyed with leading the ten of spades but decided on the king because I think the ten is unlikely to force out the ace of spades. If I’m an opponent and B leads the ten and I hold the ace-queen, I’m going to play the queen even if I sit to B’s left, since he’s going alone. I don’t have to beat my partner, just the ten. That leaves me with an ace still in my hand, which always feels good. I’ve stopped the loner and am now shifting gears to focus on the euchre (and the game).

“And if I’m on the left and void in spades, I’m thinking B’s sweating if he’s leading an offsuit ten in a loner; so I’ll throw off and look for my partner to take the trick with a higher spade or a trump. Then I’ll have the end play on the next trick. If, however, B leads the king, I have to seriously consider playing my ace of trump if I have that and not the left bower. My primary goal is to stop the loner.

“The ten is almost as likely as the king to force a trump but not quite. When I put myself in the shoes of the player to B’s left, I have a much different reaction to a ten than I do to a king. The ten indicates to me that B’s in panic mode and worried about getting euchred, while the king gives me the impression he doesn’t have the left but probably does have the ace or king of trump (but not both, or he would have led one of them).”

There are too many variables here to pin this hand down with mathematical probabilities, and you can argue with us and our reasoning all you want. I love to argue. It’s my job.

But you can’t argue with B Woods. He’s dead.

Natty Bumppo, author,
The Columbus Book of Euchre

Borf Books http://www.borfents.com
Box 413
Brownsville KY 42210

(270) 597-2187 [copyright 2002] [next]

“Here is a question I received that I also would be interested in finding out the answer to. Perhaps Dr. Math knows?” [Dr. Math is my brother the mathematics Ph.D. at Motorola who tells the engineers to jump, and how high.]

I'm doing a speech on euchre and I need some statistics. I was searching all over the internet, but still couldn't find what the probability of getting a "perfect" hand is. By "perfect hand" I mean jack, jack, queen, king, ace. I know it's very, very rare but I was hoping you would know the answer.

A . . . A . . .
Baltimore, Md.

Start with any jack: The probability of getting a jackless hand is 20/24 times 19/23 times 18/22 times 17/21 times 16/20 equals 36.48 per cent; so the probability of getting a jack is the complement of that, 63.52 per cent (another way to look at this is that if you hold a hand without a jack, that’s fairly unlucky).

Now we need the other jack, same color. Four chances out of 23, 4/23. So, the probability of holding both bowers – if their color becomes trump – is 4/23 of 63½ per cent equals 11.05 per cent. Not so rare – a little better than one in ten (but keep in mind, for more than three out of four of the scenarios depicted below, it depends on everyone else’ keeping his mouth shut – i.e., not ordering or calling trump before you get the opportunity. Not presently practically calculable, even in the 21st century).

And on down:

King of suit, 2/21; all four, 2/21 of 1.5 per cent equals 0.14 per cent – (one chance in 714 of getting the top four).

And queen, 1/20; all five, 1/20 of 0.14 per cent equals 0.007 per cent – i.e., less than a hundredth of 1 per cent, or a little less than one chance out of 14,000 hands of getting a “perfect” hand (without consideration of the suit turned or another player’s making trump. N.B.: The original calculation, before Mr. Reid’s correction, was 0.009 per cent, or one chance in a little over 11,000 hands).

Fifth trump: 3/20 of 0.29 per cent equals 0.043 per cent – i.e., the probability that you will get a “perfect” hand (but not necessarily a royal flush) is once in every 2,323 hands (again, without consideration of the suit turned or another player’s making trump. N.B.: The original calculation, before Mr. Reid’s correction, was 0.06 per cent, or once in every 1,771 hands).

If you play ten games of euchre a day (not an awful lot for a euchreholic, particularly for an internet euchreholic), that’s a hundred hands a day. At that rate you will get a “perfect hand” every 23.23 days – i.e., roughly once every three weeks.

If your correspondent still insists on euchre’s version of a “royal flush” (i.e., two jacks, no ten and no nine), he’ll still get his “perfect hand"“ once every 140 days, or nearly three a year.

Now, just for fun and nausea, let’s revisit that “perfect hand” one more time:

Actually, only the player to the left of the dealer can get a “perfect” hand, because of the possibility of sabotage – intentional or accidental – in the making of trump (i.e., someone else’ ordering or calling before you get the chance).

And because the player to the left of the dealer has the lead, all he needs is either (1) the two bowers and ace and any other trump plus a suit ace, or (2) the two bowers and any three other trump. Those – held by the player left of the dealer, and only by that player – are the real “perfect hands.” But he needs also the right suit turned.

The combined probability of J-J-A-x-x (all trump) and J-J-A-x + A (four trump plus outside ace) – with the probability that the dealer will turn a card of the desired suit factored in – is 0.00707 per cent, or once in every 14,144 hands – once every 141 days at ten games a day; you’ll get about two-and-a-half such hands a year.

But then you have to divide by four because you sit to the left of the dealer only a fourth of the time. That makes the probability 0.00176 per cent, or once in every 56,818 hands. By this definition you will get a “real” perfect hand about every 568 days – i.e., about every year-and-a-half (if you play ten games of euchre every day for a year-and-a-half!).

[Caveat: Some of the decimal numbers above are rounded slightly; so you won’t get the exact results I got if you crunch them.]

Natty Bumppo, author,
The Columbus Book of Euchre

P.S. Where does one give “speeches” on euchre???!!!

Borf Books http://www.borfents.com
Box 413
Brownsville KY 42210

(270) 597-2187 [copyright 2002] [next]

Leading before the discard: The “Muncie ploy" and the "Brownstown maneuver" – May 17, 2002

The “Muncie ploy” – pages 19, 50-51, The Columbus Book of Euchre (2nd ed.) – consists of leading before the discard, to prevent the dealer’s calling alone in time (once play begins, it is too late to declare alone).

The “Brownstown maneuver” – pages 13, 38, 51 (see also the New Appendix to The Columbus Book of Euchre, on line) – is the same thing by the dealer’s partner when the third hand has declared alone – to give the dealer an idea what to discard. Conversely, the dealer should wait for the lead before he throws off.

Ryan Romanik wrote from Michigan:

Some of your ploys seem a little shaky as far as being actually legal according to the rules of euchre. For example, I had a hard time convincing my playing group that the Brownstown maneuver was actually legal, until I found the clause in the “official” rules that if a card is led out of turn, it is placed face up, etc.

My question is: Is there similar justification for the Muncie ploy? In other words, why is it that just because you’ve led out of turn I lose my opportunity to call alone? Since the lead is out of turn nonetheless, why does it move the dealer from the “calling trump” stage to the “discarding” stage?

-Ryan!
rromanik@umich.edu

Natty Bumppo replies:

First of all, you have hit upon some of the differences between the way euchre is played in Michigan and the way it is played in Southern Indiana! But seriously:

As for the Muncie ploy, you should have no trouble finding a rule – or at least a consensus – that a loner must be declared before the first card is played. See page 141, Official Rules of Card Games (71st ed., United States Playing Card Company, Cincinnati, 1990).

I, too, have had trouble convincing my friends of the legality of the Brownstown maneuver. In fact, in the circle I play in, my house (just outside Brownsville, Ky.) is the only one in which the “maneuver” is allowed.

But both ploys are “legal,” and the reason is that neither is “illegal.” Neither of those ploys is a “lead out of turn.” It is the leader’s “turn” to lead, in both instances. He just leads before the discard. You will not easily find a rule requiring the discard to be made before the lead, or requiring the leader to wait for the discard (you certainly won’t in the Official Rules of Card Games).

And, just like drinking Postum, there’s a reason: As for the Muncie ploy, it is normally not to the leader’s advantage to lead before the discard. Normally, it is greatly to his disadvantage. So, it does not need a rule of prohibition.

And so, then, why shouldn’t an alert player in the lead take advantage of the sloth or ineptitude of an unalert dealer? After all, the dealer has an absolutely peremptory antidote – he merely declares alone before he touches the turned card (or before he calls the suit, if on second round). That’s the “Milroy squelch” (pages 19 and 51).

The Brownstown maneuver likewise is not a “lead out of turn.” And it is legal simply because it is not prohibited. It has nothing to do with the rules regarding “leads out of turn.” (Obviously, it took some smart ass lawyer to figure this one out. Guess what the author’s day job is.)

Natty Bumppo, author,
The Columbus Book of Euchre

Borf Books http://www.borfents.com
Box 413
Brownsville KY 42210

(270) 597-2187 [copyright 2002] [next]

Gerry Blue, EuchreScience webmaster, wrote:

To the best of my knowledge, Playsite never had the TRAM option. They have the option, as you know, of “auto play” if there’s only one legal play you can make.

I prefer Playsite. None of the euchre sites on line has all my favorite options; but, all things considered, Playsite appeals to me the most. I like the user interface at Pogo the best, but I’m not crazy about their ranking logic. It seems to be based on the number of games won versus the games played, where Playsite bases the change in your rating on the rating of those you beat. I also like being able to go alone if my partner orders up the right when I’m the dealer. I suppose I like a few of the fringe rules such as “shaft the dealer” and defending alone. I also like being able to select the card I intend to play before it’s my turn. But I do wish Playsite didn’t force everyone to leave the table and create a new one after each game, and I also wish watchers could kibitz.

Gerry Blue, inventor, the Euchre Laboratory

Natty Bumppo replies:

Thanks for your critique. It seems that we are in agreement on many features of both Pogo and Playsite.

Playsite did have TRAM, I am pretty sure, when I first encountered it four or five years ago. I like the “auto play” feature, but I just cannot get used to that retarded requirement of deselecting the card picked up before you can select one to discard.

And I don’t like Playsite’s “go alone” option, that not only allows a dealer to save a loner from a “non-Canadian” partner, but also allows one to defend alone on an ordinary call: That discourages the “Columbus coup” – ordering or calling with the intention of getting euchred, to pre-empt an opponent’s loner.

It might be acceptable if it would give the maker four points if he does not get euchred, but it doesn’t. It would be acceptable if it were a game “option,” but it’s not; it’s standard on Playsite. Pogo, to its credit, at least makes “defend alone” optional; and Yahoo!, to its greater credit, does not countenance “defending alone” at all. The only time defending alone makes sense in traditional euchre is when the maker is going alone; and none of the sites gives you that option.

I agree that Pogo has the friendliest and most logical user interface – among Yahoo!, Playsite and Pogo, for example, only Pogo makes it clear when someone is going alone. Pogo has the friendliest graphics also (maybe this is part of the same thing), and it is much easier to get a game started on Pogo than it is on Yahoo! Maybe these are the basic reasons I generally prefer to play on Pogo, even though I pan it severely on Borf Books’ Euchre links page and recommend Yahoo!

But Pogo’s allowance of “booting” by unanimous vote of other players (all of whom may be ignoramuses) is even more annoying and frustrating than the card deselection requirement on Playsite.

And the rating systems on all the sites are flawed. Pogo’s works like Yahoo!’s the best I can tell (one of them copied it from the other, and so did Playsite; I forget who had it first): The main consideration is one partnership’s average of ratings compared to the other’s: The higher rated partnership will gain less for a win, drop more for a loss, and vice versa.

The only way the number of games played comes in is that it takes a while to work your way up from the initial low rating. I would have no problem with that if that were all there was to it. The number of games played is not a ratings factor in itself. It goes back to the comparative rating factor I disapprove of: You have played few games; therefore you have a low rating; therefore you will gain more if you win than you will lose if you lose, and your higher rated opponents will lose more if they lose, gain less if they win.

The purpose of weighting results (on the basis of comparison of the two game partnerships’ average ratings) is commendable – to keep players from enhancing their ratings by continually beating up on incompetents – but it just doesn’t work fairly; and it discourages mixing players of different levels. How is one to get ahead if he can’t get into a game with other good players (or rig his rating with mutually consenting “lambs and lions” teams)? Just dumbing down the system to equal additions and deductions for wins and losses, regardless of the relative rankings, would be fairer in the long run.

Let’s think about it. Regardless of what happened in the past, the New York Yankees and the St. Louis Browns started even every April. And even in September, when the Yankees were always in first place and the Browns always in last place, if the Browns beat the Yanks they would not gain more than a game on them in the standings, and the Yanks would not lose more than a game. So, what’s with Yahoo!, Pogo and Playsite? They know better than the American League? Give us a break!

Natty Bumppo, author,
The Columbus Book of Euchre

Borf Books http://www.borfents.com
Box 413
Brownsville KY 42210

(270) 597-2187 [copyright 2002] [next]

“Throwing in the cards” is real life’s equivalent of “TRAM” (you do know “TRAM,” don’t you? It’s the acronym of “The rest are mine,” the automation feature that “swooshes” the cards on Pogo when the outcome of a hand is determined). The failure to “swoosh” sometimes tips a hand, too, as pointed out in my critique of euchre on line on Borf Books’ euchre links page.

Ryan gives us a good example. If his opponents have taken the third trick after he and his partner have taken two, and he does not immediately claim his third trick if that is his wont, the opponents can lead trump with abandon, on the assumption that one of them has the “boss” – to capture the remainder of Ryan and his partner’s trump (if Ryan’s partner has the boss, school is out anyway; the opponents lose nothing by their boldness).

But another reader, David Lin, pointed out on July 21, 2003, that that is the defenders’ correct assumption anyway, with the trick score 2 to 1, whether or not the maker “throws in” the cards – the defenders have to have the “boss” at that point to score a euchre.

But the failure to “throw in,” if that is customary, is encouragement for one opponent to ruff low on the fourth trick on the assumption that his partner has the fifth trick locked up with the boss.

“Tipped hands” are rare, however. The main reason not to “throw the cards in” (which my buddies and I do all the time, by the way!) is that it may prevent an audit in the event of a dispute (who took what?). So it is a particularly bad practice in tournament or money play, or when players are drinking too much (which my buddies and I do all the time, by the way!).

So, yes – play it out.

(The remedy “to play out every hand” reminds me of my admonition either to sort your cards constantly or never to sort them at all: See “Don’t sort your cards,” p. 41, The Columbus Book of Euchre, and at the New Appendix on line.)

Natty Bumppo, author,
The Columbus Book of Euchre

Ryan gets in the last word (almost):

Another reason not to “toss ’em in” or “TRAM”: It doesn’t give your opponents enough chance to renege. Sure, serious players shouldn’t make that mistake; but they do, and if you’re playing with and against people who can’t even hold their cards straight, there’s a 2-to-1 chance the reneger will be your opponent (not to mention that nitwit opponents might not catch your partner reneging anyway!).

-Ryan!
rromanik@umich.edu

Bumppo:

Good point! Same reason you sometimes defend alone against a loner when you have one sure trick but not much chance at another: If the loner reneges, you get 4 points. Page 38, The Columbus Book of Euchre.

Natty Bumppo, author,
The Columbus Book of Euchre

Borf Books http://www.borfents.com
Box 413
Brownsville KY 42210

(270) 597-2187 [copyright 2002] [next]