The Tao of Gaming

Boardgames and lesser pursuits

Rules that are just wrong, latest example

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Khora — You roll dice to take actions. Rolling high is always more economical. So the rules say that if there is a timing conflict during an action the low roller goes first. Fair.

But is it the “low roller among the people involved in the conflict?” It is not. If the low roller isn’t involved, you just start from them and go around.

So easy to at least get this right, but they don’t. Pisses me off. (Assuming I was told the rules correctly).

Written by taogaming

June 29, 2022 at 8:02 pm

Posted in Rant

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May/June Links

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A computer science prof from Berkeley gave a lecture about the problems with crypto currency, and was then interviewed by Current Affairs, titled “Why Crypto should die in a fire.” I’d been leaning against Crypto (a comment on BGG: “If crypto is currency, why do they need to advertise?” struck a chord) … now I’m sold. (I did watch the video, but the interview has everything important and is faster). (Via Slashdot)

Software crashes all the time, but software can save disoriented (or unconscious) pilots by taking control to prevent a crash.

Someone on reddit posted a link to Pagat’s rules for Cuttle, calling it the original “Combat card game” (whatever that is). Looks interesting.

I don’t know what I’d use 1 Petabit per second for; I suspect I’d find something.

Wizards of the Coast is hiring a “Senior Design Economist” for Magic.

Neil Gaiman’s anecdote about how he got over imposter syndrome, a little.

How much of the income gains from higher education go to landlords?

How Raymond Smullyan lost a bet involving the Birthday Paradox.

Kramnik on the current Candidates Tournament: “I have never seen so many bad games in a top-level tournament.”

Written by taogaming

June 26, 2022 at 3:11 pm

Posted in Linky Love

Too Many Words about Dice Realms (Vol 1 of ?)– Some Definitions and Debates

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This article is an attempt to starting clarifying my (evolving) thoughts about Dice Realms by putting them into words. There are presumably (much) better players than me, but are they writing anything? Nope. Note — My experience is 2p or 3p; I don’t know how much a fourth player changes things.

And like any varietal game, the individual setup matters enormously; but for now we’ll ignore the variable tiles (although I am assuming a standard fate die for now). As I only have ~10 games under my belt (at the start of writing this writing) these thoughts are highly preliminary … hence “Debates

Winter is Coming — The Expected Value of a Die

Remember a basic die’s sides are 2x progress (pink / improvement), 1 VP (green), 2 Grain (yellow), $2 (orange), and Defense+Grain+Coin (grey). So, a die has an expected value of 0.5 grain / turn. Winter costs you a grain per die and shows up roughly every three turns. Which means that a (non-green) die is net grain positive (as well as other stuff). But the cost (two grain along with $5) means that an early purchase might cost misery if you can’t cover a winter roll next turn.

(Of course in theory you could roll nothing but winters from now on, but we’re talking expected value and ignoring variance).

Assume the game were to go on for ~13 turns. Even if buying the die cost you misery next turn, you should make those 2VP back from rolling land (VP) and have a profit in grain/money/upgrades. (And the four upgrades you’ll get should be 2-4 VP, as well as generally useful). If it cost you two misery, then you are still likely ahead VP (roughly) and getting value from upgrades.

Dice are a limited resource, grabbing a die may also deny your opponents a die (maybe not now, but later on).

Debatable Position #1 If you can buy a die on turn one, it is right.

Buying dice becomes suspect in the late game. If you bought a die right before the game ended (particularly if you risk misery) you don’t have time to “make back your investment.” (One exception may be if you are fully upgraded, so that the last die gives you a way to dump progress/$$ into upgrades for VP, as well as maybe rolling a VP if it is green). But early game dice earn throughout. There are certainly setups where the game will end faster than you think and that is the strongest argument against a turn one die, but

Even More Debatable Position #1AA Green die on T1 is still net-positive (probably not nearly as much as a grey die….). The die earns at least 1VP/turn. If you hit misery for it every time winter is rolled, you are still up 1/3rd a VP a turn (maybe minus a few because of the first miser you wouldn’t take), plus the benefit of any synergies, and possibly some extra late upgrades for more points/VP rolled.

This isn’t to say that its right, but the main point is that in my first games I was reluctant to take a die if I risked misery next turn, and that was wrong. (Maybe if you risk three misery, but a bit is OK).

The Expected Value of an Upgrade

Let’s compare the die to the EV of an upgrade. An upgrade is 1VP (if going from a 1pip face to a 2) and 1/2 a VP (if going from a 2pip face to a 4), and nothing if going sidewise, but presumably those help in other ways. Moving up the pip chain improves efficiency; hard to measure but hopefully worth more than 1 VP a game.

The problem with an upgrade is that it only shows up one turn out of six, a bit more often with re-rolls and even more you can get tiles that re-roll (or let you set a die). But normally, when you improve from (say) 1 Progress to 2 Progress, you’ve only net gained a single Progress every six turns. (Call it 5 with rerolls). So that’s an EV of 1/5 of a progress.

A new grey die provides a Progress every three turns (and something the other turns as well). Not surprising, since a die costs much more than a progress improvement. But this leads to …

Debatable Point #2Your early upgrades should be aimed at getting dice. My auto-upgrade for “two progress” was upgrade Progress 1 to Progress 2 (twice) or 1VP – 1 Progress (Twice). But now I think that better is to upgrade “sideways” by turning 1VP into $2 (twice).

Obvious Argument — $2 can always turn into Progress, but the opposite isn’t true. This upgrade quadruples your chances of rolling $4 (before counting a re-roll) which gets you a die (with $1 from the prior turn). So you are likely to get a die much earlier. (And on the turns you don’t get $4, $2 can still upgrade. Moving your forts from $1 to $2 moves again closer to more dice).

And (after I wrote the above) I noticed that Tom had posted in one of the Dice Realms forums (which I can’t find) that “player’s who are going for dice early often cross-grade (1VP to $2)” (emphasis mine), which is not quite a ringing endorsement, but at least hints that I’m onto something.

About that Assumption ….

The biggest counter argument is “What if the game isn’t that long?” There are threads on BGG about four turn games, which seems short (for the base setup) but can happen. I guess rule zero (of many games) is “Have a good idea how soon the endgame is, because endgame effects are a big deal.”

Certainly if the bank looks close to breaking (in some why) don’t go -3 VP (for misery and a lost upgrade). But All other things being equal, a die gets better and better the longer the game, although the same is also true of an upgrade.

(“Ceteris is rarely Paribus,” as the Hideous Hog liked to say).

It can be difficult to estimate length of a game of Dice Realms. The dice variance can ring you up. Sure, you expect winter’s 1/3rd of the turns, but three in a row isn’t really that uncommon. And a few good harvests in a row can break the bank on grain.


This took me longer to write that normal, which is due to a few reasons:

  1. The TaoLing isn’t as enchanted with Dice Realms as I’d suspected / hoped ( which means my game count isn’t growing as fast as I’d like), which leads to…
  2. I’m not sure I have anything interesting to say.

So after sitting on this for a week or so, I’m going to publish it and start the debates….

Written by taogaming

June 12, 2022 at 10:08 am

Nice …

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I’m playing Bridge online with Hank, which means we’re playing Polish. (My normal partner is out, so we’ve rotated partners). One problem is that while I remember the Polish parts of Polish (the 1 Club opening), I’m struggling to remember some of the other stuff, since it’s been six months…

I pick up S: J94 H: J72 D: KQ98 C: A53 and Hank opens 1 Spade in first seat.

Fortunately we’ve already had a major suit opening come up, because Hank and I play a variation of major suit relay raises (which I first encountered via Jeff Goldsmith). It takes me a while to remember which bid shows a limit raise, but eventually I do and bid 3 Clubs. (It could also be an odd hand, but 99% of the time its a limit raise).

(I do have a full twelve count, arguably too strong for a limit raise, but there are several warning signs. 4333 distribution is bad and the jacks, particularly of hearts, are dubious. And since our 1 of a major openings are capped, they tend to be a bit lighter than normal).

Hank bids 3 Spades (“I do not want to be in game opposite a limit raise”) and I pass (along with everyone else). I’m dummy, but I’ve got BBO set up to not show all four hands, just declarers (so I can think about the hand if I want). The opening lead is the club queen.

Dummy (me) S: J94 H: J72 D: KQ98 C: A53

(Club Queen led)

Declarer (Hank) S: AQ752 H: KQ4 D:J32 C:T6

I’m happy with the auction. We have to lose a heart, a diamond and a club, and losing at least one spade seems likely. And I note that this is the case even though all three jacks between us are useful! (Without the red jacks, if the red ace was wrongly placed, we’d lose a second trick in that suit, and without the spade jack there is no legitimate line to play for no spade losers).

The main way to avoid a spade loser is to find East with the K of spades and a single small one. Finesse the queen, play the ace (dropping the king) and the jack picks up West’s last spade. Obviously that’s not great odds. Hank ducks the club (RHO playing the seven) and LHO continues with the Jack. Hank wins the ace (RHO playing the King) and leads a spade of dummy … three, queen and eight.

Our opponents are sisters, but West is a relatively new player. I think the eight is a true card. I’ve noticed the eight, and I think Hank did as well. Hank leads the diamond three and it goes seven-king-four.

My suspicions are confirmed when Hank plays the Spade Jack from dummy. I type “Nice” in the chat window even before the other cards appear as expected.

Spade jack – six – two – TEN.

This is the other way (apart from RHO having the stiff king) that the suit can be played for no losers … pinning the ten. Unlucky for West that her spades were T-8. If she had say, (T-3 and East had K-8-6) then it would be much harder to read the position, but assuming the eight was a true card then the pinning play is correct.

Against an expert West, there’s also the worry that the eight is from T-8-x trying to muddy the water. To tempt declarer into a pin instead of just laying down the spade ace, which West knows will work (in that situation). But if you’ve never seen the position before, then the mandatory (?) false card is hard to spot.

So we’ve “missed a game,” but all around it was a good game to miss. Nice.

Written by taogaming

June 8, 2022 at 8:08 pm

Posted in Bridge

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Media Roundup and Random thoughts

I wandered through the local game store and Kanban EV was on the shelves with a sticker of $230! I remember writing a Eulogy for the $50 price point, but that’s been early 20 years ago. It’s not quite Eulogy time, and there have been plenty of expensive kickstarters and games at $120 or so in game stores, but it was a shock seeing a sticker will north of $200.

There are still cheap, good games (I got Innovation for $20), but also multiple copies of Kanban, so I guess they’re expecting buyers.

Recent Media:

  • Everything Everywhere All At Once — Fun. Excellent
  • The Lincoln Lawyer — Pretty much what you’d hope for in a lawyer drama/miniseries by David E. Kelley.
  • Giri/Haji — Japanese Cop/Gangster Drama. Started mediocre, a touch long, but decent beats and a few bizarre things. Would have been less interesting as an American production. Not great, mostly predictable; but the unpredictable parts were truly “un.”
  • Hellbound — A Korean series where Angels tell sinners that they are damned and when they will be ‘collected’ by demons … and how society reacts to this revelation. This feels like OK fan faction of what might have been a good story; but again the foreign production provided one or two real surprises (although some twists and tropes I called out ahead of time)
  • Molly’s Game — If you like Aaron Sorkin, this is Aaron Sorkin.
  • Steve Jobs — Ditto, although this feels like Sorkin imitating himself.
  • Ali — Never caught this the first time around, good movie (saw it before “The Slap,” if you were wondering).
  • Margin Call — Saw this again, an under-rated flick.

Played in an actual bridge sectional for the first time this year (I think?). Very rusty, but also playing with a partner where we said “2/1” but not which flavor(In particular, what does opener’s rebid of “two of a major” mean after a 2/1 bid) so we had several auctions where we weren’t sure if we were on solid footing.

Written by taogaming

June 5, 2022 at 3:56 pm

Posted in TV & Media

Pastiche: The Birth of a Masterpiece

We live in the future. Sometimes that’s easy to forget.

Last month, I played a great card game that came out nearly a decade ago in Japan. Less than two weeks ago, there was a message on a discord from someone placing an order in Japan, and would anyone like anything? I asked for a copy of Pastiche. It shipped from Japan to Boston (along with other games) and that package was open, then my game was shipped to Texas. The whole process took under two weeks. I paid $8 bucks shipping.

Thirty Years ago, we poured through for information, scrounging up a catalog, calling Adam Spielt (and paying international rates, remember those?) to place a giant box order that took months to arrive. Lucky we weren’t trying Thirty Five Years ago … it would have been impossible.

Now? An off hand comment, a few messages, an email, and done. We live in the future.

So I got a tiny box of cards. Beautiful cards. But no English rules (I remembered perhaps 90% of them, but not setup details). No problem, Google knew.

And so now, twenty four hours later, I have recorded the most plays of Pastiche on BGG of any user, which isn’t too surprising given a predominantly English site and a relatively unknown Japanese game. But it’s a shame. Pastiche flew under everyone’s radar for years, and under my radar until recently; but it’s an excellent rummy game.

Players draw (“Read”) and meld (“Publish a novel”) similar to most rummy games, but you can meld runs, triplets, straight flush, three or four pair (not necessarily consecutive), and some odd ones. But the deck in Pastiche is odd, there are seven suits of seven cards, but one suit (Mythology) is 1-7, the next suit is 2-8, all the way up to Magic Realism which is 7-13. So there are seven ‘7s’ and only a single 1 and 13. (One of the melds is simply “The 1 and The 13”

Pastiche’s trick (such as it is) is that meld’s don’t score points directly and you can grab cards from anyone’s meld (including your own). (The rules don’t call it this, but I refer to this as “Plagiarize”). But once a meld is reduce to a single card, then enough people have read it that it is now a Masterpiece, and that scores points (based on how tough the meld was to make).

More importantly, people can always use the final card of a masterpiece as a meld, paying the original author one card from hand. So it still costs a card, but you don’t need to remove that one card to turn your own novel into a masterpiece. (And you can use your own masterpieces for free) … Towards the late game, seven or eight card melds may be playable with only a few cards, and hit the table already a masterpiece!

Melds score 1-7 (ish) points, and when you have fifteen points of Masterpiece, the end game has hit and just a few turns remain.

I am not a huge Japanese game fan, but Pastiche fits in what I think of as “The Japanese Mold.” A tiny box. A short game, simple yet elegant aesthetics. And — in this case — great game play.

Rating — Enthusiastic.

Written by taogaming

May 26, 2022 at 5:10 pm

Posted in Reviews

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Dice Realms

Dice Realms was always an auto-buy:

The price tag? Not significant enough to stop me (I did order online … but also because I thought I’d get the copy sooner than my FLGS would have it, and I was right).

I’m not going to review the game, Joe Huber’s review explains it (if you don’t know). These are just random initial thoughts:

First — The fiddly nature of popping of die faces and resetting doesn’t bother me.

However, the memory burden of “which die did I put X on” is significant enough to be mildly annoying. It’s worse trying to review the other players’ tableaus …. easy to do at a glance in Race, nigh-impossible here. Even if you track who is buying what (which isn’t a terrible burden) it matters who is returning what and which die they are upgrading.

“I get a Jack of All Trades” (which allows you to set the die if it is rolled). Now it really matters — is that on a die with an attack, or a die with a temple (gain 6VP, which is a fair chunk of the bank).

So the memory burden is higher than Dominion (at least, to play well). If you are playing seriously everyone will have to to announce their moves. So, a semi-serious game of Dice Realms seems preferable (I suppose that’s true of most games, at least for me).

Second — The strategy seems more opaque than Dominion. Dice Realms has more randomness. You have dice randomness (more variability than card randomness) plus the fate die. That means that even if a setup has a dominant strategy, it would take longer to recognize / convince due to variance (coupled with humanity’s copious cognitive biases).

But also, I suspect even opening moves are more debatable. I think stealing Bridge World’s “Master Solver’s Club” for openings would be interesting (like I did for Race for the Galaxy …. right around when I switched to this blog, nearly 15 years ago!). For example, you roll two upgrades on T1 and decide to keep them. Assuming (for sake of argument) that upgrading two progress (pink) faces from level 1 to level 2 is correct …. do you put them both on the same die? Does it matter if you spent your first re-roll or not? How would the variable die faces affect this decision?

There are not obvious questions … and that’s just dealing with the first roll. It will take longer to unravel them than in other games.

(My assumption after a game or two I thought two upgrades was obviously the best first roll you could make on your dice … I am not so confident now. And I am do not believe that upgrading two pink is correct even ignoring what random tiles might exist. I think there is a better play, but these are untested hypothesis right now).

Again — this is a good thing. Dominion was not interesting when people could produce a reasonable flowchart for what strategy to pursue given the setup of the base game (of course Intrigue and the later expansions solved that problem).

Third — The ending conditions of breaking the bank look like Race / Roll /etc, but feels different, because you can break the bank on grain (which is gained and spent!), so what appears to be midgame can teeter on the brink of endgame (if everyone rolls grain and no winter shows up) and then suddenly veer back to midgame (or end). This has already happened in a few of our games. In some setups Misery (negative VPs) also ebb and flow (as some tiles let you get rid of it).

Fourth — The existence of tiles that modify the fate die mean that this base game feels more like a base + expansion.

The combined result of the above points makes me believe that Dice Realms has more replay value than most of Tom’s other games (which are hardly slouches in that department. I have over 125 games of Res Arcana before expansions, nearly 250 of Jump Drive, 100 for The City, 300+ for Race, etc).

That being said —

Setup and tear down is a negative. It’s the sort of game that I think is best to play 2-3 times, just because getting it in and out of the box is somewhat of a bear (relative to the game length). It’s not quite “One game is an hour, two is an hour and a half” but probably one game is 45 minutes, two games is 1h 15. (Really each game is 30m, and boxing and unboxing is 15 minutes).

It is excellent if you leave it out on your game table, which is how the TaoLing and I will likely be playing it in the coming weeks.

Rating — Suggest.

Anyway, I’ll write up very rough strategy thoughts when I have more games under my belt.

Written by taogaming

May 25, 2022 at 9:25 pm

Posted in Reviews

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Ark Nova Open Thread

There are times when my resistance to playing a game means that I am greatly hampered during game night, and Ark Nova has become the latest. It is in constant play. From my (brief glimpses) Ark Nova seems cast from the same flawed mold as Terraforming Mars (another hamperer):

  • Fiddly and long…
  • Containing a massive deck of cards…
  • of which you only see a small fraction of (each game)…

So, in my mind, a 2.5 hour single hand of poker (perhaps a few hands).

Am I wrong? Open thread thoughts on Ark Nova.

Written by taogaming

May 18, 2022 at 7:51 pm

Posted in Open Thread

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Kit Woolsey’s Analysis of Nook’s match

Recently, the news that an AI defeated 8 world champions “in bridge” made the news. I wrote a blurb. Kit Woolsey (a world class bridge and backgammon player) analyzed all 800 deals and recently published the conclusion of his analysis. You should — of course — read the whole thing, but Woolsey notes a number of terrible plays Nook makes … but those plays work because Nook understands (at a deep level) how WB5 (the robot defenders) plays and how to nudge them into bad decisions.

While going through the hands, I have seen Nook make these seemingly pointless cashes of an ace, yet quite often WB5 misdefends after that line of play.  It is likely that in its millions of training hands vs. WB5, Nook has seen that this play has the best chance of succeeding.

Those exploits are technical, and resolve around the fact that WB5 takes no inferences from earlier plays and runs a model of “most likely hand to defeat contracts.” Woolsey constructs an example hand to show how it works. The main exploits are 1) WB5 always signals count honestly, and 2) WB5 assumes the declarer is playing double-dummy, so will never give declarer a guess and will always cover honor leads (etc).

Yet for all of that Woolsey is surprisingly (IMO) upbeat about Nook’s performance:

We can’t draw any meaningful conclusions from the score of the challenge match as to how Nook compares with human experts at declarer play.  The problem is that the competitors were playing two different games.  The experts were playing “bridge”.  Nook was playing “exploit WB5”.  Since the conditions of the contest heavily favored playing “exploit WB5”, it is no surprise that Nook came out ahead.

Within the context of the game Nook had trained to play, how did Nook perform? Quite well. If a human expert studied hard at how to exploit WB5, would that expert be a favorite against Nook?  Probably, but not by much.  If Nook had similar training vs. human opponents, there is every reason to believe that Nook would be playing at world-class level. (Ed — Emphasis mine)

Worth the full read

Written by taogaming

May 15, 2022 at 9:58 pm

Posted in Artificial Opponents, Bridge

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A Hand with Several Interesting Points

Playing online, I pick up S:AT96 H:KJ76 D:AJ3 C:A5 and it goes three passes to me. We are Non-vulnerable, and in this partnership that means my 1NT opening would be weak (11-14 HCP …. even in fourth seat, which I don’t love but there it is) so I open 1 Diamond. Opponents are silent (they are vulnerable) and partner raises to 2 Diamonds, a standard 6-9 HCP raise.

Game is still possible so I bid 2 NT (showing 17-19ish) and play it there. LHO leads the spade three.

Dummy: S: K7x H:xx D:Q8xx C:Q7xx

Spade 3 led

My hand: S:AT96 H:KJ76 D:AJ3 C:A5

Spade 3 – x – Jack and I win the Ace.

I could shoot back the spade ten. Presumably this will be covered and I’ll have 3 spades, 2 diamonds (assuming I take the finesse, either it wins or the Queen is good) a club and I’ll need some luck. But I have a sneaky thought. I’d love for the opponents to lead any suit. Maybe not clubs. But what if I attack clubs? Club ace and a club to the queen. If LHO has the king of clubs, I’m up to another trick …. and the opponents will likely attack other suits.

Now, there’s a downside, and a big one. If RHO has KJxx of clubs he may cash three tricks and I’m going to be hard pressed to discard. If my clubs were even a touch better, I think attacking clubs might be right. But the spots aren’t there.

But … I did it anyway. Club ace and a small club. LHO hitched and then won the king and then played the Queen of spades. Obviously this was excellent for me. I now have four spades + 2 Clubs + 2 diamonds. I won the king of spades, naturally (RHO pitching a small heart) .

Now, I could cash the club queen, but that would expose my club weakness and I think I have some interesting plays for overtricks. First of all, if the diamond finesse looses right away, I’ll always be able to get back to the club queen. And if it wins … well.

I take the diamond finesse. It wins. I now cash two more spades, setting up LHO’s long spade but presenting RHO with a real problem. He pitches a diamond and then a heart. (I pitch a heart from dummy on the fourth spade). RHO’s discards are revealing (RHO is Hank, an expert and often my partner in these stories).

I suspect he started with 1=4=4=4 distribution, but 1-543 in some combination is possible. I don’t think he’s bared his king of diamonds, so at least four diamonds. (Also, people with five card suits usually discard two of those cards immediately, unless they know that declarer/dummy also has four. Here’s the current situation

          S: -- H: x D:Qxx C:Q7
S:X ???                           ??? D:Kx(x)?
          S: -- H:KJxx D:Ax C:--

RHO’s two heart pitches … I don’t think he started with Qxxx …. it would be difficult to give up a slow heart trick against a declarer showing real values there. I think Hank started with Axxx or maybe xxxx …. and if he started with four small, he might have pitched three.

My goal now is to put LHO on lead, so that a heart return is great and a diamond return is OK. Taking what I now, I lead the jack of hearts from hand, expecting LHO to have the queen.

LHO wins the queen (all following) and now he could cash the last spade, but that spade my well and truly squeeze RHO. This is IMPs, so the goal is to set the contract. LHO leads a heart to RHO’s ace. Hank can’t very well lead a diamond (which would give me a free finesse) and so has to lead a club. I pitch my small diamond, cross to my hand with the diamond ace, and my heart King drops LHO’s last heart, so my fourth heart is good. LHO’s precaution notwithstanding, RHO had already been squeezed.

          S:K74 H:xx D:Q8xx C:Q7xx
S:Q8xxx H:QT9 D:xx C:KT8 S:J H:Axxx D:KT9x C:J9xx
S:AT9x H:KJxx D:AJx C:A5

LHO could have done better at the end by leading a diamond, but that would have been a disaster if I’d had the Ten. On the actual play it would save a trick as I would win ace and then endplay east in diamonds (and I’d also likely would have wished that I’d pitched dummy’s club and kept both hearts).

Hank could be blamed for holding onto his “worthless” fourth club but if I’d actually had a third club then I would have communication to the board and that would have also cost a trick, so in that sense my play of the club early did inflict the deception I’d hoped for (although I still think it was a mistake).

But there were a number of interesting points:

  • The deceptive club play (albeit wrong) did induce some bad discards as both defenders assumed I would not strand a winner or attack a weak suit.
  • Cashing the spades to set up the long spade for West
  • The lead of the HJ from the hand to “endplay” west, who actually recognized that a potential suicide squeeze was intended and who declined to cash his winner….
  • … but the squeeze had already occurred.

I did really like the heart jack lead in the middle of the hand. Rarely is my card reading that accurate. I remember playing ~30 years ago against the club’s Hideous Hog and how a few small innocuous (so I thought) discards painted a picture of the entire hand for him. I won’t say I had the full picture, but I had enough.

Written by taogaming

April 27, 2022 at 4:39 pm

Posted in Bridge