Sketches for Streaming Market Data

Sketches have always struck me as kinda magic.

With an infinite time-series of data, we usually keep a window: the last 20 bars, the last 1,000 ticks, the last five minutes. Then recompute whatever statistic you want over the window. This is fine until you have thousands of symbols, long lookbacks, or tight loops where sorting is expensive.

A lot of statistics don’t require a window. You can reduce a stream to a small state, update that state when a new observation arrives, and throw the observation away. This is what skream does. It’s a Clojure library for streaming statistics I wrote a while back.

Exponential Mean and Variance

A simple moving average remembers everything in its window and then forgets the oldest observation. In an exponential average, old observations decay instead of vanishing.

The important parameter is the half-life: how many observations until an observation is worth half as much? If the half-life is h, then alpha = 1 - 0.5^(1/h). skream takes alpha directly. The state is just the current EMA plus a count.

(require '[skream.core :as sk])

(def s
  (-> (sk/create-skream)
      (sk/track-exponential-moving-average 0.05)))

(def s
  (reduce sk/add-num s returns))

(get s [:ema 0.05])

The default alpha is 0.125. Keep one Skream per instrument and update it on every return. Variance is a separate tracker:

(def s
  (-> (sk/create-skream)
      sk/track-variance
      sk/track-standard-deviation))

(def s
  (reduce sk/add-num s returns))

(:var s)
(:stdev s)

Three numbers per instrument cheaper than keeping the history around. See also the infamous infinite-memory issue in Pandas. And skream has the usual cumulative mean, higher moments, skewness, and kurtosis stats too.

Quantiles Without a Window

The P² algorithm, from Jain and Chlamtac, estimates a quantile using five markers. The markers track the minimum, maximum, desired quantile, and two points around it. New observations update their positions. When the markers get out of place, their heights are adjusted using parabolic interpolation. The amount of state doesn’t grow with the number of observations.

The skream version is straightforward:

(def s
  (-> (sk/create-skream)
      (sk/track-quantile-ish 0.95)))

(def s
  (reduce sk/add-num s prices))

(get s [:quantile 0.95])

For the median, there is a convenience function:

(def s
  (-> (sk/create-skream)
      sk/track-median-ish))

(def s
  (reduce sk/add-num s prices))

(:median s)

After 25 SPY closes, skream produces roughly:

{:quantile 193.72229
 :qs [187.55 191.74467 193.72229 195.5992 196.48]
 :ns [1 7 13 19 25]}

:qs are the marker heights. :ns are their positions. The middle marker is the median.

There are two catches. P² estimates one quantile, so if you want the 5th, 50th, and 95th percentiles, you run three estimators. More importantly, P² isn’t mergeable. If you have a cluster processing different pieces of a feed and want one global quantile, P² is the wrong tool. Use KLL, t-digest, or another mergeable sketch.

Count Things Without Counting Everything

A Count-Min sketch is a small array of counters plus a few hash functions. Each key increments one counter in each row. To estimate the count, take the minimum across the rows. It can only overestimate. With width w = e/ε and depth d = ln(1/δ), the error is bounded by εN with probability 1−δ.

skream calls this track-element-counts-ish:

(def s
  (-> (sk/create-skream)
      (sk/track-element-counts-ish 256 128)))

(def s
  (reduce sk/add-num s symbols))

(sk/get-element-count-ish s "AAPL")

This is useful when the alternative is keeping a giant hash table around just to discover that one symbol generated an unusually large number of messages.

HyperLogLog estimates cardinality: how many distinct things have I seen? Unique order IDs, unique symbols, unique clients, whatever. With m registers, the standard error is approximately 1.04 / sqrt(m). Sixteen thousand registers gets you roughly 0.8% error while consuming about 12 KB.

In skream, the number of registers is 2^b, so 14 bits gives 16,384 registers:

(def s
  (-> (sk/create-skream)
      (sk/track-distinct-value-count-ish 14)))

(def s
  (reduce sk/add-num s order-ids))

(get s [:hll 14])

The exact answer might require millions of IDs. The approximate answer requires 16,384 registers.

A Bloom filter answers one question: have I seen this before? It has false positives but no false negatives. That makes it useful for feed replay and deduplication. If it says “no,” you haven’t seen the message. If it says “yes,” maybe you have.

skream uses multiple SHA-1-derived hashes for this:

(def s
  (-> (sk/create-skream)
      (sk/track-member-ish? 6 8)))

(def s
  (reduce sk/add-num s message-ids))

(sk/member-ish? s message-id)

The 6 is the number of bits used for each hash bucket and 8 is the number of hash functions. Again, fixed memory, but an arbitrarily long stream.

Feature Hashing

Feature hashing is another sketch, although it usually gets presented as a machine-learning trick rather than a streaming data structure. Suppose you have a stream of sparse categorical features: symbols, venues, order types, words, whatever. Instead of growing a dictionary from feature names to columns, hash each feature into one of m buckets and keep only the resulting vector: feature → hash → bucket → update.

If two features land in the same bucket, they share share a model parameter or set of weights. With signed hashing, a second independent hash assigns each feature either +1 or -1, so a collision either adds or subtracts their contributions. This is useful because collisions do not systematically inflate a bucket: over many collisions, the random signs make the cross-terms tend to cancel, mostly preserving inner products. The parameter tying also reduces the model’s degrees of freedom, so collisions can act as regularization. The two effects are distinct: the random sign controls the distortion caused by collisions; the shared parameter constrains the model.

This is the same trick as the other sketches here: throw away information deliberately so the state stays bounded. Feature hashing just makes the trade particularly obvious. You’re compressing an unbounded feature space while constraining the model at the same time.

Mutual Information

Correlation is easy but less useful when the relationship is nonlinear. Mutual information can find nonlinear dependence. A simple streaming approximation is to keep fixed histograms of (x, y) and their marginals, then calculate Σ p(x,y) log(p(x,y) / (p(x)p(y))) when you want the answer.

skream does this with multiple Skreams: build a histogram for each series, a co-histogram for the pair, and then track the mutual information between them.

(def ms
  (sk/create-multi-skream))

(def ms
  (-> ms
      (sk/assoc-multi-skream :x (sk/create-skream))
      (sk/assoc-multi-skream :y (sk/create-skream))
      (sk/track-multi-mutual-information :x :y -5.0 5.0 32)))

(def ms
  (reduce (fn [ms [x y]]
            (sk/add-multi-num ms :x x :y y))
          ms
          observations))

Mutual information estimates are sensitive to binning and biased when there are not enough observations per bin. Change the bins and you can change the answer, so use it to rank things worth investigating.

Wrapup

Prices are discrete. P² interpolation can produce values between ticks. That’s mathematically cute but buggy.

Histogram methods have their own problem: they depend on the bins. skream has Gaussian-spaced bins, which are useful when you want more resolution around the center of the distribution.

So why bother? Because most streaming systems don’t need the data. They need a statistic about the data. Keeping every observation is often just an indirect way of calculating that statistic later, at considerably greater expense.

A fixed-memory estimator turns data → storage → sorting → calculation into data → update → discard. The second version is generally cheaper, faster, and much harder to accidentally turn into a memory leak.

skream contains the usual collection: moments, variance, skewness, kurtosis, EMA, P² quantiles, Bloom filters, Count-Min, HyperLogLog, histograms, and histogram mutual information. Everything is fixed-memory except the simple moving average, because a simple moving average is definitionally a moving window.

Dice Game: Sevening

Setup

Pour one of the little Chessex boxes of 36 six-sided dice in the middle of the table to make the pool.

Turns

Each player has a bank, zero or more dice kept face-up in front of them.

On their turn, a player first takes two or more dice from the pool and announces the count. Each other player may push one die from their bank forward, the number that player is “buying.” No more than one player can buy each number, with priority going in seating order.

Next the player actually throws their dice. If any two dice thrown sum to seven, the shooter has crapped out. All the thrown dice go back to the pool, pushed dice return to their owners, and no one scores. Otherwise, if a bought number was thrown, that bettor takes all thrown dice of that number into their bank. They also keep their pushed die. However if none of the thrown dice match the bettor’s bought number, the pushed die is lost to the pool. Finally, all thrown dice not bought  by a bettor go into the thrower’s bank.

The game ends when fewer than two dice are left in the pool. Then total the number of pips in your bank, and the most wins.

Strategy

The more dice the shooter takes, the likelier any number lands. Back a shooter who takes four or more, and buy your highest die. You win the thrower’s matching dice, so a big throw feeds the bettors — the thrower can take fewer to starve them.

Tasting a Higher Proof

Fred Minnick just released his well-regarded ranking of the top 100 American whiskies for 2022. He started with 800 whiskies, and over several rounds, narrowed things down to his top 100. All else equal, I suspect that higher proof whiskies tend to do better in this ranking. Is this because undiluted, cask-strength whiskies are more complex in the nose, flavor, and finish? Or is the reasoning is circular — maybe the sort of whisky that does well undiluted is better. Maybe Fred just likes an efficient way to get buzzed?

To answer this question, I pulled Minnick’s top 100 picks into a spreadsheet and cleaned-up the data. Here is the distribution of the proof of the 100 whiskies:

That outlier on the right is the infamous Jack Daniel’s Coy Hill.

Then I did a simple regression analysis. I use a whisky’s proof to predict its ranking. Since this is a very small dataset, I am doing traditional full-sample analysis, with no test set. It turns out, the proof (ha!) is there in the data: Minnick prefers higher proof whiskies. In fact, over 20% of the variation in his top 100 ranking can be explained by just the proof of the whisky! The relationship pops in a scatterplot:

That coefficient of -0.188 on proof means that your whisky can improve its rank by 1 if you increase its proof by about 5. The relationship is weaker (14% explained) if you remove the top & bottom 5 proof whiskies as potential outliers.

Minnick does not seem to be biased by price. There is almost no relationship between a whisky’s price and its rank, especially when you throw out the pricey Michter’s 20 as an outlier.

If you combine both proof and price into a multivariate regression, you can explain a bit more of the variance in rank (about 25%). The data is here, if you want to experiment yourself.

Like the Electoral College but Worse

We should expect Trump to announce electoral victory on the night of November 3rd. Or earlier the next day. This will be due to some combination of stronger-than-expected in-person voting results and discrediting mail-in votes due to supposed fraud. By this point, ACB will be seated on the Supreme Court. With Florida in 2000 as precedent, the Democratic leadership would do everything possible to avoid a Supreme Court decision.

Trump may be ahead in some states’ early & in-person vote counts, but with small enough margins that the expected “blue shift” in mail-in votes would swing to Biden. These are your classic swing states. Importantly, some of these states have divided government, with Democratic governors and Republican control of the state legislatures. The 4 divided swing states are Michigan, North Carolina, Pennsylvania, and Wisconsin.

MI’s lower house is at stake in November, and will probably stay Republican. Both of the houses in NC & PA & WI are at stake, and all 6 will probably stay Republican. NC’s Democratic governor Roy Cooper is running for reelection, but seems safe. So we can expect the 4 divided swing states to still be divided before and after the election.

The 4 divided swing states may each submit two conflicting slates of electors, like several states did in 1876 and Hawaii in 1960. At the time, voter fraud and disenfranchisement were again the center of controversy.

There is enough ambiguity & confusion around the Electoral Count Act of 1887 passed after the 1876 drama for the elector slate of the state governor or the slate of the legislature to carry — and also around which federal house accepts the counts. There is an interpretation that would completely exclude conflicting electoral slates. Given that the 4 divided swing states have a total of 61 electors, this could mean both Trump and Biden fail to achieve the electoral majority. In this scenario of no electoral majority, the state delegations in the federal House of Representatives vote for the president. Given the very real pandemic and very fake mail-in vote fraud, maybe a state is confused about its own voting. So, “just” let its representatives vote instead…

The state delegation vote is an extremely undemocratic version of the already-undemocratic electoral college: Each state gets a single vote. Here the state of Delaware is literally as important as California!

State delegations would vote by simple majority of representatives in the House of Representatives. (Not the Senate.) The Democratic party has 22 state delegations, while the Republicans have 26, and 2 delegations are tied. Of the tossup House of Representatives elections, 7 representatives could swing their state’s delegation majority from Republican to Democratic. The Democrats would need a net gain of 4 state delegation majorities to get the majority of 26 of 50 state delegation votes.

In order of increasing margin-of-victory for Trump in 2016, the 7 tossup House seats that would swing a state delegation majority are currently held by Brian Fitzpatrick (PA-01), Fred Upton (MI-06), Scott Perry (PA-10), Justin Amash (MI-03), Ross Spano (FL-15), Don Young (AK-AL), and Greg Gianforte (MT-AL). Here PA and MI are somewhat double-counted, since all else equal, only one of the seats held by Fitzpatrick & Perry would need to flip to flip the state delegation. The same for Upton & Amash in MI.

Justin Amash (MI-03) is retiring, Ross Spano (FL-15) was not re-nominated, and Greg Gianforte (MT-AL) is retiring to run for governor. The other 4 are running again in their districts as incumbents.

In this not-entirely implausible scenario, each of these 7 representatives faces three potential outcomes: a) Their district stays Republican, and they vote for Trump in the state delegation; b) The tossup district flips to a Democratic representative, but the incumbent Republican “goes faithless” and votes for Trump in the delegation anyway; or c) The district flips Democratic, and the representative votes for Biden. Also keep in mind that Justin Amash (MI-03) is a Libertarian Trump critic who left the Republican party.

Pelosi and the Democratic leadership should be focused on these 7 house races, as well as fervently horse-trading to encourage the Democratic flip scenario. Get those seven to commit to following the wishes of their constituency, any mandate from two years ago be damned!

Bro. Do you even bake?

The recipe for the famous Tartine country loaf is less helpful than advertising for the bakery and new age woo woo. Pretentious garbage, really. Here is my consolidating upon a practical, clear recipe for sourdough bread. The only ingredients should be flour, water, and salt. The bread should be a crusty, rustic, (mostly) whole grain.

Grow a Starter

In the morning, add 100g of unsifted, all-purpose (AP) flour and 100g of water to a tall, lidded, glass jar. Stir with a spatula, and leave it sit, covered in a warm place all day. The environment should be distinctly warm, and so this often means turning on the oven at its lowest setting for a few hours (e.g. bake at 170°F).

Every morning, pour off all but about 125g of the starter. Use this poured-off batter to make a fry bread with sesame oil & scallions & five spice, or do something fancier. Add 50g of unsifted AP flour & 50g of water to the starter, stir with a spatula, and scrape down the insides of the jar. As usual, the environment should be warm.

Your starter is ready for bread when it is frothy & bubbly, and doubles in size by the afternoon. This will probably take a week-or-so of daily feedings.

Make a Leaven

The night before you want to bake bread, spoon a heaping tablespoon of starter into a large glass bowl. Add 75g of warm (80°F) water, and 75g of unsifted AP flour, and stir with a spatula. Cover the bowl with plastic wrap, poke a few holes, and leave it to sit overnight at room temperature.

After making the leaven, tuck your starter into the refrigerator and stop feeding. When you want to bake bread again, remove the starter from the refrigerator in the evening, and feed it in the morning as usual for a few days.

The next morning, confirm that a teaspoon of your leaven spooned off the top can float in a bowl of water. Your leaven may need more time or warmth. If so try again at lunchtime.

Mixing

Add 650g of warm (80°F) water to your leaven, and stir it until only a few clumps remain. Add 325g of unsifted AP flour and 700g of unsifted whole wheat flour to the bowl. Work the dough until all the flour is just wet. Let this rest covered for 45 minutes, for the autolyse.

Dissolve 20g of salt in 50g of water. Use a salt with lots of minerals, like sea salt or even plain ‘ole iodized. Pour the salt water over the dough, and repeatedly pinch to incorporate.

This dough is about 71% hydrated, ignoring that first tablespoon of starter. And the dough is relatively stiff, especially compared with the trendy overly-hydrated recipes.

Fermentation

Leave the dough covered at room temperature. Every 30 minutes, with your hands wet from washing, pull up & fold the dough from the side of the bowl. Do this 4 times with a quarter turn of the bowl between each folding. So that’s 4 folds every 30 minutes for 3 hours. Put 6 counters next to the bowl as a physical mnemonic, removing one each folding.

Shaping

Cut the dough in half with a metal dough scraper. Half of the dough will be about 955 grams. Punch and fold out internal air pockets, and then scoop the two boules into rough spheres. Cover the boules with bowls, and let them bench rest for 30 minutes.

Using a metal dough scraper, pull the boule of dough along the sticky countertop, to develop surface tension. Turn the football shape and pull again. Do this just until a bit of tearing occurs on the surface.

Generously flour a clean towel with rice flour, firmly pressing the rice flour into the towel. Flip a boule onto the center of the floured towel, leaving the seamed side facing upward. Lift the boule and its towel like a hammock, and drop it into a large bowl or bread basket. Cover, and repeat with the other boule.

Proofing

Leave the bowls in the refrigerator overnight, to proof.

Baking

Preheat the oven to 500°F. Place a sheet of parchment on top of an oven-proof plate, and turn the parchment & plate upside-down onto one of the proofing bowls. Flip the whole bundle upside down, to drop the boule onto the parchment. Set aside the towel and proofing bowl. Brush off the rice flour.

Score the top of the boule deeply with a wet knife.

Cover the plate, parchment, and boule with the base of a dutch oven. (Do not use the lid.) Bake for 20 minutes. Reduce the temperature to 450°F, open the oven door briefly to cool the oven, and bake covered for another 10 minutes. Remove the dutch oven from the plate & parchment, and continue to bake uncovered for 25 minutes. Cool the boule.

Going Out While Social Distancing

Wanna go to that kaiseki in The Mission? They have a 7 address, so our whole crew will be there.

My ‘rents just moved into the 123 High Street building. Now we can meet at the pub on the corner.

He does not stand a chance of a getting a star in Fam Three. The empty storefront next door is in Fam Five, though.

I expect us to be playing whack-a-mole with this pandemic for a few years, and am worried some indulgences of modern life will never come back. For example, fine dining is damn-near-impossible to do virtually. I have a background in the hospitality industry, and have had the privilege to eat some amazing meals in my life. So this is personal.

Now by fine dining, I mean the by-definition pretentious, wasteful, and amazing conversation between diner and chef via the medium of tiny bites on giant white plates. A prix fixe or à la carte menu enjoyed with wine & company over a few luxurious hours. Including the dreaded communal table thing too, I guess. But how are we going to eat at fancy restaurants while we continue to socially distance? And how are restaurant employees going to get back to making a (modest) living? Take-out fried chicken & cocktails from a Michelin star place desperate for cash flow just ain’t financially sustainable. Crenn is doing fancy comfort food like it’s October of 2001, but how is she going to pay rent in Russian Hill on $55 per head?

Lately a lot of my research is connecting a company’s stock price with the digital exhaust left when we interact with the world. A challenging part of the job is controlling for the bias in a cohort of people. When is a group actually representative of a population, or actually random? So while I am nothing close to a computational epidemiologist, and while every machine learning & data scientist is pretending to be a virus expert this week, I have one idea that might help with fine dining while we are in social isolation.

Take a Number for Going Out

Imagine getting your driver’s license or passport checked at the entrance of a restaurant, where they confirm one simple fact: What is the last, right-most, least-significant digit of your mailing address? (Ignore fractions.) This digit is your membership in an slightly-different, in-real-life family — in which of ten virtual neighborhoods do you arbitrarily belong? And importantly, does your number match the last digit of the restaurant’s address? If the two IRL Fam numbers do not match, the restaurant would be mandated to refuse service. That’s it. Think through some implications of this simple restriction:

Maintains Social Isolation

When you go out to eat according to IRL Fam number, you are only ever physically near a fraction of the people in the world. And importantly, these people are always a semi-random subset of the same fraction of the population. The only people who are eating at the restaurant tonight are those who have the same number, those who are in the same IRL Fam. You might even get to know each other.

This is different from just going to local restaurants in the your zipcode, where a rando might jump a cab from across town for the restaurant’s particular charm. (This is especially relevant for experimental or avant garde places that have never relied on walk-ins.) The IRL Fam system is also fundamentally different from going to a different, random restaurant every weekend, because in this case you would still be exposed to a random set of people. And this is very different from restricting the number of people in a particular restaurant, simultaneously. A recent study from Cornell showed how even very small classes still would leave the student community highly connected. This would also thrash most restaurant’s finances.

What’s an address in 2020?

We could theoretically assign a random number, or use your mobile phone number, or even (shudder) use a Social Security number. However, there are additional benefits to using a physical, mailing address for layering our virtual spatial separation atop the existing physical world. Using your mailing address defaults a specific set of people into breaking your social distancing rules: Your roommates, family members, and those in your apartment building. Assuming you still like your kids & spouses after shelter-in-place eases, these are exactly the people you usually want to go out with. And these are the people from whom you are de facto not social distancing from, anyway! You share the same space, breath the same air, push the same elevators buttons, and so on.

What about the service?

This might require that restaurant employees only work full-time, and only at a single establishment. Would employees also need to have a matching IRL Fam? I think that would be too extreme, but goes in the right direction. Maybe we finally abandon the bullshit labor arbitrage of the gig economy, and pass a law establishing full-time de facto employment (i.e. benefits) for anyone who is works 40 hours a week for the same legal entity. San Francisco is already doing this with Uber drivers.

When’s your birthday?

This is no more a violation of privacy than when nightclub security checks the ID of your date who is looking particularly baby-faced tonight… Let’s mandate zero record-keeping or data retention on the IDs themselves, once the IRL Fam number is confirmed. I suppose patrons would need to have an ID with a mailing address on hand, which is a admittedly a bit classist.

Do they have valet parking?

Here is a significant downside. If you are not allowed in 90% of the restaurants in town, you are more likely to drive further to find an interesting one in your IRL Fam.

Is this all a game?

Given the prevalence of mostly-empty nightclubs with long lines, there is a chance the artificial exclusivity of the IRL Fam system would be fun and dramatic. An apartment with an address matching The New Hotness restaurant would be more desirable. And ironically, this exclusivity would be arbitrary and therefore, relatively fair!

Scaling & the Resurgence

This system could start in a traditionally-quirky place like San Francisco, and expand to restaurants & clubs & bars in other cities. And when the next pandemic (resurgence?) inevitably pops up, when the next shelter-in-place mandate occurs, contact tracing via IRL Fam number would be easier.

Saison

Dinner at Saison was really solid. Spectacular service with attention to detail, an open kitchen with almost-haphazard arrangements of tables around the high-ceilinged, taxidermied space. The smell of the wood-fired stove filled the room. Our winter menu was from late December, 2019. My favorite beverage was a sake, Shirataki’s Jozen Mizunogotoshi (junmai ginjo).

  • We started with champagne and tea made from a bundle of herbs in water. This reminded me of putting a sachet of herbs de Provence in a broth.
  • Then tiny cuts of sea bream sashimi seared on charcoal, served with sea lettuces, orange yuzu, sesame seeds in an oil, and sriracha chili water.
  • Lovely “nose to tail” dish of dungeness crab, featuring every part of the animal including the tomalley. Served with a thick almond milk sauce, and grapefruit.
  • Seared scallop in an oily berbere-like sauce. My wife had a tofu dish with carrots & kimchi.
  • Then we had trout with its roe alongside fartichokes, higher quality than the aquacultured McFarland Springs trout that’s everywhere else now-a-days.
  • Tiny white bread poppy seed rolls, served warm in a little basket on the table.
  • Black cod served with a chestnut puree, and a punchy (miso?) broth.
  • One of our favorite items was uni served over a piece of grilled sourdough, looking a bit like nigiri. The texture was wet from a bread sauce being spooned over, presumably made from their house-fermented bread hanging above the kitchen.
  • Spectacularly-beautiful radish dish, with a variety of colorful radishes & radish greens & flowers presented on a high, white plate.
  • Venison loin sous vide with raw garlic inside, in a demi sauce with ribbons of pickled kohlrabi & grated horseradish, and chanterelles.
  • The standout of the meal was the roasted honey nut squash mashed with a crunchy breadcrumb & herb mixture that tasted like Israeli salad.
  • Weak cheese course that was a bland, soft buffalo cheese wrapped in banana leaves and served with a nice flatbread cracker. Given the high bar of Saison’s ingredients, I would have preferred an actual, editorial cheese course.
  • Then a persimmon and creme fraiche dish, less savory.
  • The first dessert was a disappointment. Something with candy cap mushrooms & chocolate & tea, but the mushroom just ate gimmicky. I would preferred something baked cake-y or tart-y with more crunch, acid, and texture.
  • The second dessert with huckleberry & yuzu was for my birthday, and was very nice.

Philanthropy Picks (2019)

Here is a list of the philanthropies and charities where we donated this Giving Tuesday, after another messy year of the Dumpster administration:

Texas Hold ‘Em Variant: Buying the River

Texas Hold ‘Em is usually what people mean when they think of poker now-a-days. After the last poker night I attended, I thought of a variant of Texas Hold ‘Em inspired by the card shopping in Dominion that adds more reveals of partial information to the game, while keeping things essentially Texas Hold ‘Em -like.

  1. Give each player at the table three pips or markers unique to the player. Each player could have three pawns of the same but unique color, or three glass stones, or coins, or whatever. One of the three pips should sit in front of the player’s seat for the entire game, so it is easy to identify which player is which color (e.g. “Ben is the green pips”).
  2. Play your hand of Texas Hold ‘Em as usual, until after the betting round following the flop. At this point, each player can make a five card hand with their pocket cards and the flop.
  3. Flip up the turn (fourth) card. At this point players conduct a betting round for the “purchase” of the card. Importantly, folding in the turn card’s betting round does not knock the player out of the hand. Folding just means the player is not allowed to use the turn in their final hand. Sticking around until the pseudo-showdown of this betting round means the player is allowed to use the turn card in their final hand. A player indicates that they have made it to the turn card’s showdown, and therefore may use the turn card in their final hand, by placing one of their three pips on the card. All money bet in the turn card’s betting round is placed in the communal pot, as usual. To keep things simple, players should probably not be allowed to go “all in” on the turn card’s betting round.
  4. Flip up the river (fifth) card, and do a second purchase betting round just like the round done for the turn card. Again only players who make it to the river card’s showdown may use the river in their final hands.
  5. When all players have access to five to seven cards to make their final hands, do one final betting round. This final betting round reverts to the usual rules, where folding means dropping out of the hand.