The Tao of Gaming

Boardgames and lesser pursuits

High Frontier Basic Game Strategy Thoughts

(This was originally published in incomplete form. I hit “publish” instead of “save.” Lots of updates since then).

I remember playing Fugger, Welser, Medici dand realizing the basic game was too … basic. (I later relayed this to Frank and he said “it wasn’t for gamers like us, that’s what the advanced game is for.”)

High Frontier isn’t exactly the same thing. You need at least one basic game to learn the mechanics. (I needed lots). Jumping straight into the advanced game is optimistic. Even adding only the support module ridiculously increases the number of moving parts. But even for slow people such as myself the basic game does seem too basic after a few plays.

It ends just after it gets going. Industrialize a second colony, you are done (or almost). After the first few games,  TaoLing and I played “longer” extended games to seven colonies, where you might get something like a claim on Sycorax, but our most recent 7 colony game took …. 40 minutes. We’ve started adding advanced modules.

The basic game is not without interest, so some thoughts.

  • This is a race game. Only one action a turn, but also space travel in addition. If you start your trip a turn or two earlier that can be a big advantage because its hard (but not impossible) to make up time later on.
  • One rule I was taught wrong is that you can’t bid if you have three (non-crew) cards in hand. It turns out you can bid if you have less than four (so, three is OK).
  • My big mistake in my early games: buying random cards, then trying to make something work. Most cards are good for something, but trying to figure out what is hard.
  • In general, Robonauts before Refineries. Makes sense — Robonauts prospect. Yes, you can use your ISRU 4 crew but here’s the list of ISRU 4 sites inside of Jupiter: Mars (10 gravity, ugh), Ceres (a good target, although 6 gravity probably means you’ll need your crew) and eight inconvenient size-one sites (which aren’t near anything). It’s not a great list. Even an ISRU of 3 opens up a lot of options.
  • If you only looked at the asteroid belt for your first mission, you’d probably be right. (For your first game narrowing your decision space is a good idea). If you are playing to seven (or some higher number depending on # of players, which isn’t a variant) you can start looking at Jupiter’s moons or even more distant.
  • Remember — the map represents delta-v. Sites on opposite sides of the board but in the same belt are surprisingly close (in terms of number of burns and turns). You can run from Lutetia (a 3M-3 hydration site) to Hertha (ditto) for two burns in a single turn (via Sol-Jupiter L1 burn). Think of the board as “energy bands.”
  • There is no “C” class refinery, FYI. Type D and S sites are much rare (in the basic games) so those cards are slightly less useful.
  • Weight matters, but less with good fuel efficiency. A nice rule of thumb I found on BGG states “Your wet mass/dry mass ratio will need to be roughly equal to your fuel single-burn fuel consumption (or better).” So if you have the Metastable Helium thruster (5 Mass, 5 Net Thrust * 1 fuel per burn), then your wet mass doesn’t have to much exceed your dry mass, so you can get a heavy robonaut and refinery and still go tooling around for 4 water. But if you get the Mirror Steamer (0 Mass, 3 Net Thrust * 4 Fuel per burn, Solar, Push) you are going to have real trouble if your dry mass gets above three-ish, so you’ll probably need two trips. Bid up the 1 fuel/burn cards.
  • Getting your first factory ASAP is a big deal. It provides:
    • 8 free water for refueling. Even if your robonaut and refinery can’t be built, you can take a turn to refuel and send your (now light) rocket back to LEO to pick them back up instead of having to re-boost and refuel the rocket.
    • ET production. Not only are the black side of cards better (much, much better), you get a card out there a few years in advance, save the cost of re-boosting, etc.  ET producing a robonaut to prospect for your second factory (using your on-site thruster) is a big deal. If you have a robonaut and refinery of the type you just colonized, it’s probably a winner. (With both for Vs, aim for Vesta, which at size six means you can’t fail the prospecting roll, and only has a half landing burn. Getting both Ms aim for Lutetia then Hertha, for a 75% chance of a claim. Ds and Ss

Common planning pitfalls to avoid:

  1. Can you land? Remember, your net thrust must exceed the sites size. Some ways to get around this (if your main thruster isn’t good enough).
    • Afterburning.
    • Size games. Take everything, drop a part in orbit to lower a size class (increasing net thrust). Leave the first part on the site,take off, pick up the last part. (Dropping off and picking up is a free action, but you can’t pick up in the middle of a move).
    • Use your crew to land. It costs no fuel (if there isn’t a lander burn). Vesta and Ceres with their half lander burns are reasonable. (If you have to pay a full lander burn, your main crew’s rocket may be prohibitively expensive).
  2. Will you be able to take off? (This mainly applies to aerobraking). You can easily trap yourself if you use your crew to go someplace like the moon. (If you can’t take off, you can turn your crew into a colonist and get some VP).
  3. Do you have enough fuel? Seems obvious, but don’t forget fuel for afterburns. Size tricks may cost you some fuel as well
    • Consider Demos (or some other high hydration site) for a turn or two of refueling. Particularly if you have a low ISRU, you can get a lot of fuel that way. Seeing a ‘pit stop’ at the (already busted) Demos to refuel was my first “aha” moment.
  4. Do you have the ISRU rating to prospect the site (or refuel)? (Even after ten games I’ve still just said, “Oh, I’ll go there” and then realized my robonaut couldn’t cut it because I was so focused on fuel/thrust/etc.

Sites of Interest

The training book’s guide is good and worth reading for your first few games. Some thoughts:

Planets are Hard. You can go for Mercury (North Pole) or Mars but you’ll need 11 thrust (or aerobraking rolls). But those are basically one way trips unless you can build a factory. For those, you’ll need a crew with a 10 Net thrust and afterburn. You could also just send down a robonaut and refinery, but the advantage of getting your first factory is basically negated because you can’t really ET produce or use the factory to refuel unless you have a powerful crew rocket. On the other hand, these can be a guaranteed second factory.

The moon is easier, but you’ll need a good ISRU.

Ceres is a sure thing with four hydration, requires only 7 thrust (usually within the reach of a basic game crew) and only a half burn. Depending on your thruster you may need to stop at Demos. Vesta is also a sure thing but slightly farther away and requires an ISRU of 2. (To compensate, its a V world, which is likely to score better and will have a few refineries that can be ET produced there).


In the basic game the most important thing is Fuel per burn, because lower means you can go farther. High thrust is nice (because that lets you land on more places, or maybe get there a turn or two earlier) but you often get around that by taking your crew and using it (assuming no lander burns, or maybe a half burn). In the advanced game the worse rockets are balanced by needing more supports, or worse rad-hardness, but in the basic game? Nope.

If you ordered thrusters by FPB in the basic game, you’d be close to right. (Ignoring the solar sails, because 0 net thrust is a problem).

Key is [#Mass, Thrust * Fuel per Burn (After Burn cost, Class), P = Push, S = Solar]. I’m not going to worry too much about the advanced (black) side because you won’t for your first games.

In rough order of worst to best:

Photon Heliogyro / Photon Kite Sail [0M, 0*0 (-,C) Solar] — Basically the same. Not really useful in the basic game (said the guy who almost never goes inside the earth orbit]. You could use these to get maybe a free burn if you are a small light ship, so perhaps I shouldn’t discount this.

Mirror Steamer [0M, 3*4(2,D) SP] — Zero mass, but 4 fpb. Ugh. The one thing that’s nice is that you could boost this with a robonaut and leave really early, take a pot shot at Demos and refuel. But the problem is that the mass savings from boosting are (in the basic game) a one time savings. You’ll be paying for fuel the rest of the game. Also, this can’t land too many places.

Ablative Plate [4M, 2*2(1,V) P] — Two fpb isn’t bad, but nothing else is great. High mass, low thrust. If you get the black side you get a mass reduction and a thrust increase, but its nothing to write home about. You’ll almost certainly need to take your crew to land anywhere. The rare case where low fpb isn’t great.

Cermet NERVA [2M, 7*4(1,S)] — OK, terrible Fuel per Burn (fpb), but the 7 thrust means you can land on Ceres or Vesta (which are sure things], but you are likely making two trips. If you can flip this you lose one thrust (but can afterburn) but your fpb drops to 2, which makes this pretty good.

Hall Effect [2M, 3*2(-,C)P] — No afterburn and a low thrust means you’ll need your crew, but otherwise good.

Mass Driver [5M, 4*3(-,M)P, Dirt] –This is heavy, 3 fpb isn’t great, but being a dirt thruster compensates. You can always grab 10 fuel anywhere (dirt rockets refuel at ten and ignores ISRU rating!) so you really only need to pay to get to Demos and then jaunt out. If you flip this over you go to 3M 2*0.5, which basically means you never run out of fuel, but you’ll need another rocket to land most places.

De Laval Nozzle [4M, 5*2(2,M)P] — Decent thrust, decent fpb. Can even land on Ceres or Vesta (often taking two trips).

Ponderomotive VASIMR [3M, 3*1(1,V)P] — Compare with the mirror steamer. You pay 3 more mass, but you save so much fpb.

Metastable Helium [5M, 5*1(1,V)] — The king of rockets. Yes, its heavy. But 1 fpb rules. If you flip it over you’ll drop some mass and your fpb goes to a ridiculous 1/3rd, but even unflipped its a workhorse in the asteroid belt. With 5 thrust (maybe 4 or 3 due to weight) you can often make a hohmann pivot every turn and gain a lot of time. And you save time by taking your robo+refinery in one trip. Letting this go cheaply is a mistake.


Buggys let you get a re-roll or multiple sites (on a planet), so that’s nice. Missiles have a built in thruster (Uusually with terrible fpb, but in this case you save an auction and a part, so you could buy this and start scooting around early to make a bunch of pot shot claims and then buy/send a refinery later). And Rayguns let you go for multiple sites from orbit. Unlike thrusters (in the basic game) there’s lots of differences between robonauts.

There are a few different ‘classses’ of robonauts:

  • The 4 fpb missile. These are good to grab as a first card if you can launch and run to Demos (etc) to refuel and go get a claim, planning on getting a thruster and refinery later.
  • The rayguns. These let you hit a bunch of asteroids at once.
  • The oddballs (including buggies).

A quick note of sites: C are common, M aren’t common, but there are a few good targets. There are many S targets but they tend to have lower hydration (often zero). V and

[#Mass, type-ISRU (Type) ]

In alphabetical order:

Cat Fusion Z-pinch Torch — 3M, Buggy-2 (D).  Decent mass, decent ISRU.  Turns into a higher mass ISRU 0 Missile.

Explosive Gas Dynamic Laser — 3M, Raygun-2 (S). Improves to 2M Ray-0

Flywheel Tractor — 2M, Buggy-3 (S).  Improves to 1M Buggy-1.

Free Electron Laser — 5M Raygun-1 (S). Don’t let the 5 mass worry you (I mean, unless you have a 3-4 fpb thruster). If you get the Free Electron Laser you may want to go to the Karin cluster and hope to get one of Karin-a, b or c. That’s a 50/50 shot in one turn (you can raygun produce without going onto the hazard roll). If you get the claim you can ET produce this (as the Wakefield E-beam Missile with a quite decent 4*2(2) dirt rocket, but it becomes a Missile-1.

Kuck Mosquito — 1M Missile-3, 10 * 8(2) (V). The Mosquito pairs nicely with Ablative Plate or other low net thrust thruster, in that you only use this for the landing. You save weight on crew, its mass is low. If you happen to build it on a V planet, you can ET produce the Ablative Laser, which is a 3 * 1(3, push) Missile 2 with no mass. No raygun, but it can hop around quickly.

MET Steamer — 3M Missile-2 5*4(1) Push (C). This guy is a reasonable first buy. Buy, boost, fuel, go to Demos to potshot and/or refuel. By itself it can make a run at Ceres (small size for +1 thrust, afterburn for another). You’ll need another rocket to bring the refinery, but then you can ET produce the Nanobot, a zero mass Buggy-1.

Neutral Beam — 5M Raygun-2 (S). Slightly inferior to the Free Electron Laser, but this does flip over to the a 3*1/2(1) Missile.

Nuclear Drill — 2M Missile-3 5*4(1, Push) (M). Like the MET Steamer, this can be used as an early scout, planning on bring a rocket+ refinery later. This is an odd card in that the black side has a much higher mass (5), but it does become a Raygun-0 (while still having a thruster), which means you can scout a bunch of small asteroids (like the Koronis group) in one go.

Phase-Locked Diode Laser — 3M Raygun-3 (C). A very good robonaut, because there are lots of C targets, and it flips over to 0M.

Rock Splitter — 3M Buggy-4 (V). Buggy is good, but ‘4’ is bad. You could claim 2 Mars sites, I suppose. But there has to be a worst robonaut.

Solar-pumped MHD Exciplex Laser — 5M Raygun-2 (C). Doesn’t the name just roll off the tongue and fall like lead to the floor? This is another one of the 5M rayguns, and this one flips over (Quantum Cascade Laser) to a 3 mass ray-0. Ray-0 is great, and as a ‘c’ type card, this is the easiest to get.

Tungsten Resistojet — 2M 5*4(1) Missile-3 (M). Another decent “early thruster explorer.”. This flips over to a decent 4*2(1) Push missile-1.


In the basic game, basically you just want to get one. If it matches your target, that’s nice. Mass 3 is nicer than mass four, but unless you have a bad fpb its not a huge deal.

Written by taogaming

May 28, 2017 at 10:15 pm

Posted in Strategy

Tagged with

A lot of research on the question of Kickstarters

is a nice thing, and the resulting article is worth a read.

(Intelligent curmudgeonry leads to the same result much faster, but you have to appreciate the effort of doing the math).

In other news, AlphaGo is retiring undefeated. (The main news from Game 2 is that according to AlphaGo’s analysis, Ke Jie was ‘playing perfectly’ through the first hundred moves. Ke Jie thought he was winning and said his excitement may have led to the mistakes that cost him the game). I’d like to see Deepmind work on something of more value (AI medicine, or driving) but the last two years of Go has been interesting.

Played a few games of non-basic High Frontier (just with basic rules + supports. Nothing else) and its still quite demanding. I may play a few tries at the Advanced Solitaire CEO. Apart from one game of 7 wonders duel and two sessions of bridge, I have played literally nothing else the last month.

Written by taogaming

May 27, 2017 at 10:54 pm

Posted in Linky Love, Session Reports

Tagged with ,

Watching AlphaGo

Apparently its much stronger while using only 10% of its CPU. (Echoes of the “humans only use 10% of their brain” myth). The interesting thing is that apparently Ke Jie used some of AlphaGo’s opening moves and there’s a weird grouping in the upper left.  (Even though the game was over, I’m watching a ‘real time’ video with commentary….with some web browsing while waiting for moves)

I’m certainly not good enough to comment, but even with a glancing knowledge you can see how AlphaGo has changed the conventional wisdom about the game…

Written by taogaming

May 23, 2017 at 8:22 pm

Posted in Uncategorized

Not much going on

I haven’t even played Factorio in a week. It’s just been a slow month with general bad news and blasé feelings all around. (Two funerals and a friend in the hospital will do that, I suppose).

I did teach High Frontier a few times … and the Taoling and I played a multiple (basic) games today, although our last game we extended by requiring 7 colonies (instead of four) to end it. I continue to prove that I am bad at this game, I got swept by the boy. Although … we restarted once when he misplanned his first mission after some rules confusion. (Yes, your crew has an ISRU rating, but they are not a robonaut for purposes of industrialization. In his defense, he asked me but I thought he was asking something else).

He also ended a game with an illegal landing (he had 10 thrust but needed 11), but I just gave it to him with the commissioner’s asterisk.

I’ve been thinking that perhaps a PBF CEO solitaire game (me and interested readers versus the game) may be a good way to learn some of the nuances of the advanced game. Any interest?

The only other (new) game I’ve played recently is 7 Wonders: Duel, which was good enough that I’d play again. Not enthusiastic, but not indifferent. Somewhere between them, until I play a few more times.

Written by taogaming

May 21, 2017 at 8:24 pm

Posted in Session Reports

Tagged with ,

A well bid hand

Playing online against random opponents, red vs white (at IMPs) I pick up.

S: x H: Ax D:AT8 C:AJ65432

A straight flush in clubs, with a few good ones to boot. And three aces.

I open 1 Club naturally enough (no Polish club tonight!) and partner responds 1 Heart.

RHO steps in with 1 Spade and I bid 2 Clubs. I really want to bid 2.5, but I decided to go a bit low. In hindsight I think it may be better to stretch to get to a game, but either could work. I’d be happy if it came back to me and I could bid 3C.  Also, since we’re playing support doubles, my bid tends to deny 3 or more hearts.

LHO raises his partner to 2 Spades, and partner bids 3NT. RHO is back in it with 4 Spades.

Hm. Partner may have taken a chance, but we are white and they are red. I believe we are in a forcing situation. Partner bid a game, so we won’t let them play undoubled.

Given that, I pass. That must be suggesting not doubling and playing somewhere else. It should imply a singleton spade. It pretty much should ask about clubs, although I could also be 4=6 in the minors. I expect partner to double, and I won’t be unhappy if partner doubles — three aces are three tricks (hopefully), but who knows? We could make a club slam and 4 spades could earn us almost nothing or — heaven forfend — make.

Partner thinks for a bit and bids 5 Clubs, which ends the auction.

I get the three of spades lead and after dummy hits there isn’t much to the play


                    S: AQx H:QJTxx D:Q C:QT97

S:9xx H:Kxxxx D:J9xxx C:--            S:KJT8xx H:7 D:Kxxx C:Kx

                   S:x H:Ax D:AT8 C:AJ65432

With the club king onside I could make six. Taking the hook is totally safe (if it looses then I can at most lose one more trick) and I probably should have, apparently there was more to the play than I noticed, but its a measly overtrick and I’m playing online and in any case this article isn’t about the play and shut up.

Four spades likely won’t make, but will be a cheap date. (Diamond ace, diamond ruff, heart ace, diamond ruff and we get the spade ace for down 2, +300, instead of +620. The club ace lead looks terrible but will likely transpose into the same line, club ace ruffed, spade and partner wins high and leads the DQ to get a ruff, heart ace, another ruff. Although … after the club opening lead ruffed a declarer who peeks at the cards can lead the HK to hold things to off one).

East likely figured the save should be cheap, and he was right, although if West had a touch more defense. A further bid of 5S starts to look bad. It might be a phantom or push us into a slam. West’s bids are defensible and he self-rated as novice (I didn’t check East, but he seemed like a reasonable intermediate). Considering the poor bidding I see by “advanced” players I think both acquited themselves well.

And — of course — partner’s bid of 5 Clubs was correct.

I comment “nice bidding all around,” and go to the next hand.

Written by taogaming

May 17, 2017 at 9:51 pm

Posted in Bridge

Factorio Tutorial — Simple Production Ratios

I see a fair number of questions on production ratios (on reddit) and amazingly, nothing on the wiki seems to deal with it, so here it goes.  (This is really just a draft I plan on cleaning up and putting on the wiki).

The beginner says “Aha, I need a ton of <insert something here> so I’ll build some factories for it.” Then the factories sit idle most of the time. Adding factories doesn’t work if you don’t have the necessary inputs. So, how to figure that out? The easiest way is decide how many outputs per second you want.

For simple things (such as red science) you can build a lot of factories because the inputs (copper + gears) are either fast to make or basically infinite. (OK, not really, but if you aren’t smelting enough copper you have bigger problems). But let’s consider science pack 3 (blue science). Here’s the formula (as of 0.15):

1 Advanced (Red) Circuit + 1 Engine Unit + 1 Assembling Machine 1 (Grey) and 12 seconds makes 1 blue science.

(Thanks to Dave McW’s wonderful cheat sheet for this).

So, the easiest way to is to target some # of packs per second. Let’s say you want one. Picking round numbers makes it easy.

As the old saying goes ‘You can’t make a baby in one month by getting nine women pregnant.’

But you can average a baby a month that way.

To average 1 blue/second, we need 12 factories. (I’m ignoring the speed multiplier for assembling machines. It isn’t actually 12 seconds, depending on the factories. If you have all blue assembling machines (level 2) and change everything to level 3s, the number you get will speed up, but there will be no bottlenecks or slowdowns if they are all even).

Rule of thumb — If you want one unit output per second, you need as many factories as the time it takes.(Again, ignoring speed multipliers). If you want Z per second, you need Z times the number of seconds it takes one factory.

So, we need 12 factories producing blue packs. Now the reason to pick a nice round number like “one blue a second” is that we now know that we need one red circuit per second, one assembling machine per second, and one engine unit per second. We have to have enough inputs.

So, what does an Engine Unit take to make?

1 Steel + 1 Iron + 2 Pipes and 10 seconds makes an engine unit.

In order to support one blue science a second, we need 1 engine per second, which means 10 dedicated engine assemblers. Similarly, we need six red circuit assemblers. We only need half of an assembly one assembler, since it only takes 0.5 seconds. We can make these factories dedicated for this output (which may make sense for some objects) or we may have a big production area (for, say red circuits) so that any overflow can be used elsewhere.

Let’s look at a more complex example: Production Science Packs (purple)

1 Pumpjack + 1 Electric Engine Unit + 1 Electric Furnace + 14 seconds gives us 2 production science packs.

If we want one purple per second, we need seven factories dedicated to production (since they produce two each every 14 seconds).  Every fourteen seconds our seven factories dump out their two purple each to give us one purple per second, and every fourteen seconds they each take in a pumpjack, electric engine and furnace.

So we only need 7 of each input per 14 seconds.

We need 1/2 of a pumpjack per second (or 1 pump jack per two seconds). Ditto the other two.

Electric Engines take an engine unit (sigh), 2x electric circuits and 15 units of lubricant and 10 seconds.

If we want a dedicated line we need five factories (for 1 every other second), which will also require 5 factories for engine units (again, one every other second).  (Remember our rule, we want Z per second. Z is “one-half” and the factories take 10s, so 0.5 x 10 = 5 factories.

“It’s really easy to forget the two outputs per unit time,” he wrote looking at his current factory and suddenly realizing why there’s such a backlog of electric engine units. Ah well, I can divert some of that production and my pump jack production….In fact, there are a number of practical matters. If you only use purple science packs intermittently, you can get by with lower inputs and you’ll buffer some up while researching things that don’t require purple).

So far we’ve just spoken of production speed, but if you start getting into big numbers, you may have to worry about throughput. Maximum throughput of a yellow belt is 13.33 items per second.  If you need 15 or 20 items per second, you’ll requirea faster built (or a second belt) otherwise the first factories in your line will consume all the inputs and choke off your remaining factories. For our examples, that hasn’t been a huge concern (although technically it means that our one purple per second is actually 13.33 purple per 14s, assuming we have perfectly packed yellow belts). But if we wanted to go to two per second, we’d need to upgrade our belts (red belts are exactly twice as fast). If we wanted to go to 5 a second, that would require multiple lines (or maybe having a staggered line where we produce a few intermediates, then a few purples. But that way lies madness).

You can do this to see compare if you have enough labs to consume your science production (or too many labs) although that’s tricky because the colors you need (and times) change based on what you are researching. But typically research takes 30s or 60s (some of the early game research takes less, and some military researches take 45 and braking speed takes 35!) If you produce one (of each color per science) then you can keep 30 labs working all the time, and your 61st lab is guaranteed to sit idle (assuming you never stopped), but in reality you will stop from time to time….

I haven’t done the math on launching one Rocket Per Minute, but throughput becomes a big concern.  1000 Rocket Control Units (which are required per rocket) requires just shy of 40k iron per minute, 650ish iron per second (smelting and transport). Of course those actually have a bunch of intermediate steps, but that’s 17 lanes of express belts just for iron. (In reality, its a bunch of trains to various outposts to make green circuits, etc). And rockets have a bunch of other parts.



Written by taogaming

May 2, 2017 at 10:26 pm

Posted in Artificial Opponents, Strategy

Tagged with

If you were borderline on Factorio

They’ve just released 0.15 (up to 0.15.2 for some bugfixes). I’m sitting here waiting impatiently for it to download. Nuclear power, rebalanced combat, a ‘marathon’ mode (critical items take a lot more materials to build), and prebuilt settings for various styles of play….

It is a sign of good sportsmanship on my part that I didn’t skip gaming to download it yesterday (when it released), but that’s only because I’d promised that I’d teach High Frontier.

Update — It’s slower going (7 types of science instead of 4 — and purple science is no longer “stuff you get for free by killing natives”). I’ve got a horrible spaghetti maze because I haven’t been looking ahead. I should probably punt, but my goal is to use this base as a starting point for a big base, so its ok. But I do like many things:

  • Flamethrowers are still good, but much more expensive. Bullets have been buffed, because they were terrible.
  • Infinite science (even if some of it seems to be a bad deal, like mining productivity).
  • Lots of quality of life fixes (showing oil patches underground, etc).

I need to get logistics bots for this factory. It’s not pretty. Gotta find a new copper patch, too. Have basically run out.

Written by taogaming

April 25, 2017 at 7:32 pm