Ridere, ludere, hoc est vivere.

Showing posts with label Pass the Pigs. Show all posts
Showing posts with label Pass the Pigs. Show all posts

Friday, April 29, 2016

Gaming in a hospital room - revisited

A little over four years ago, I wrote a couple of posts on what works and what doesn't when playing games in a hospital room or waiting room.  We find ourselves in a similar situation this week, although the medical circumstances are decidedly more serious.  All the same, it is helpful to revisit the principles that make for a good pasttime under such trying circumstances - portability, compactness, simplicity, humor, interruptibility, and brevity.  What follows is an amalgamation of highlights from the two posts.

Friday, August 22, 2014

Third annual-ish "What to pack for a vacation"

I like looking into which boardgames work for taking on family summer vacations.  The last time I looked at this question was July 2012.  This year we have plans to visit points of interest in southwest Virginia - the Skyline Drive, Lexington, the Natural Bridge, and Monticello.  We specifically will be leaving laptops at home.  Anticipating some quality family downtime, of course that means boardgames.

Friday, January 13, 2012

Risk management and pigs: Running the numbers

Pig on left demonstrates the very
difficult "leaning jowler" while pig on
right wallows on table, unimpressed
In my last post I discussed the personal thresholds that my wife and I have when playing the push-your-luck game Pass the Pigs.  For those not familiar with the game, it consists simply of two little rubber pigs that can be rolled like dice.  Each will come to rest in one of six positions, and the resulting score depends on the combination of the two resulting positions from one throw.  A player can elect to keep rolling the pigs and racking up the score, but if on any throw one pig lands on its left side and the other on its right, the result is a "pig out" and no points are scored on that turn.  So the push-your-luck aspect comes in deciding how far to go before stopping to keep the points scored on that turn rather than risk pigging out on the next throw.

My habit has been to stop rolling when I've reached a score of 11 or higher (unless I'm behind, in which case I'll take a chance on catching up).  Kathy's personal threshold is a score of 15.  Our friend "SPC" commented back to say that his threshold is 18.  But all of that was pretty much based on a qualitative sense of risk tolerance, not any real actuarial analysis.

As it happened, back in October, the intrepid boardgame geek Mike W. actually kept track of 895 rolls of two pigs over ten games and posted the resulting statistics.  These data provided a golden opportunity to do some real optimization analysis.  Release the spreadsheets!

I started with Mike's breakdown of 1790 individual pig results:

Result, Number of Occurrences, Percentage

On Side, 1243, 69.4%
Razorback, 388, 21.7%
Hoofer, 112, 6.3%
Snouter, 30, 1.7%
Leaning Jowler, 17, 0.9%

I broke out the "On Side" results and assumed half were on the left, half on the right, then made a matrix of all possible combinations of two pigs:


Probability Left side Right side Razorback Hoofer Snouter Leaning jowler
Left side 0.120409 0.120409 0.075299 0.021861 0.005899 0.003123
Right side 0.120409 0.120409 0.075299 0.021861 0.005899 0.003123
Razorback 0.075299 0.075299 0.047089 0.013671 0.003689 0.001953
Hoofer 0.021861 0.021861 0.013671 0.003969 0.001071 0.000567
Snouter 0.005899 0.005899 0.003689 0.001071 0.000289 0.000153
Leaning jowler 0.003123 0.003123 0.001953 0.000567 0.000153 0.000081



Now, given a starting score s, I treated a result of one left-side pig and one right-side pig as have a value of -s, and all other results having the positive score value in the game (five points for a razorback, 20 points for a double hoofer, etc).  The expected value of a roll of two pigs is the linear combination of probabilities and corresponding scores, where the "pig outs" have a value of -s for a given starting score s.

For the first roll of the turn, s = 0, and the expected value turns out to be +4.17.  For every point of s at risk, the expected value goes down by 0.24 (the probability of a "pig out").  So for any initial score s, the expected value of the next roll is


s
Expected value
0
4.17
1
3.93
2
3.69
3
3.45
4
3.21
5
2.97
6
2.72
7
2.48
8
2.24
9
2.00
10
1.76
11
1.52
12
1.28
13
1.04
14
0.80
15
0.56
16
0.32
17
0.08
18
-0.17


These results really surprised me.  They indicate pretty clearly that my instinct for stopping at 11 points is way too conservative.  With only 11 points at stake, the next roll still has an expected value of 1.52 - better than a sider.  Even my wife's threshold of 15 is a bit safe, since the subsequent roll would still have an expected value of 0.56.  But most amazing is that "SPC's" risk tolerance is perfect (according to these data).  If he rolls on 17 but stops on 18, he is playing PtP right down to the tip of the snout.  On scores of 18 or higher, the downside risk outweighs the upside, and it's time to stop (unless the opponent has a significant lead and the game is in jeopardy).

This revelation of my own conservative play reminds me again of my poor showing in Can't Stop at Congress of Gamers (and before that at PrezCon).  I think I'm going to have to run the numbers on CS some time and see what I can discover about my risk threshold there.

Tuesday, January 10, 2012

Luck, risk management, and pigs

Beer, wine, pretzels, and pigs - my final losing "pig out"
My wife and I were playing Pass the Pigs (designer David Moffattpublisher Winning Movesthis evening before dinner, and my son happened by and said, "I thought you didn't like games based on luck."

What a great question.  I don't like games based on luck - games like Life, Sorry, War, and any other game in which luck renders decision-making moot.  But I certainly do like risk management games, and PtP is squarely in that category.  I've posted before about my early observations on how the teenage brain works in assessing risk.  In our first family game of Incan Gold,
[My son] bolstered my working hypothesis on teenagers and risk assessment.  He was always still in the expedition when the second monster of a suit came up, so he ended up with no treasure after five rounds.
On the other hand, I remember getting my butt kicked in Can't Stop at Congress of Gamers last fall because of that very phenomenon.

One brilliant element of PtP is that since the pigs aren't really dice, it's very difficult to calculate probability in the conventional sense.  The pigs are oddly shaped, and because I'm too lazy to run 1000 trials of pigs to estimate the expected value of a roll (although somebody else wasn't), well, I just wing it on the risk assessment.  My "wing it" threshold for PtP is typically eleven points.  (Actually, maybe I shouldn't post that number online.)  If I'm significantly behind, I'll take bigger chances, but overall, I'm still pretty conservative.  My wife said her threshold was 15 points, but after I told her mine was eleven, she started stopping at eleven, too.  And she won.  So what does that tell you?

***

So now that I've been thinking about the fact that somebody else actually did run the numbers on the pigs, my inner mathematician compels me to calculate the optimal threshold for rolling again vs. not rolling again.  I think that will be a topic for a future post...

Wednesday, September 14, 2011

Gaming in a hospital room - what works, what doesn't

I missed my customary Monday blog post because I was in the hospital with a family member.  (The details aren't important, and he's home and fully recovered now.)  He was well enough yesterday to ask to play a game.  We had brought a few games with us for the visit, and the hospital also had a recreation room with a few titles that we could borrow.  We discovered a few things about gaming in the context of a hospital room that we'll remember for next time.

What worked:  Pass the Pigs (designer David Moffatt [or Moffitt] of the original title Pig Mania, now available as Pass the Pigs from publisher Winning Moves) is great for cheering up a hospital patient for a number of reasons.  It is terrifically portable.  It requires very little space on which to play and no set-up to speak of.  It requires little mental and physical effort to take one's turn.  It's good for a laugh.  The game can be interrupted easily without consequence.  It finishes quickly.  It lends itself easily to a re-match if "the pigs are against you" in the first round.

We also brought Uno, which, if we'd played it, I think might have worked almost as well.  There's a little more difficulty in sitting up in bed and holding a hand of cards, depending on the circumstances (like an IV or an awkward bed configuration).  But again, Uno doesn't require a lot of thought or effort, it's good for a laugh, and it interrupts easily.

What didn't work:  The game we borrowed from the hospital game room was Clue: Secrets and Spies (Hasbro).  We actually got this for Christmas last year and played it once as a family, to a decidedly lukewarm reception.  I had wanted to re-visit this title in the hope that perhaps it would gain some appeal with fresh eyes.

Unfortunately, we didn't really get the chance to properly evaluate Clue:S&S as a game.  The hospital room didn't have a proper game table, so we used the over-bed table (normally used for meals in bed).  The game board overlapped the edges of the table, so it was easily knocked.  Game set-up was a little "fiddly" for the context of a hospital room.  In this case, we were particularly hamstrung by the borrowed copy of the game that we had available.  Three significant game pieces were missing.  Two could be replaced with coins representing the missing pieces, but one - a black light for revealing secret text on cards - was indispensible.  The accommodations necessary to play this game under the given circumstances were too great, and we abandoned the effort.

I should make note of one other consideration for playing games in a hospital room.  Hospital-acquired infection is an ever-present risk, mitigated by simple but important hygienic precautions.  It is wise to ensure that hands are sanitized before handling game pieces.  Normally I don't think about who's been handling the pigs, cards, or dice in the game I'm playing, but medical professionals take a number of precautions to minimize the spread of germs in a place where sick people naturally congregate.  (I was particularly mindful of this issue with the borrowed game from the recreation room.)  The hospital had a hand sanitizer mounted outside the door to every room, and antimicrobial soap was available at every sink.  We found ourselves paying a little extra attention to keeping each other healthy and to keeping our own games uncontaminated so that we wouldn't bring home an extra souvenir from the hospital.