## Followup to a leisure-time post

A couple of weeks ago, I posted a long essay about a certain leisure activity that’s proving to be a great way to deal with interstitial time at the computer–the times when something’s taking a while to load or when I need a brief break within a long or boring task, and have already walked around.

That essay included the note that, in my geeky desire to track how long it actually takes to go through 200 coins (\$50 of quarters) playing optimally but not playing maximum coins, I found that the third run–actually the fourth–was taking a while.

I finally finished it, in what would have been the equivalent of maybe three years of normal gaming back in the old days, maybe five years now: 29,001 hands, or a payback percentage of 99.31%. Which is less than the theoretical payback if playing maximum coins, but considerably better than the theoretical payback playing one coin (98.4%).

Added a bit later: I forgot one thing–checking up on my belief that I’d been ahead of the game for at least two years of light gaming here and there. Easy: In this run, I was continually ahead for at least 19,000 hands in the middle of the game–which at current gaming rates is probably three years of playing. In the long run, of course, the odds caught up with me. Then again, when a tiny variation can shift things that far, you run into the answer to “In the long run…” — “In the long run, we’re all dead.”

### Considerably better?

Yes. Numbers get very strange when you deal with percentages at the edge. So, for example:

• In the third run, I played 11,310 hands for a payback of 98.23%.
• In the fourth run, I played 29,001 hands for a payback of 99.31%.
• The difference in percentage: “trivial”–1.08%. The difference in actual playing: Nearly three times the number of hands.

I also tracked the effects of my “system” of varying bets, which should yield favorable results if I’m getting streaky hot hands (3 of a kind or better) and terrible results if I’m going hot & cold. In this case, the “system” was favorable to the tune of 54 coins–but, looking at actual hands, that really means I would have played about 250 fewer hands without varying bets, or about 28,751 hands (99.30%).

That item also shows the problem with playing max coins if you’re gaming, not gambling: it doesn’t take much of a cool streak to run through \$50 at \$1.25/hand. Try 92 hands (maybe 40 minutes play in a casino) today, and I’ve seen even faster descent.

This was an extraordinary run, with more than one royal flush (which I’d never had in the past–never) albeit no straight flushes (there should have been about three in 30,000 hands. As for everything else, though, while any given playing session can be incredibly streaky–e.g., seven four-of-a-kinds in 1,500 hands or three in 892 hands–over a long period, you do tend toward the mean (and this long run was maybe my long-term lousy play or lousy luck regressing toward the mean). As in, over 17,800 of the hands (the last 2/3 of the play, mostly):

• 0.19% of hands were four of a kind, compared to expected 0.24%
• 1.14% were full houses, compared to expected 1.15%
• 1.12% were flushes, compared to expected 1.10%.
• 1.18% were straights, compared to expected 1.12%
• 7.34% were three of a kind, compared to expected 7.44%
• 13.22% were two pair, compared to expected 12.92%
• 21.08% were jacks or better, compared to expected 21.46%
• 54.73% were losers, compared to expected 54.56%

If you’d asked me, I’d have said I get more 3 of a kind than I expect, more full houses and fewer straights–which says a lot about expectations! (Those odds also show why the payoff for full houses is so important: It pays much better than straights or flushes but hits just about as often–also why drawing to a non-flush inside straight is always stupid, since the odds are terrible and the payoff’s lousy.)

I’ve made the one “expert play” adjustment based on not playing max coins: Namely, when dealt four to a flush, of which three are royal, I keep the four (where “expert play” would have me drop them). The really agonizing one–where you get a full flush dealt, four of which are to a royal flush–it still, just barely, makes sense to drop the non-royal card, but that sure is painful.

Well, a little less painful since no money is involved.

I think that’s the end of these gaming posts, at least for a while. If I never get a run like this again, which seems likely, this one was still fun, even if it was a minute there, two minutes there, at most five minutes elsewhere…