Richard Boston wrote:
Someone recently asked about how many hands or how long for the true
percentages to kick in. Well here's some interesting examples of
how it's not in the thousands. Also some great examples of when
even playing positive games that .2 or .5% difference doesn't
really help a whole lot.
A few days ago I was playing various games because that were
themselves not positive but I had a promotion that made it so. I
didn't see a quad for well over 5000 hands. Not a single one. And
when I finally did see some it came out to only about 3 quads in
nearly 7000 hands. Regardless of positive or negative game, if you
get on a roll like this you are going to lose big time.
Another thing I love to laugh about is all the angst over a .2
or .5% difference from one game to the next. Across a two week span
I'd say that I haven't had a session over 90% return. This is
playing both positive and negative games (w/ a promo) and it still
did not matter ...
I understand what you're saying here, Richard, and there's a lot
about it that's rational. Among other things, paraphrasing what
Stuart expressed, when your ER is regularly being kicked around five
to ten percent, a small fraction of a percent seems dwarfed in
comparison.
Over the last few weeks I've sought to make the point that there's a
keen distinction to be drawn between the sizable uncertainty in vp
results that we have to stomach as players and the type of
uncertainty involved when we talk about the difference in expectation
playing a "full pay" paytable vs "short pay".
If you set two players down for a series of sessions, totaling a few
hundred thousand hands -- one playing 9/6 Jacks, the other 9/5
Jacks -- There's a considerable degree of uncertainty as to which
player will come out ahead. Among other things, a disparate number
of RF's could tip the balance in either direction.
However, if you narrow the focus to just the return received from
Flush hits, over this length of play it's a near certainty that the
9/6 player will come out ahead. The variance in the number of hits
that will be experienced by either player during the play isn't large
enough for there to be any appreciable likelihood that the 9/5 player
had a sufficiently greater number of Flushes to counter the short
payout.
Bottom line, over the course of just a moderate length of play, you
can reliably look for a short paytable player to come out behind on
the hands payouts related to the paytable shortage ... i.e. play
short-pay and you can count on it costing you, no matter how your
related luck plays out.
···
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When you turn to taking a look at the difference in expectation in
playing one game vs. another (e.g. 9/6 JB vs 9/6 DDB), the picture is
hardly as clear cut. And, all things considered, I can understand
why someone might elect to play DDB over JB. They clearly enjoy some
different things in their play than I do and it may well be that
they've made a very prudent choice.
But I'd only make that "prudent" call if they have a decent grasp of
the consequences of playing one vs the other. It's not enough to
simply say that one game isn't strictly better than the other because
over the course of the player's expected play there's great
uncertainty on which game they might come out ahead.
No matter how you slice it, in the example games above, Jacks is the
hands on favorite to come out ahead. The strong variance of DDB
keeps that from becoming anywhere a certainty, that that same
variance puts the DDB player at much greater risk of losing their
bankroll.
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It can be difficult to buy onto a notion that has a relatively
marginal role in our day to day play and instead takes time to play
out. But that doesn't take any of the substance away.
- Harry
