fivespot wrote:
risk of ruin is a silly metric to be using here, since most
of us aren't locked into a single game forever and ever, we'll move
up or down as our bankroll grows or shrinks.
a more useful figure is kelly-optimal bankroll sizing, figuring out
what stakes will maximize long-term bankroll growth.
Similar to bl, I'll offer my take.
It's reasonable to say that most casual players manage their bankroll
session to session -- allow for a loss based upon resources at hand,
fully expecting that over time they'll replenish any drain due to loss
from future income. If one wanted to quantify their bankroll, Jean
Scott suggests that it would be measured by the aggregate loss their
willing to absorb over a given period of time before quitting the game
(possibly restarting once they've come to terms with that loss and are
prepared to continue allocating/risking future earnings.
However, I'll suggest that the prudent player has a predetermined loss
tolerance in mind -- whether funded from existing reserves, or to be
funded on a "play as you go" basis. It's the best means by which to
avoid (or minimize) "gambler's regret" -- the sinking feeling one is
vulnerable to in sensing that one foolishly made play decisions that
resulted in ruin (and, in hindsight, in the heat of the moment
absorbed more than acceptable losses).
The consequence is that in one form or another, most players operate
under a reasonably well defined bankroll constraint. Whether they
manage their play according to it is another matter. But some
measurement of their play against bankroll risk is very desirable.
···
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The notion that a player will simply manage their bankroll by
adjusting denomination as necessary is simplistic. Unlike many table
games, the betting increments available in video poker are dramatic,
where betting must often be doubled or halved to effect an adjustment.
This can be further exaggerated when play is restricted to strong
games and those games are available in very limited denoms (e.g. $1
and $.25 only).
The consequences of a downward shift in vp denom can't be easily
dismissed either. For most recreational players, the comps aspect of
play is a critical source of play satisfaction. A cut in play
denomination will likely mean a sharply reduced daily coin in and a
sizable cut in benefits extended by the casino.
The benefit factor is one that likely induces many players to overplay
their bankroll, being hesitant to downsize and hoping that luck plays
in their favor in the near term and restores them to a comfortable
bankroll. With short term prospects negatively skewed, I'd anticipate
that this often ends very disappointingly -- with many walking from
the game rather than pushing on at a lower denom.
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All this said, most active players intuitively do manage their play
according to a reasonable perception of risk. The play a small number
of paytables and in fairly short order find the denomination for which
the implicit swings are most comfortable and yet generate sufficient
excitement. Resorting to statistical ROR calculators and formulae are
hardly necessary.
But most players encounter infrequent occasions where there's a
temptation to stray into unfamiliar turf, where they don't have the
necessary experience from which to have a reasonable intuitive sense
of risk.
These might include unique opportunities -- a juicy progressive with a
reduced base paytable or a casino promotion for which the optimal
machines involve a denomination jump, for example. It's difficult to
make an off-the-cuff call whether this reward/risk tradeoff is
consistent with their current bankroll limitation.
I assert in these cases is player is best positioned if they can
assess exactly how the risk of these plays compared with the risks
that they regularly take on in the existing play. At the very least,
forewarned with this information, they can make a more intelligent
play decision and will more likely be prepared to accept the
consequences, if adverse, without remorse.
------
Another play dimension worth considering is the temptation to take
"pot shots" with one's bankroll. Many players will temporarily jump
to a more risky play or jump denomination in hope of a quick hit. A
stronger familiarity with the risk of ruin concept, and how their
bankroll measures up against their current play, will mean more
rational decisions when it comes to pot shots.
There's a definite irrationality that often comes into play with pot
shots. A player enjoys a very good run of luck and reasons that they
can afford to risk a little of it on a riskier, but high paying play.
What's missing is a recognition that such good runs are to be
expected and are a necessary component of sustaining a play --
offsetting the equally expected dry spells. To risk funds on a play
that isn't sustainable in the long run is to accept a permanent
bankroll drain if not successful -- you can't expect that, in the
course of things, the regular play will replenish the losses.
An example is a $.25 player who steps up to $.50 or $1 play
occasionally (or a $1 player taking a shot at $2). It's only
reasonable that is very unlikely that a loss taken on $.50 play will
be offset by a good run at half that denomination.
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All of the preceding is to argue that ROR is a very tangible and
pertinent concept to active players who put serious money at risk.
There are software calculators that readily calculate ROR from various
sources (VP for Winners, includes one, for example; free ones are on
the internet as well), so getting hard numbers is not a hurdle for the
casual player.
It's some of the practical considerations that require a little
education to best understand how to apply ROR to play decisions
(including what thresholds to set and the understanding that most
players want to measure against the specific bankroll limitation that
would lead the player to make a concrete change in their play, rather
than against total bankroll resources).
------
With respect to kelly bankroll numbers -- While Kelly has some limited
useful application to vp, in general I find it wholly unsuited.
Kelly optimizes bankroll growth, yet I don't think that's an apt goal
for a casual player. If you're standing in an 30th floor office in a
building and I tell you that the quickest way to the sidewalk is to
walk out the window, that hardly suggests that's a prudent action.
That's an extreme analogy, but it's meant simply to suggest that kelly
risk is generally higher than a casual player is comfortable with.
Further, Kelly is best applied to games such as blackjack, where the
increment in betting options is relatively small. It's very easy to
make betting adjustments as bankroll shifts (of course, it's to be
noted that a player thinking in Kelly terms is unlikely to be making
minimum table bets on average). VP allows very limited discretion in
adjusting wager.
- Harry
