--- In vpFREE@yahoogroups.com, "John.G.Zaroff" <John.G.Zaroff@d...>
wrote:
There was some discussion on the cost of royals. Toonces made the
point that if you give up a high pair for a 3 card royal draw, you
will only fill in the royal 1 in 1081 times and that the cost of the
misplay is much more than the couple of cents that Winpoker shows.
It's true that you will 'miss' most of the time but you still have to
include the chance of hitting the royal. If you don't want to
include the low probability hands, you would have to radically alter
your play for a lot of hands. Here are a couple of examples, using
9/6 JOB as the game:
3h4h6hQcAs. Holding SF3i, 0 HC is worth 2.6688 and holding AQ is
worth 2.3913. For the SF3i, 0 HC 17.33% of the return comes from the
2/1081 Straight Flush hit. If you dismiss the straight flush as a
rare event, AQ becomes the better play.
10sJsQs3sQh. RF3 is worth 7.3219 and FL4, 2 HC is worth 6.383.
If you discount the royal, FL4 is better play. You will fill in a
flush 9 out of 47 times but will only fill in the royal 1 out of 1081
times. The royal portion accounts for about half the value of the
RF3 draw.
ยทยทยท
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My point was not to suggest that you should alter strategy to ignore
low probability events. My point was to deconstuct the low
probability event into two conditional probabilities. The reason is
that when someone says "The play costs me 2 cents, but I have a
1/1081 chance at the royal", people interpret that to think "Well, if
it only costs me a few cents to go for the royal, and the royal is
$1000, my 1 royal every 1081 hands more than makes up for the nickel
I was giving up."
If you are thinking of it as +1000 dollars if you hit the royal and
negative 5 cents if you don't, you're misanalysing the situation. If
you properly think of it as costing you $1 GIVEN THAT YOU MISSED THE
ROYAL, you avoid falling for this thinking.
We can deconstruct your other examples the same way. On your first
hand, if you don't get the straight flush, trying for the straight
flush cost you 4.6 cents. 1079 out of 1081 times this will happen,
costing you a total of $49.90. But the other 2 times you get the
straight flush, worth $62.50 each, or $125 total. The difference is
$75 or 300 coins, over 1081 hands, IN FAVOR OF trying for the
straight flush. 300/1081 = .2775, the difference in EV we started
with.
The difference between this and the example I started with is that
the $1000 you get for the royal doesn't make up for the $1080 it cost
you to try for it.