9/6 JOB:
R(1)=0.011512207xR(9) + 0.011014511xR(6) + 0.011229367xR(4) +
0.074448699xR(3) + 0.129278902xR(2) + 0.214585031xR(1) + 0.545434669
R(1)=0.977463360089361
50%=30 bets (note quad returns 25 bets)
90%=101 bets
99%=202 bets
10/7/5 DB:
R(1)=0.01118989xR(10) + 0.014953347xR(7) + 0.015019409xR(5) +
0.072199448xR(3) + 0.12465837xR(1) + 0.192379047xR(1) + 0.567136051
R(1)=0.987010990701288
50%=53 (note low quad returns 50 bets)
90%=176
99%=352
You've clearly caught on to how this works.
Here's one to try for 10/7/5 DB: Probability of surviving until you hit
a non-royal straight flush in spades.
Fair warning: this is a trick question.
On Monday 14 November 2005 09:26 pm, nightoftheiguana2000 wrote:
9/6 JOB:
R(1)=0.011512207xR(9) + 0.011014511xR(6) + 0.011229367xR(4) +
0.074448699xR(3) + 0.129278902xR(2) + 0.214585031xR(1) + 0.545434669
R(1)=0.977463360089361
50%=30 bets (note quad returns 25 bets)
90%=101 bets
99%=202 bets10/7/5 DB:
R(1)=0.01118989xR(10) + 0.014953347xR(7) + 0.015019409xR(5) +
0.072199448xR(3) + 0.12465837xR(1) + 0.192379047xR(1) + 0.567136051
R(1)=0.987010990701288
50%=53 (note low quad returns 50 bets)
90%=176
99%=352
Hmmmm...
10/7/5 DB till bust is 0.99987577532735, 50%=5579 bets (~7 royals)
If you pull the spade straight flushes, the straight flush probability
drops by 3/4 and the result is 0.99843143227039, 50%=442 bets
That can't possibly be correct. So, obviously, you can't pull a
component if lower probability components (like the royal) still
exist. But at the moment I can't figure out why that would be the case.
Can you explain it?
On second thought, could it be correct? 10/7/5 till a royal is
0.99904780749845, 50%=728 bets; 10/7/5 till a royal or straight flush
is 0.996813385697963, 50%=217 bets ... But is that correct or is there
a problem with wins>sf like the aces?
--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x...> wrote:
Here's one to try for 10/7/5 DB: Probability of surviving until you hit
a non-royal straight flush in spades.Fair warning: this is a trick question.
The reason that it is a trick question is that there's a logic trap
here. With only 1/4 of str-flushes "removed" the residual EV
is over 100% The trap is thinking that this implies that the player
can play forever, neither busting nor hitting the target.
You didn't fall for it. Your answer is correct.
I'm fairly certain one poster here will object, claiming that the
player _can_ keep playing forever without busting or hitting
the target, so I'll explain.
I'll use the term "reachable" to describe any single final hand or
group of final hands that the playing strategy will permit to occur.
I believe it is possible to devise strategies with unreachable hands.
You can pick an arbitrary group of final hands and make that a
target for a "risk of no X" calculation. The probability for hitting
this target on a single draw will be some number larger than zero
but less than one. Now, suppose we allow the player to start with
a single unit and play forever with unlimited credit, so they never
go broke. Can this player avoid the target forever? The answer
is "no". Let q = p(no-target) be the probability of failing to hit
the target on any single trial. Then p(no-target, N) = q^N. This
is a number less than one, and it approaches zero as N grows
toward infinity. So, even for a player who has no risk of going
broke, it is impossible to avoid the target forever with a finite
probability that is greater than zero. Adding a barrier that forces
the player to quit after going broke only makes it less likely for the
player to keep playing while avoiding the target.
Note that in the argument above, it doesn't matter if the "residual"
EV favors the player or not, and it doesn't matter if the overall
game is favorable or unfavorable. It just isn't possible to avoid
any reachable hand indefinitely.
Critics of my method should think about that very carefully. It
implies that in "risk of no X" calculations, the sum
p(ruin, n) + p(target, n) approach unity as n approaches infinity,
and any state that resembles p(still playing, n) is a transient state
that cannot survive indefinitely.
On Tuesday 15 November 2005 02:05 pm, nightoftheiguana2000 wrote:
--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x...> wrote:
> Here's one to try for 10/7/5 DB: Probability of surviving until you hit
> a non-royal straight flush in spades.
>
> Fair warning: this is a trick question.Hmmmm...
10/7/5 DB till bust is 0.99987577532735, 50%=5579 bets (~7 royals)
If you pull the spade straight flushes, the straight flush probability
drops by 3/4 and the result is 0.99843143227039, 50%=442 betsThat can't possibly be correct. So, obviously, you can't pull a
component if lower probability components (like the royal) still
exist. But at the moment I can't figure out why that would be the case.Can you explain it?