I took a longer look at hop's graph. Great post. If a picture is worth a thousand words, the graph is worth ten thousand- but don't worry, I won't go that far- just a few observations...
hophoofer wrote: ↑Sun Dec 06, 2020 7:10 pm
I simulated 100K hands. For the
same dealt hand, the program plays perfect 9/6 JOB (99.54%) and 9/7 TDB (99.6%) strategies.
It's proper that the same dealt hands are used for both games of course, and while the number of hands is what some might say is or is approaching long-term results, it really represents only about 4% of the total dealt hands possible, we don't know which ones, and how many were repeated.
Waiting4RF wrote: ↑Sun Dec 06, 2020 8:41 pm
After 100,000 hands, the bankrolls are pretty close but JOB is the winner with 2 royals. What does another 100,000 hands look like?
JOB "wins" in this simulation. Over the loooong run though, with either many more hands or many more simulations of 100K, TDB will "win" overall/"win" more often. For me, a statistically significant number would be 10 million hands or if you prefer, and probably more interesting, 100 simulations of 100K.
The expected loss for each game over 100K hands is about 2000-2500 units (?). In this simulation, it looks like JOB = -3500 and TDB = -5000. Either slightly worse hands than average were dealt or the random draws were slightly below par for the games, or both. JOB expected # of royals, TDB has (9) 4000 credit hands, which is pretty much the expected number. Hard to tell for sure but looks like (13) 2000 credit hands. The expected would be about 16, so maybe -5000 units on account of that. By and large though, fairly typical scenario- if my numbers are correct.
billryan wrote: ↑Sun Dec 06, 2020 11:06 pm
They shoulda quit when they were ahead.
Good one! But when? They were both ahead 5 or 6 times, sometimes at the same time (maybe they carpooled to the computer lab). Naturally they should quit at their respective maximum, if they have the necessary special powers. I don't think we're looking at Jeane Dixon and Nostradamus here, so when do you think? I have my own guess, hindsight being 20/20...
FAA wrote: ↑Tue Dec 08, 2020 2:10 pm
After 100,000 hands, the bankrolls are pretty close but JOB is the winner with 2 royals.
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This is certainly excellent news for the slow and steady crowd.
Exactly. Except it's not news at all, let alone excellent. It's nearly what's expected except for JOB "winning" this one. 99.58 > 99.54, so for the loooong run play TDB (9/7)! Unless the added 0.04% is not worth the excitement:
Most mundane
1. Watch paint dry
2. Watch grass grow
3. Play Jacks or Better (no offense to those who do, just my opinion). If that keeps you awake, head for Keno or the Big Wheel (again, no offense).
Most exciting
1.
Russian roulette. That's the wheel with five zeros.
2. Elizabeth Hurley (or desired substitute) knocking on your door asking to stay the night on account of car trouble. And can you help get her out of those drenched clothes...
3. Play Triple Double Bonus, preferably at dollar and up. Add exotic and expensive bonus feature when you get bored to supercharge the volatility and move it to #2....cause after all, you can play VP ALL night.