Okay - a friend finally explained to me my problem with the math of 10-play. Actually it isn't a problem with the math; it's a problem of semantics.
He says that playing 4420 base 10-play hands gives a 63% chance of hitting at least one Royal. For him, that is a "reasonable expectation." Playing 5000 base hands gives about a 69% chance, which is even more "reasonable," in his opinion.
I guess I have much higher expectations for the word "reasonable." Before I would reasonably expect to get a royal in a 10-hour session I would have to have at least a 95% chance. I am a terribly conservative gambler. In fact I have learned from experience that I am happier if I NEVER expect anything particular in the short term. I guess I have gone through too many long long losing stretches.
I ALWAYS expect to win and get my fair share of royals in the long term. Brad and I have 15 years of experience that proves this is a very doable thing for us. But for the short term there are absolutely no guarantees - and I don't expect anything and therefore I am never disappointed! And when the big wins and the jackpots do appear I am ecstatic!!!!
By the way, Brad and I did something today we hadn't done for a very long time - play VP all day long. We played quarter 10-play for a total of 11 hours between us and did not get a royal. Lost $4000. Switched to quarter Hundred Play "to have more fun." Played 4 hours total - got one royal and won back the $4000 plus a profit of $305. Now that is fun!!!!!
By the way, for the inexperienced, all this math about royal cycles, etc.: remember that you could get the royals "right on time" but you are likely to still lose in the long term if you are playing a negative game!!!!
Since I worship at the altar of long-term EV, royal cycles have never been very important to me. They rarely come "on time" anyway and knowing how many cycles I am "behind" is information that would just be discouraging. I like to look to the future with optimism!
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Jean $¢ott - http://www.FrugalGambler.biz
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We never have a win/loss stop limit so hitting a royal isn't the signal for us to quit. We are almost always playing until we reach a specific goal, like earning enough points for a certain promotion or for a certain bounce-back level. If there isn't a specific goal, yes, we would usually play longer if there were bonus points or there was a very good promotion, making the EV high. But the usual reason for quitting is that we get tired and/or the smoke is getting to us. Funny about Sunday, the smoke didn't bother us as much as usual - but we were very tired when we finally came home.