To me, the real key here is whether this concept of "bankroll preservation" should ever indicate a preference for a play with a slightly smaller EV. If you don't have enough money to play the game correctly, I don't see how you could make a case for playing the game incorrectly; your "correct play" with an inadequate bankroll is, in fact, "don't play at all."
To me, it seems like every time you make a decision that gives up money, even if it's a nickel, you are making a decision that DEPLETES your bankroll a little more quickly, no matter the size of the bankroll -- and even if that decision comes up infrequently. Just because the decision is not frequent, and the cost of making the wrong decision is small, does not seem to me to justify playing a hand incorrectly.
All this is academic in my case; I play games where my EV AFTER TAXES (I don't file as a professional gambler) is probably terrible, I have NOT learned all the penalty card variations for precisely correct play, and I probably make enough occasional mistakes that my errors are more important -- but even with all that, why give up a nickel intentionally when you know better?
2.2. Re: Proper hold JOB 3 card royal vs. 4 card flush?????
Posted by: "Bob Dancer"
bobdancervp@hotmail.com bobdancerlasvegas
Date: Mon Sep 29, 2014 1:43 pm ((PDT))
Norma wrote: Holding the four clubs: EV = 1.2766
Holding 3 to the royal: EV = 1.2868
You would have to play an awful lot of hands for that small difference to matter.
When
the EV is this close, relative volatility is more important than EV. I
don't know how Winpoker computes, but it seems obvious that drawing one
card to a flush is way less volatile than going for the royal. It's a
matter of bankroll survival.
Ignoring small possible contributions by a high pair:
Probabilities:
One card flush draw: 9/47
Two card royal draw: (2/47)(1/46)
Ratio: 207:1 in favor of the one card draw to a flush.
Your conclusion is defensible, maybe, but the way you got there was questionable.
The difference between the plays is about 5 cents for the 5-coin dollar player. Or 1 cent for the quarter player. Or $5 for the $100 player. Multiply those numbers accordingly if you're playing Triple Play, Five Play, etc. Whether that's a lot or a little can be argued. On a personal basis, a 5 cent error for dollar 5-coin players is HUGE. I suppose you could say I play "an awful lot of hands"
You're comparing the frequency of a flush (worth 30 coins) with the frequency of a royal flush (worth 4,000 coins). You are looking at how often something happens rather than how much it pays. Even if you accept that as reasonable methodology, why do you count the number of 30-coin flushes when you're drawing one card and not count the number of 30-coin flushes and 20-coin straights when you're drawing two cards? Instead of 1-out-of-1081 chances to get a royal from AKT, you get 51-chances-out-of-1081 to get a royal, flush, or straight. Big difference.
I'm not sure why you neglect high pairs. You get a high pair from AKT about 22% of the time. You get a high pair from AKT4 less than 13% of the time,which is slightly more than half as often. I know a high pair is small compared to a flush, but not nearly as much smaller as a flush is to a royal flush.
When it comes down to how often do you get ANYTHING POSITIVE from the two draws, it's 30% of the time from AKT and 32% of the time from AKT4. While these numbers aren't identical, they are nowhere near as different as the 207-1 ratio you cited in your post.
Bankroll preservation is an essential part of intelligent gambling --- which is your main point, and you're correct in this. But if you're regularly making safety plays this large, you have no chance to be playing a positive game no matter how large the slot club is.
Bob
