I agree with Albert that the overall cost is extremely small when individual cost is small and the play is rare.
We're talking about the specific 3-card RF of Ace, Ten, with a J, Q or K.
When we have that hand in JOB, holding the 4th flush card costs 1% of our bet. (5 cents on a $5 bet.) How often do we get the hand?
I think we get that hand about 0.1% of the time. (my calc is shown below)
So, by keeping the 4th flush card, we will lower our EV by 1% of 0.1% of our total bets. For every $1 million we bet, we give up $10 in EV by holding the 4th flush card.
How did I get the 0.1% figure? I'm going to take the time to write it out because (1) if I've done it correctly, it may help someone do similar calc's, and (2) if I'm wrong, I want to know where!
So, here goes: How many ways are there to get a hand with A, T, another RF card, and a 4th suited card?
Say I want to know the chance of getting 5 cards in this order:
Ace, Ten, otherRFcard, other suited card, other non-suited card
Card Ways Why
Ace 4 4 suits to choose from
Ten 1 has to be same suit
OtherRF card 3 can be J, Q, or K of same suit
4th flush card 8 can only be 2-9, same suit
5th card 27 can be 2-10 of any different suit
To get the total number of ways to deal out a hand in that order, you multiply the "Ways". 4 * 1 * 3 * 8 * 27 = 2592
But we don't care what order the cards are in, so we have to figure out how many ways the 5 cards can be ordered.
There are 5 ways to pick which card will be 1st, 4 ways to pick the 2nd card, 3 ways to pick the 3rd card, 2 ways to pick the 4th card, and just 1 way to pick the 5th card. Multiplying 5*4*3*2*1 makes 120 ways to order the five different cards.
So, the total number of ways to be dealt a hand with A,T,(J,Q,or K), small suited, and small non-suited is 2592 * 120 = 311,040.
That seems like a lot, but it's a small fraction of the 52 * 51 * 50 * 49 * 48 ways to deal out ANY five cards. That number is 311,875,200.
Therefore, the chance of being dealt a 3-card RF with A,T with a 4th small (2-9) flush card and a small (2-10) non-suited card is 311,040 / 311,875,200.= 0.1%
And the total cost of holding the 4th flush card on that hand is 1% of 0.1% = 0.001% of your total bet.
I'm not endorsing holding the 4th flush card as a general play in JOB. As "5-card" mentioned, the cost is much bigger on other 3-card RF's. The Ace/Ten 3-card RF's are only a small fraction of the total times you might have a 3-card RF with a 4th flush card.
--Dunbar
---In vpFREE@yahoogroups.com, <ehpee@...> wrote :
I think that the one factor that both of you are missing is the frequency of the situation.
On average how often does this situation come up ?
I'm guessing it's not too often.
If I am correct then the whole argument is akin to discussing how many angels can dance on the head of a pin.
Worrying about losing 5 cents on a play is not really that important when the play happens once a day, but it is very important if it happens 20 times an hour.
A.P.
From: "Bob Dancer bobdancervp@... [vpFREE]" <vpFREE@yahoogroups.com>
To: "vpfree@yahoogroups.com" <vpfree@yahoogroups.com>
Sent: Monday, September 29, 2014 4:43 PM
Subject: RE: [vpFREE] Re: Proper hold JOB 3 card royal vs. 4 card flush?????
To: "vpfree@yahoogroups.com" <vpfree@yahoogroups.com>
Sent: Monday, September 29, 2014 4:43 PM
Subject: RE: [vpFREE] Re: Proper hold JOB 3 card royal vs. 4 card flush?????
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.
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
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
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