vpFREE2 Forums

An unusual hand

#1

I ran into something interesting while playing "reduced pay deuces wild" with the following payoff table (to 1, with 5 coins in):

RF: 800
4D: 200
WR: 25
5K: 15
SF: 9
4K: 4
FH: 4
FL: 3
ST: 2
3K: 1

Dealt: 2S, 2C, JS, JD, 10S

It turns out that the E.V. of 4.9362 is identical for discarding either the 10S or the JD!

This is so surprising that I made a hand calculation:

Discarding the 10S:
4 cards will give a 5K, and 43 cards a 4K
(4*15 + 43*4) / 47 = 232/47 = 4.9362

Discarding the JD:
5 cards will get a WR; 3 for a SF; 6 for a 4K; 4 for a FL;
18 for a ST; and 12 for a 3K
(5*25 + 3*9 + 5*4 + 4*3 + 18*2 + 12*1) / 47 = 232/47 = 4.9362

Question: Is there any "volatility" issue here that would decide the better discard?

Or is this really a flat-ass tie?

(As it happened, I discarded the JD and drew a deuce for the wild royal.)

Note: For the "full pay" deuces wild payout schedule, there is no tie.
Discard the 10: EV = 5.8511
Discard the JD: EV = 4.9574

- - Norma

#2

Since it pays more if it doesn't improve, I'd keep the 4 of a kind.
I'm too lazy to do the math, but I'm confident that it's the lower
volatility play. For the same reason, also without having ever done
the math, I keep an inside straight draw over 3 to a straight flush
with 2 gaps and a straight penalty in FPDW. I've always disagreed
with WinPoker's summation of the frequencies of ending hands in full
pay Kings or Better Joker's Wild, since, with a certain hand in which
an ace and a joker is against J9s and a joker (the other card has to
be a 6 that's suited with the ace), the EVs are identical but it has
the player keep the straight flush draw, whereas, for the sake of
lower volatility, I'd keep the pair of aces. There's one Deuces Wild
game in which the royal draw is better for the hand that you
mentioned, but I can't remember what it is.

···

I ran into something interesting while playing "reduced pay deuces wild" with the following payoff table (to 1, with 5 coins in):

RF: 800
4D: 200
WR: 25
5K: 15
SF: 9
4K: 4
FH: 4
FL: 3
ST: 2
3K: 1

Dealt: 2S, 2C, JS, JD, 10S

It turns out that the E.V. of 4.9362 is identical for discarding either the 10S or the JD!

This is so surprising that I made a hand calculation:

Discarding the 10S:
4 cards will give a 5K, and 43 cards a 4K
(4*15 + 43*4) / 47 = 232/47 = 4.9362

Discarding the JD:
5 cards will get a WR; 3 for a SF; 6 for a 4K; 4 for a FL;
18 for a ST; and 12 for a 3K
(5*25 + 3*9 + 5*4 + 4*3 + 18*2 + 12*1) / 47 = 232/47 = 4.9362

Question: Is there any "volatility" issue here that would decide the better discard?

Or is this really a flat-ass tie?

(As it happened, I discarded the JD and drew a deuce for the wild royal.)

Note: For the "full pay" deuces wild payout schedule, there is no tie.
Discard the 10: EV = 5.8511
Discard the JD: EV = 4.9574

- - Norma

#3

I tend to agree.

There are some situations where volatility is more important that EV. Particularly when there is only a slight difference in EV between two choices.

A good FPDW example is a 3-deuce 5-of-a kind hand. There is a slight difference in EV, depending on whether the pair is higher than 9 or not. But (for the same reasoning you give) the volatility is lower if you just keep the hand as dealt, rather than going for the four deuces.

Though I have to admit that I grit my teeth when I do that.

- - Norma

···

--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:

Since it pays more if it doesn't improve, I'd keep the 4 of a kind.
I'm too lazy to do the math, but I'm confident that it's the lower
volatility play. For the same reason, also without having ever done
the math, I keep an inside straight draw over 3 to a straight flush
with 2 gaps and a straight penalty in FPDW. I've always disagreed
with WinPoker's summation of the frequencies of ending hands in full
pay Kings or Better Joker's Wild, since, with a certain hand in which
an ace and a joker is against J9s and a joker (the other card has to
be a 6 that's suited with the ace), the EVs are identical but it has
the player keep the straight flush draw, whereas, for the sake of
lower volatility, I'd keep the pair of aces. There's one Deuces Wild
game in which the royal draw is better for the hand that you
mentioned, but I can't remember what it is.

>I ran into something interesting while playing "reduced pay deuces wild" with the following payoff table (to 1, with 5 coins in):
>
>RF: 800
>4D: 200
>WR: 25
>5K: 15
>SF: 9
>4K: 4
>FH: 4
>FL: 3
>ST: 2
>3K: 1
>
>Dealt: 2S, 2C, JS, JD, 10S
>
>It turns out that the E.V. of 4.9362 is identical for discarding either the 10S or the JD!
>
>This is so surprising that I made a hand calculation:
>
>Discarding the 10S:
>4 cards will give a 5K, and 43 cards a 4K
>(4*15 + 43*4) / 47 = 232/47 = 4.9362
>
>Discarding the JD:
>5 cards will get a WR; 3 for a SF; 6 for a 4K; 4 for a FL;
>18 for a ST; and 12 for a 3K
>(5*25 + 3*9 + 5*4 + 4*3 + 18*2 + 12*1) / 47 = 232/47 = 4.9362
>
>Question: Is there any "volatility" issue here that would decide the better discard?
>
>Or is this really a flat-ass tie?
>
>(As it happened, I discarded the JD and drew a deuce for the wild royal.)
>
>Note: For the "full pay" deuces wild payout schedule, there is no tie.
>Discard the 10: EV = 5.8511
>Discard the JD: EV = 4.9574
>
>- - Norma
>

#4

Since it pays more if it doesn't improve, I'd keep the 4 of a kind.
I'm too lazy to do the math, but I'm confident that it's the lower
volatility play.

Completely agree.

There's one Deuces Wild game in which the royal draw is better for the hand that you mentioned, but I can't remember what it is.

APDW, which makes sense, with the straight flush paying 11 instead of 9.

EE

···

--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:

#5