What's the value of this hand?

What's the EV ($$) of the following hand? Flush pays 5. Don't care about future multipliers or nothing like that.

I'm getting 18.319149 from WOO hand analyzer. Multiply that by $0.25 [how much you're betting on paytable], multipy by 9 [since you have 3 1x's and 2 3x's]. Getting $41.218?

If you're like me, you'll completely brick it! :-)~

Why not do it with the multipliers, it's more fun =)...

I'm going to assume you're playing 5 coins, so your flush pays "25" and your straight pays "20"... 9/5. From the hand you have you can make a pairs (A-Q-J), a regular straight, a flush, a royal flush, or you could brick =P. I'll do the math for them in that order... The total ER is the summation of each individual hands ER, since they are in fact separate draws from separate decks.

Hands Explained: 9/48 times you hit a high pair and win 25 cents (5*.5). 3/48 times you hit a straight and win $1 (20*.5). 8/48 times you hit a regular flush and win $1.25 (25*.5). 1 out of 48 times you'll hit a royal flush and win $200 (4000*.5). Lastly, 27/48 times you'll hit a brick and win 0, losing your total 25 cent wager on that hand.

Hand 1: (9/48)*(.25) + (3/48)*(1) + (8/48)*(1.25) + (1/48)*(200) + (27/48)*(-1) = .047 + .063 + 4.167 - .563 = 3.714, or a 371.4% ER.
Hand 2: [(9/48)*(.25) + (3/48)*(1) + (8/48)*(1.25) + (1/48)*(200) + (27/48)*(-1)] * 3 = [.047 + .063 + 4.167 - .563] * 3 = [3.714] * 3 = 11.142, or a 1,114.2% ER.
Hand 3: [(9/48)*(.25) + (3/48)*(1) + (8/48)*(1.25) + (1/48)*(200) + (27/48)*(-1)] * 3 = [.047 + .063 + 4.167 - .563] * 3 = [3.714] * 3 = 11.142, or a 1,114.2% ER.
Hand 4: (9/48)*(.25) + (3/48)*(1) + (8/48)*(1.25) + (1/48)*(200) + (27/48)*(-1) = .047 + .063 + 4.167 - .563 = 3.714, or a 371.4% ER.
Hand 5: (9/48)*(.25) + (3/48)*(1) + (8/48)*(1.25) + (1/48)*(200) + (27/48)*(-1) = .047 + .063 + 4.167 - .563 = 3.714, or a 371.4% ER.

Assuming your investment on each hand was 5 coins of 5 cents, then you have a total investment on each hand of 25 cents.

Hand 1 ER = .25 * 3.714 = .93
Hand 2 ER = .25 * 11.142 = 2.785
Hand 3 ER = .25 * 11.142 = 2.785
Hand 4 ER = .25 * 3.714 = .93
Hand 4 ER = .25 * 3.714 = .93

Thus, for your total investment of $1.25, your expected return was approximately $8.36... a 668.8% Expected Return. I think your "multiply by 9" is incorrect.

For the love of all that you hold dear show us the final picture! From you requesting the math... I fear the worse. Like someone getting outdrawn in poker going "What are the odds?!?!" =p

Quote: Mission146

It depends on what card you threw away.

Dammit, I stand corrected by Mission. This should be information you know and can be accounted for. However my analysis should be very close.

Quote: Romes

Dammit, I stand corrected by Mission. This should be information you know and can be accounted for. However my analysis should be very close.

I deleted my post after I noticed the card, your analysis is close to correct as the OP did not throw away a winning hand. The only thing is you must divide by 47 in all of your equations, not 48.

Dividing by 47 in all will increase the value a bit as paying hands become more likely, as a result.

UPDATED assuming the 10s was thrown away....

Quote: Mission146

I deleted my post after I noticed the card, your analysis is close to correct as the OP did not throw away a winning hand. The only thing is you must divide by 47 in all of your equations, not 48...

Yep, already on it =).

Hand 1: (9/47)*(.25) + (3/47)*(1) + (8/47)*(1.25) + (1/47)*(200) + (27/47)*(-1) = .048 + .064 + 4.255 - .575 = 3.792, or a 379.2% ER.

Hand 2: [(9/47)*(.25) + (3/47)*(1) + (8/47)*(1.25) + (1/47)*(200) + (27/47)*(-1)]*3 = [.048 + .064 + 4.255 - .575]*3 = [3.792]*3 = 11.376, or a 1,137.6% ER.

Hand 3: [(9/47)*(.25) + (3/47)*(1) + (8/47)*(1.25) + (1/47)*(200) + (27/47)*(-1)]*3 = [.048 + .064 + 4.255 - .575]*3 = [3.792]*3 = 11.376, or a 1,137.6% ER.

Hand 4: (9/47)*(.25) + (3/47)*(1) + (8/47)*(1.25) + (1/47)*(200) + (27/47)*(-1) = .048 + .064 + 4.255 - .575 = 3.792, or a 379.2% ER.
Hand 5: (9/47)*(.25) + (3/47)*(1) + (8/47)*(1.25) + (1/47)*(200) + (27/47)*(-1) = .048 + .064 + 4.255 - .575 = 3.792, or a 379.2% ER.

Assuming your investment on each hand was 5 coins of 5 cents, then you have a total investment on each hand of 25 cents.

Hand 1 ER = .25 * 3.792 = .95
Hand 2 ER = .25 * 11.376 = 2.844
Hand 3 ER = .25 * 11.376 = 2.844
Hand 4 ER = .25 * 3.792 = .95
Hand 4 ER = .25 * 3.792 = .95

Thus, for your total investment of $1.25, your expected return was approximately $8.54... a 683.2% Expected Return.

To clarify things from the Wiz's hand calculator:

According to the hand analyzer... your ER throwing the 10 away is 18.319 units per hand... The math should be:

Hand 1: (18.319)*(.05) = .92
Hand 2: [(18.319)*(.05)]*3 = 2.75
Hand 3: [(18.319)*(.05)]*3 = 2.75
Hand 4: (18.319)*(.05) = .92
Hand 5: (18.319)*(.05) = .92

Given that your "unit" is a nickle... this would still give you an ER of $8.26 on your $1.25 total bet, about a 660.8% ER. Slightly off, but only just barely. I believe my above analysis is more exact. I'm showing a 19 unit expected return (per hand, before multipliers).

...NOW TELL US WHAT HAPPENED! lol

Quote: Romes

...NOW TELL US WHAT HAPPENED! lol

With a picture!!

I'd bid it up to 50 just for the immediate opportunity factor and the thrill if all filled. Results please, we're waiting patiently and Romes worked his ass off.