Uth: EoR if Flush pays 2:1? and a Progressive question

1) Normally flush pays 3:2 for the Blind bet.
If it paid 2:1, the HE is 0.9%.
(Edit: https://wizardofvegas.com/forum/questions-and-answers/gambling/36944-math-of-ultimate-texas-holdem/#post841494 )
What is the element of risk?

2) Progressive: Flop flush or better with 1st 3 cards + your 2 cards
$1 pays flush $100, full house $150, quads $200
(Don't remember straight flush or royal)
What's the house edge?

3) What if Flush pays 3:2 but Royal only pays 100x?
What's the HE?
Edit:
For every 100 the effective payout on a royal goes down, the house edge will go up by 0.308%?

So if the royal payout is $20k instead of $50k then 30k/100 x .308% is 92% lower???
Obviously wrong.
Help with math?

1). How do you get the HE of 0.9%? Flush occurs 3.03% of the hands, so the player EV gain is 3.03%x0.5=1.515%; therefore, the new HE is 2.185%-1.515%=0.67%.

2). Usually, $1 pays flush $40, full house $50, quads $300.

Quote: aceside

1). How do you get the HE of 0.9%? Flush occurs 3.03% of the hands, so the player EV gain is 3.03%x0.5=1.515%; therefore, the new HE is 2.185%-1.515%=0.67%.

2). Usually, $1 pays flush $40, full house $50, quads $300.
link to original post

0.9% HE:
https://wizardofvegas.com/forum/questions-and-answers/gambling/36944-math-of-ultimate-texas-holdem/#post841494

So I should play the $1 Progressive if $100/150/200?

I’d like to get a third opinion on this 0.9% HE number.

The payout numbers of yours are ridiculous high. Of course.

Quote: aceside

I’d like to get a third opinion on this 0.9% HE number.

The payout numbers of yours are ridiculous high. Of course.
link to original post

A Flush is the outcome on 2.5715% of hands (excluding straight flush and royal flush which don't have a change in payout.)
With an increased payout of 0.5 on a flush hand, the incremental player EV is 1.2857%.

The standard UTH EV is 2.185% with perfect strategy. Thus, the new value of house edge with this payout change on flushes is 2.185% - 1.2857% = 0.899222%

Source: UTH Math on increased payout on flushes See in particular the post by charliepatrick

I see the problem with my calculation. The 3.03% is the total flush hands, while the 2.572% is the player winning flush hands. Thank you.

Quote: aceside

I see the problem with my calculation. The 3.03% is the total flush hands, while the 2.572% is the player winning flush hands. Thank you.
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You asked a very intelligent question and I spent a lot of time sweating blood while evaluating everything. here was my explanation before you figured it out yourself.

First, the values in the Wikipedia Poker Probabilities article are correct. The methodology in Wikipedia is poorly documented but I derived the flush probability using my own methods of combination math and I confirm that the 5-card flush combinations with seven cards are 4047664 and the flush probability is 3.0255% - in agreement with Wikipedia.

The Wizard's numbers in the WOO UTH table also appear to be correct. His numbers are the number of player flushes that beat the dealer's hand and receive a payout.

a) The WOO UTH table does not call out instances in which player has a flush but dealer's hole cards include one or two suited cards that allow dealer to make a higher flush than player (or a straight/Royal flush). Those instances are lumped into lines on the WOO UTH table labeled 'Dealer Wins" without calling out what hands the player lost with.

b) Further, there are instances in which the five common cards are all suited (making a flush) and neither the player nor dealer can improve the flush on the board with a card of that suit in their hole cards. So these are when the player has a flush but it is also the identical flush that dealer has. These instances are lumped into rows on the WOO UTH table that are labeled 'Push" without calling out the kind of hand that player had.

The bottom-line: you've been ignoring those instances in which player has made a flush but either loses or pushes. The HE is indeed approximately 0.9% given the rule change on the payout of a winning flush (2:1 rather than 3:2).

EDIT: pwned by aceside.

Quote: 100xOdds

3) What if Flush pays 3:2 but Royal only pays 100x?
What's the HE?

A Royal occurs 0.0032% of the time and normally pays 500:1. If you change the payout to 100:1, the change of house edge is roughly 0.0032%x400=1.28%. Here I assume a player Royal always wins, but this is not the case. I’ve encountered royals within the community five cards several times. The probability of a Royal on the five community cards is 0.000154%. This is as rare as a lifetime event.

Quote: aceside

Quote: 100xOdds

3) What if Flush pays 3:2 but Royal only pays 100x?
What's the HE?

A Royal occurs 0.0032% of the time and normally pays 500:1. If you change the payout to 100:1, the change of house edge is roughly 0.0032%x400=1.28%. Here I assume a player Royal always wins, but this is not the case. I’ve encountered royals within the community five cards several times. The probability of a Royal on the five community cards is 0.000154%. This is as rare as a lifetime event.
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Wow.. house edge goes up 1.28% , almost 50% more.

Community Royal happened to me a couple years ago.
Let's see if I can find my pic.

Quote: gordonm888

Quote: aceside

I’d like to get a third opinion on this 0.9% HE number.

The payout numbers of yours are ridiculous high. Of course.
link to original post

A Flush is the outcome on 2.5715% of hands (excluding straight flush and royal flush which don't have a change in payout.)
With an increased payout of 0.5 on a flush hand, the incremental player EV is 1.2857%.

The standard UTH EV is 2.185% with perfect strategy. Thus, the new value of house edge with this payout change on flushes is 2.185% - 1.2857% = 0.899222%

Source: UTH Math on increased payout on flushes See in particular the post by charliepatrick
link to original post

Hmm..The HE is based on just the ante bet.
If ante+blind, then the HE is only .45%? :o

This is perfectly correct.