"Mikvet88" wrote: So my question is, "Does this affect the house edge when playing this game"? I know the house edge is 3.51%. I would think that it does but I am just not sure!

Michael

Yes, it would raise the house edge by approximately 0.11%. It sounds like this was one of the alternate pay tables, not the standard ones used in the United States casinos. U.S. casinos typically pay 1000 to 1 for a Royal.

The casinos that only pay 500 to 1 for a Royal have a house edge of either 3.43 or 3.74 depending on the pay out on the other hands.

[pre]House edge 3.43% 3.74%

Royal Flush 500 500
Straight Flush 100 200
Four of a kind 25 50
Full House 15 11
Flush 10 8
Straight 5 5
Three of a kind 3 3
Two pair 2 2
Tens or better 1 1[/pre]

Hey Skinny,
What about the fact that they don’t even pay the 500 – 1 because of the $20,000 maximum payout? I know the house edge is figured on winning verses losing a particular hand. This guy WON the hand! So being that they are shorting him $17,500, does THAT chenge the house edge?

Michael

"Mikvet88" wrote: Hey Skinny,
What about the fact that they don’t even pay the 500 – 1 because of the $20,000 maximum payout? I know the house edge is figured on winning verses losing a particular hand. This guy WON the hand! So being that they are shorting him $17,500, does THAT chenge the house edge?

Michael

Yes Michael, it does change the house edge. I mentioned above that it RAISES the house edge by approximately 0.11%. I then showed you 2 pay tables that are used that have a house edge of 3.43% or 3.74% if the top payout were 500 – 1.

When they short the player because of the maximum pay out of $20,000, it effectively reduces the pay out for a Royal Flush from 500 – 1 to 266.67 – 1. That increases the house edge to 3.54% or 3.85% depending on which of the 2 pay tables I showed were being used in that game.

For those interested in the calculations involved here is the math:

[pre]Hand Pays Bet Win Combinations Probability Return
Royal Flush 500 3 1500 80 0.000002 0.002309
Royal Flush 266.67 3 800 80 0.000002 0.001231[/pre]

The difference in the expected return is 0.2309% – 0.1231% = 0.1078%.
That rounds to a 0.11% increase in the house edge.

The pay outs on the other hands are not reduced in value since they are all less than 266.67 – 1. So the expected return for all other pay outs remain the same. But because the pay out for a Royal is reduced the expected value or return for that hand is lower and the house edge is increased accordingly.

I know a 0.11% house edge does not seem like a lot because it is only around 3% of the total house edge. But that is because the Royal Flush only contributes a little over 6% to the total house edge. When you cut the return almost in half by reducing the pay out from $37,500 to $20,000, you reduce the contribution to the house edge accordingly. You reduce that contribution from 6% of the total house edge to around 3% of the house edge and it only adds about 3% to the house edge. They are not impacting the other 95+% pay outs for the other hands by their limit on the maximum pay out. So that 95+% of the house edge does not change.

Does this help you understand the answer to your question or have I made it more confusing? 🙂

Actually it now makes perfect sense. I didnt think about the fact that it would indeed only raise the house edge on the Royal because all other hands would fall in less then the $20,000. However, I am assuming that that would change if you raised your bets so the payout on a smaller hand would put you over the $20,000. Thank you for the response.

Michael

PS: I am so vastly impressed with your knowledge and configurations. When writing my original post, I was hoping that you would have responded.

"Mikvet88" wrote: However, I am assuming that that would change if you raised your bets so the payout on a smaller hand would put you over the $20,000. Thank you for the response.

You are welcome and your assumption is correct. I can not take all the credit for the data. I use Michael Shackleford’s website (wizardofodds.com) to get the initial data. Then I do my own calculations to adjust it for the specific question asked.

"Skinny" wrote: I can not take all the credit for the data. I use Michael Shackleford’s website (wizardofodds.com) to get the initial data. Then I do my own calculations to adjust it for the specific question asked.

Skinny is not only a great guy, but modest as well.

And he’s not even paying me to say that… 😉

😎 😎 😎

Sure he’s not 😉