morpheus74
morpheus74
Joined: May 17, 2012
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October 28th, 2020 at 9:38:04 AM permalink
HI,

I usually play blackjack and Ultimate Texas Holdem, my favorite game now. It is said that its house edge (2.5% per ante, approx) is good, It seems to be so but I have doubts.

In blackjack, across hundreds of rounds I can get several naturals, doubling and spliting many times, surrender and so on. Everything required to calculate the house edge is there, happening frequently. Same for roulette, baccarat and craps.

But in poker games with high jackpots, as Royal Flush in Ultimate Texas Hold'em, I need to play 33000 rounds as an average to get one Royal Flush. So, for me playing in the casino, it is like royal flush does not exist. The same goes for Straight Flush, I could say.

But when calculating house edge, these two ranking hands and their payouts have been considered.

Is this reliable? Of course I know house edge is a theoretical value, but for practical purposes, and in order to compare it to other games, would be a better idea to remove Royal flush and maybe Straight flush? The house edge would increase, but closer to the real world.

Does it makes any sense?

Sorry for my english.

Many thanks.
gordonm888
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gordonm888
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October 28th, 2020 at 12:53:37 PM permalink
Player Expected Value, or EV, is an incredibly useful metric for a casino game. Note: a house edge of 2.5% means that the player has an EV of 97.5% or 0.975.

But, I agree with you. EV or house edge is not the only thing that counts for most gamblers.

There are APs (advantage Players) who chase the occasional progressive jackpot that has gotten so high that it makes the overall game a +EV game for gamblers. These APs talk about the "cycle" for the progressive jackpot: i.e., if its a 1 in 100,000 event that pays out the large jackpot then the cycle length for the jackpot is 100,000 bets.

What you have pointed out is that the cycle length for the Royal Flush payout in UTH is about 33,000 rounds. The royal flush represents (I think) almost 1.5% of the return on your UTH bet, so for any given session when you are playing only a few dozen hands it feels like the House Edge is more like 4% than 2.5% - because you are very unlikely to get a royal flush in the short term/

Some metrics that address this (sort of) are "variance" and "risk of ruin." "Risk of Ruin" refers to a situation where your bankroll for gambling on a given night or vacation is limited (as it is for almost all of us) and if your bet size is 1/m of your bankroll and you play for n rounds (and n>>m), then there is a risk of wiping out your bankroll. That risk of ruin is higher for a game like UTH whenever you play much fewer than, say, 1,000 rounds because some of your statistical "return" is tied up in a 1/33000 event -an event that will infrequently occur during a normal betting session.

Of course, in the long-term you will expect to hit some of those royal flushes - but only if there is a long-term!

So, I commend you for your thoughtful analysis of the game. And you are correct - I wish we had a standard metric that addressed this kind of concern. Because anyone buying a lottery ticket is very likely to experience a very low return (or zero return) on the purchase while someone placing a bet on BJ or on a sports team has a much higher chance of making a one-time profit.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
Commish
Commish
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October 28th, 2020 at 3:15:14 PM permalink
Although rare they do happen. In my first 5 years of playing I saw 15 royal flushes and none were mine. Now after 11 years I have seen 30 and 3 were mine. On the better side odds wise I have had 78 straight flushes. Except for this year I do play a lot!
Vegasrider
Vegasrider
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October 28th, 2020 at 7:15:21 PM permalink
In UTH, you only have to hold one card to get paid on the RF. Has that been factored in? Iíve hit two RF in UTH, both within a month or two.
morpheus74
morpheus74
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October 29th, 2020 at 10:51:27 AM permalink
You are right..... I only count the blind bet, not the trips bet. And the blind bet does not pay on pushes, so if the royal flush is on the table, the player does not win the blind.

And my numbers are for all RF, so it is even worse.....I have to track the number of RFs as you say, beating the dealer.

I will do it soon, I work as software developer and as hobby, I develop simulation software, I'm finishing now he one for UTC. My aim is also to develop strategies based on modify the basic strategy depend on whether you can see other player cards.

Many thanks for your comment, veru useful.
morpheus74
morpheus74
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October 29th, 2020 at 10:57:43 AM permalink
Thanks so much. I will do that analysis, in order to get the actual house edge without Royal Flush and SFlush. And also, as counting only the winner Royal flushes, since if the RF is on the table, I loss the blind payout.

I think the same problem happens with Video Poker, the Royal Flush is such a rare play that the actual edge will be worse than 0.5 for Jacks or Better (sorry, I'm more used to house edge than Player Expected Value, in the end both are the same concept, just the way around).
Commish
Commish
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October 29th, 2020 at 1:36:04 PM permalink
Having seen 30 RF I have never seen one on the board. Since it does happen I do not understand why you would not factor it in any analysis.
CharmedQuark
CharmedQuark
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October 29th, 2020 at 2:39:49 PM permalink
<<<--Is this reliable? Of course I know house edge is a theoretical value, but for practical purposes, and in order to compare it to other games, would be a better idea to remove Royal flush and maybe Straight flush? The house edge would increase, but closer to the real world.-->>

I did this over 5 years ago on another thread. Included removing Quads and I believe one other hand. The house edge came out to over 7%.
gordonm888
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gordonm888
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Thanks for this post from:
morpheus74
October 29th, 2020 at 3:55:29 PM permalink
Quote: CharmedQuark

<<<--Is this reliable? Of course I know house edge is a theoretical value, but for practical purposes, and in order to compare it to other games, would be a better idea to remove Royal flush and maybe Straight flush? The house edge would increase, but closer to the real world.-->>

I did this over 5 years ago on another thread. Included removing Quads and I believe one other hand. The house edge came out to over 7%.



Okay, UTH HE = approx 2.2%. UTH without Royal Flush has HE = 3.7% approximate.

So, if your typical session is 100 bets:

99.7% of the time, you sessions will have an EV of 0.963 (or HE = 3.7%)

In 0.3% of your sessions you will make a royal flush and will have an EV of approximately 6.00. That is, you will have an expected return (on average) of 600 bet units during your 100 round session in which you initially wager 1 bet unit.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.

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