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Joined: Jun 17, 2011
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February 25th, 2017 at 12:43:26 AM permalink
Bad advice for Three Card Poker
I had always assumed it was better to play the Ante/Raise part of 3CP rather than the Pair+ or Prime. This was because the quoted House Edge on various casino pamphlets was 2% for the base game and 2.7% for Pair+. I had naively assumed it cost less to make a £2 game bet than the £2 Pair+ until a few days ago.

Introduction to High Card Poker
There’s a new game (High Card Poker) appearing in Southampton in a few weeks’ time. It is similar to 3CP - one deck, Ante and Raise principle - except hand rankings are the Blackjack total of the three cards. Then if the player has a pair that total is doubled, or if the player has trips it is tripled.

The dealer qualifies with 20, it seems the player strategy is to call with 21 or more. There are various bonuses paid for totals of 61 (1/1) up to the maximum of 99 (25/1).

Analysis and Simulation results
I’ve been looking at the game and worked out the "House Edge" at about 3.33% (based on the initial Ante bet). My initial assumption was this game was much worse than 3CP, but to confirm my calculations I ran some simulations and, since it was fairly easy, added logic to play 3CP.
3CP Play Q64+ = 3.36%; Play blind = 7.56%.
HCP Play 21+ = 3.34%; Play blind = 11.59%

"House Edge"
Thus it seems the cost to the player of 3CP and HCP is almost identical (which in hindsight is probably how the bonus pay-table has been set).

Also https://wizardofodds.com/games/three-card-poker/ quotes 3.37%

Which is correct?
There's an alternative measure called "Element Of Risk" which takes into account that on average the player will make more than 1 bet (divides the expected loss per game by the expected number of bets). This is where the 2% comes from.

My view is that if a player is using the quoted "House Edge" to decide which game or side bet costs less to play, then the measure should be based on {one of} the initial bet{s}.

Thus do you think the pamphlets (or description at http://www.ukcasinotablegames.info/poker.html ) are misleading?

Many thanks
Joined: Oct 14, 2009
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February 25th, 2017 at 6:28:54 AM permalink
Yes, I think it is misleading. The house edge is correctly defined as the ratio of the expected loss to the initial wager.
It's not whether you win or lose; it's whether or not you had a good bet.

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