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Poker Keno

Introduction



Poker Keno is a simple, poker-based game available at the Sky Vegas Internet casino. The player makes a bet and is dealt seven cards, Texas Hold 'Em style. He wins if he has at least a pair of jacks. I'm not sure what it has to do with keno, other than perhaps because there is no actual skill required. It's entirely a game of luck.

Rules

  1. The player bets from 20p to £50.
  2. The player is dealt two hole cards and five community cards.
  3. The player is paid based on the poker value of the best five of the seven cards, according to the pay table below.
  4. If the player bet at least £2, then he will be eligible to win a progressive jackpot if he has the ace and king of hearts as his hole cards and completes a royal flush on the board.

Following is the pay table. All wins are on a "for one" basis.

Pay Table

Hand Pays
Royal flush 250
Straight flush 100
Four of a kind 20
Full house 7
Flush 5
Straight 3
Three of a kind 2
Two pair 1
Pairs of jacks or better 0.5
All other 0


Analysis

The following table shows the probability and return of each possible outcome, before considering the jackpot bonus. The lower right cell shows a return of 94.07%. In other words, a house edge of 5.93%.

Return Table

Hand Pays Combinations Probability Return
Royal flush 250 4,324 0.000032 0.008080
Straight flush 100 37,260 0.000279 0.027851
Four of a kind 20 224,848 0.001681 0.033613
Full house 7 3,473,184 0.025961 0.181727
Flush 5 4,047,644 0.030255 0.151275
Straight 3 6,180,020 0.046194 0.138581
Three of a kind 2 6,461,620 0.048299 0.096597
Two pair 1 31,433,400 0.234955 0.234955
Pairs of jacks or better 0.5 18,188,280 0.135952 0.067976
All other 0 63,733,980 0.476393 0.000000
Total 133,784,560 1.000000 0.940656


The optimal bet size is £2, because you qualify for the jackpot, while minimizing your expected loss in the base game. At a £2 bet, the return goes up by 1.92% for every £100,000 in the meter. The break-even point (exactly zero house edge) is at a meter of £308,463.07 for £2 bet.