High Card Flush
A couple of readers have asked about Galaxy Gaming’s new High Card Flush game, which has a few placements now, and may be picking up some steam. The game is pretty simple, where each player and the dealer receive 7 cards. Each hand is measured by its highest flush, where a flush is first ranked by its length (number of cards of same suit), then by its card values. Each player must Ante before the hand, then wagers a 1x-3x Play bet (depending on flush size), or folds. The dealer qualifies with a three-card, 9-high flush. If the dealer doesn’t qualify, the Play bets push, and the remaining Antes are paid even-money. If the dealer qualifies, the Ante and Play bets receive even-money action against the dealer hand.
As you would expect, collusion helps in this game. A Monte Carlo analysis shows that with 6 confederates, perfect knowledge of the dealt cards gives each spot at least a +7.3% edge over the house. But practically, you’d be lucky if you could even communicate the suit counts (number of cards of each suit) dealt. If you figure out a non-suspicious way of doing this, then the following simple strategy yields a +3.1% edge over the house:
| Flush Size | Play Bet |
|---|---|
| 1 or 2 cards | 1x for suit counts (9, 11, 11, 11) or (10, 10, 11, 11), else fold others |
| 3 card, Jack-high or lower | 1x for suit counts (9, 11, 11, 11) or (10, 10, 11, 11), else fold others |
| 3 card, Queen-high | 1x if lowest suit count is 9 or higher, else fold. |
| 3 card, King-high or better | 1x if lowest suit count is 8 or higher, else fold. |
| 4 cards | 1x |
| 5 cards | 2x |
| 6 or 7 cards | 3x |
where the suit counts 4-tuple is the sorted number of cards of each suit.
Phil’Em Up Poker
When I playing Mississippi Stud in Vegas last week, I overheard someone mention a game called Phil’Em Up Poker. I looked at the game, to see if collusion would yield an edge. The rules are pretty simple. The game is played with a 52-card deck plus a Joker which may be used for Aces, straights, and flushes. Each player bets an Ante, and receives two hole cards. Two community cards are dealt face up. Each player may either make an additional 1x bet (i.e., “double-up” his action), or check, before the 3rd community card is exposed. If a player makes a pair of Tens or better, he wins according to a paytable. There is no dealer hand. The house edge is a reasonable 3.3%.
| Hand | Bet | Combinations | Probability | Payout | Return |
|---|---|---|---|---|---|
| FIVE_ACES | 2 | 5 | 0.00000035 | 1000 | 0.000697 |
| natural ROYAL_FLUSH | 2 | 20 | 0.00000139 | 250 | 0.000697 |
| wild ROYAL_FLUSH | 2 | 100 | 0.00000697 | 100 | 0.001394 |
| natural STRAIGHT_FLUSH | 2 | 180 | 0.00001254 | 50 | 0.001254 |
| wild STRAIGHT_FLUSH | 2 | 720 | 0.00005018 | 25 | 0.002509 |
| FOUR_OF_A_KIND | 2 | 4,140 | 0.00028853 | 20 | 0.011541 |
| FULL_HOUSE | 2 | 21,840 | 0.00152212 | 15 | 0.045664 |
| FLUSH | 2 | 39,020 | 0.00271946 | 9 | 0.048950 |
| STRAIGHT | 2 | 77,460 | 0.00539850 | 7 | 0.075579 |
| THREE_OF_A_KIND | 2 | 211,200 | 0.01471939 | 3 | 0.088316 |
| TWO_PAIRS | 2 | 365,640 | 0.02548294 | 2 | 0.101932 |
| High Pair | 2 | 1,562,112 | 0.10886993 | 1 | 0.217740 |
| Low Pair | 2 | 75,648 | 0.00527222 | -1 | -0.010544 |
| HIGH_CARD | 2 | 339,708 | 0.02367563 | -1 | -0.047351 |
| STRAIGHT | 1 | 25,200 | 0.00175629 | 7 | 0.012294 |
| THREE_OF_A_KIND | 1 | 105,600 | 0.00735969 | 3 | 0.022079 |
| TWO_PAIRS | 1 | 327,360 | 0.02281505 | 2 | 0.045630 |
| High Pair | 1 | 922,608 | 0.06430030 | 1 | 0.064300 |
| Low Pair | 1 | 3,514,752 | 0.24495734 | -1 | -0.244957 |
| HIGH_CARD | 1 | 6,755,112 | 0.47079118 | -1 | -0.470791 |
| total | 14,348,425 | -0.033067 | |||
| expected | 14,348,425 |
Collusion doesn’t help. That’s because only 3.8% of hands are bet on a draw only. Collusion will change few decisions, and result in little gain. With 7-player collusion, perfect play will only reduce the house edge to 3.2%.
Discount Gambling 
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