# Discount Gambling

## High Card Flush

Posted in +EV, collusion by stephenhow on April 22, 2013

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:

High Card Flush Advanced Strategy (6 Player Hands Seen)
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

Posted in collusion by stephenhow on April 19, 2013

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%.

Optimal Outcomes for Phil’Em Up Poker
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%.