Are you holding the best cards? Don’t be so sure
Often times video poker players are dealt hands in which one of the holds is so tempting they just cannot resist. For example, suppose you are playing Jacks or Better and are dealt the following hand. How would you play it?
I would venture to guess that most players would shun the guaranteed 20-coin payout for the ﬁve- card straight (with ﬁve coins wagered), and instead, hold the tempting four-card straight ﬂush with the much greater potential 250-coin payout. However, that would be a big mistake. Even though the straight ﬂush pays a lot, it still isn’t enough to break up the paying straight. Here’s the proof.
When you hold the four-card straight ﬂush, the possible outcomes (and probability of occurrence) are as listed in Table 1.
If you multiply the probability of each outcome by its corresponding payout and sum each result, you arrive at an average payout (or Expected Value, abbreviated EV) of 17.23, meaning on average, your ﬁve-coin wager will get you a payout of 17.23 coins. Sometimes you will get lucky and hit the straight ﬂush and win 250 coins but other times you could wind up with only a ﬂush, straight, or worse, no payout. The average payout, however, will be 17.23 coins and that, dear readers, is less than the guaranteed 20 coins you will win if you hold the paying straight. Therefore, you should always hold the paying straight over the four-card straight ﬂush.
Does the above example imply that you should never discard a winning hand when you play video poker? No it doesn’t. Look at the following hands and decide how you would play them.
Your choice in the ﬁrst hand is to hold either the high pair (Qs) or the four-card straight ﬂush with a gap (8-9-10-Q). Most players opt for the sure thing and hold the two high cards with a calculated EV of 7.68. If instead, you break the high pair and hold the four-card straight ﬂush (8-9-10-Q), the EV is 11.91. The choice of which hold is better is clear. Over time, you will win 4.23 coins more, on average, if you hold the four-card straight ﬂush (even with a gap) over the paying high pair.
The second hand contains a ﬁve-card ﬂush with a guaranteed 30-coin payout. However, it also contains a four-card royal ﬂush. The EV of the latter is a whopping 97.76. Therefore, it would be a big mistake to take the sure ﬁve-card ﬂush over the four-card royal ﬂush. The correct play is to break the paying ﬂush and hold the four-card royal ﬂush.
I know holding the paying ﬂush is very tempting but look at it this way. Even though most of the time you will not hit the royal, the one time you do will more than make up for your losses. (Be patient when you play video poker.)
Here’s another tempting hold. Suppose you are dealt the following hand:
The temptation here is to hold the three-card straight ﬂush over the low pair. Again, that would be a mistake because the EV for holding the 4-5-6 is only 3 03 whereas the EV for holding the low pair is 4.12.
The bottom line is this: Don’t be tempted into making one hold over another because one payout is higher (or lower) than the other. The only way to know which hold is best is to learn the basic playing strategy for whatever video poker game you like to play. With a basic strategy table (or card), the holds are usually ranked from highest EV to lowest. You don’t have to memorize EVs or know how to calculate them. Just pick the hold that has the highest ranking (highest up in the table) and you will automatically be making the play with a greater EV. It’s that simple.
The only two holds that trump a high pair in a non-wild card game is a four-card royal ﬂush and a four-card straight ﬂush (with or without gaps). Against any other non-paying possible holds, you should hold the high pair. Likewise, the only time you would break a paying ﬂush or straight is when you hold a four-card royal ﬂush (but not against a four-card straight ﬂush, the better hold here is the high pair).