Temptations from getting 4-card royal on video poker

I was playing video poker this past week when dealt a 5-card Flush right off of the deal. Good news, right? Well, it was also a 4-card Royal.
Still good news, right? After all, either I keep the Flush and take my money or I go for the Royal.
The only move is to go for the Royal if the expected value (EV) of a 4-card Royal is more than the expected value of the Flush. It’s not even close. The 4-card Royal has a whopping 18-plus EV while the Flush is only 6. Of course, the problem is I would be throwing away a sure winner for a possible winner.
If I recall correctly, it was actually an open ended 4-card Royal (10 thru King). This means the suited Ace is the big winner. A suited 9 would be a nice winner. There would be six other cards that could make a Flush and six more to make a Straight.
Then there are nine more that would at least give me a High Pair so I could at least push my wager. That’s a total of 21 of 47 cards that result in a winning hand, albeit all but two would be for no more than my original Flush.
Needless to say, I wound up drawing a 5 of some suit I didn’t care the least bit about. That said, if faced with the same situation again, I would make the same decision.
There are times we need to throw away sure winners in order to go for an even bigger winner. The decision is not based on gut feel or instinct, but rather, completely on the mathematics of the situation. In the case I faced this week, I had a 1-in-47 chance of winning the big prize.
Since the big prize was a whopping $800, it would have been the right choice even if it were the only possible winner. Other times, it is the impact of the opportunity to still win smaller prizes that makes the decision what it is.
That said, it is not a good idea to simply always chase the bigger prize. If dealt a Straight or a Flush that is also a 4-card Straight Flush, we do not break up our sure winner. Yes, the Straight Flush pays 50 and we still have many opportunities to catch a Straight or a Flush, but it simply is not enough to make it worth throwing away a sure winner.
However, if you are dealt a 4-card Straight Flush (even inside) that is also a High Pair, we do throw away this sure winner. Because the hand being thrown away pays only 1, the opportunity to win 50 is enough to compel us to make this decision, but only because we will also have numerous other opportunities to draw a Straight or a Flush.
These types of decisions are among the hardest a player has to make at video poker. When I say hardest, I don’t mean the learning, but rather decisions that can be somewhat painful.
Do you keep the Low Pair of the 4-card Straight? Well, both are losing hands if you do nothing. Both require some luck on the draw to become winners. Yes, there are times when it appears you made the wrong decision because the card drawn will be one that helped the choice not made. But, you’re not really giving up anything to make this decision.
You put in your initial wager and if nothing is done, the hand is a loser. So, you make your decision (hopefully one based on expected value) and not drawing a winning hand, well, you didn’t lose anymore than your original wager.
When you have to discard a sure winner to go for a hand that is only a 30% winner, but offers the opportunity for bigger wins, it is almost like wagering a second time. And, in a manner of speaking, you are.
The moment you are dealt a Flush on the deal, those units won are yours. You can press the five Hold buttons and take that money. When deciding to discard one of those cards, you are really wagering everything you would’ve won if staying pat in the hopes of an even bigger prize.
It is not an easy decision, but one that needs to be made correctly. Not to downplay the importance of always making the right decision, but if you are dealt 9-9-10-J-Q, the difference between the Low Pair and the 4-card Straight with 2 High Cards is a mere 0.01 of Expected Value. The difference between a Flush and a 4-card Royal is more than 12.
Playing this one wrong would be like playing 1,200 4-card Straights over the Low Pair. The goal, as always is to make the right choice based on the hand that has the higher Expected Value. This is why a player would not discard a Straight Flush to go for a 4-card Royal.
The hard decision is not to simply chase the highest possible single payout.

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