Dumb Video Poker Question

This is probably going to sound like a really stupid question but I was looking at the strategies for various video poker games on the Wizard of Odds site and other places and most of the strategies place a dealt Straight Flush higher on the strategy than 4 to a Royal Flush. If you were dealt same suit KQJ109 you'd have a 1/47 chance to draw to a Royal if you throw out the 9, but the strategy has you take the dealt straight flush. Wouldn't the large difference in payout between the straight flush and royal justify not keeping the dealt straight flush. I trust the strategy but I guess I just wanted to understand the math. Any help appreciated.

If my math is correct, going for the royal is worth $93.08 cents on a $1 machine ($5/pull, royal is $4000).

1/47 * 4000 for a royal
3/47 * 20 for a strqight (ace)
3/47 * 20 for a straight (9)
7/47 * 30 for a flush
12/47 * 5 for a high pair

Holding a dealt SF is worth $250.


That being said, there are times when it might be better to go for the royal, like in a VP tournament. Or if you're playing a $5 machine and you're trying to avoid w2gs. Hitting for $1250 with a w2g isnt what you want. But getting a w2g from a $20k payout ain't all that bad

Quote: M4Goober

This is probably going to sound like a really stupid question but I was looking at the strategies for various video poker games on the Wizard of Odds site and other places and most of the strategies place a dealt Straight Flush higher on the strategy than 4 to a Royal Flush. If you were dealt same suit KQJ109 you'd have a 1/47 chance to draw to a Royal if you throw out the 9, but the strategy has you take the dealt straight flush. Wouldn't the large difference in payout between the straight flush and royal justify not keeping the dealt straight flush. I trust the strategy but I guess I just wanted to understand the math. Any help appreciated.

To make it simple, playing a 9/6 JOB, a Straight Flush is usually worth 250 coins playing 5 coins bet. Drawing at the RF is worth 93.53 coins playing 5 coins bet.

Quote: M4Goober

This is probably going to sound like a really stupid question but I was looking at the strategies for various video poker games on the Wizard of Odds site and other places and most of the strategies place a dealt Straight Flush higher on the strategy than 4 to a Royal Flush. If you were dealt same suit KQJ109 you'd have a 1/47 chance to draw to a Royal if you throw out the 9, but the strategy has you take the dealt straight flush. Wouldn't the large difference in payout between the straight flush and royal justify not keeping the dealt straight flush. I trust the strategy but I guess I just wanted to understand the math. Any help appreciated.

If you have a straight flush in JoB it pays 50x your bet. A 4-card Royal is worth about 19x your bet. In this example you keep the straight flush. But if you're playing Deuces Wild where a straight flush pays only 9x your bet you go for the 4-card royal.

Thanks for the responses guys. That clarifies things a bit. My calculations of the return for the Royal were way off. This makes sense. So the whole strategy is calculated by taking every possible hand and calculating the return if you hold 1, 2, 3, 4, or 5 cards and which cards you hold, and using those returns to decide which cards are better to hold. Makes sense. Thanks

Quote: M4Goober

Thanks for the responses guys. That clarifies things a bit. My calculations of the return for the Royal were way off. This makes sense. So the whole strategy is calculated by taking every possible hand and calculating the return if you hold 1, 2, 3, 4, or 5 cards and which cards you hold, and using those returns to decide which cards are better to hold. Makes sense. Thanks

Yes. This maximizes the EV without regard to variance.

Quote: M4Goober

most of the strategies place a dealt Straight Flush higher on the strategy than 4 to a Royal Flush. If you were dealt same suit KQJ109 you'd have a 1/47 chance to draw to a Royal if you throw out the 9, but the strategy has you take the dealt straight flush. Wouldn't the large difference in payout between the straight flush and royal justify not keeping the dealt straight flush.

Yes, the royal flush gives you a very high payout. But the straigt flush does also. To make the draw the right choice, you would need a *47* times larger payout on the RF than the SF (without considering backdoor draws). Usually you have something like 10-20.