What’s a bird in the hand worth?

Nov 7, 2005 1:11 AM

Imagine a new twist to the game of blackjack. Every time you are dealt a blackjack, you have the option to accept a third card. If it’s a 10 or face card you win. If it’s an ace, you win even more. If it’s anything else, you lose your original wager and the winnings from your blackjack. Any takers?

Hopefully, you’ve been reading my columns long enough now to know that you couldn’t answer that question until you know the payouts for winning. There is only one game I can think of where this type of situation actually occurs. The game is video poker.

The hands do not occur very often, but they do occur. If you’re dealt a straight, that contains a 4-card straight flush, or a 3-card royal, what should you do? Ditto for a flush.

Or perhaps you are dealt two pair or a full house that contain aces in a Double Double Bonus game. What is the right play?

Expert strategy dictates that these decisions should be made based on which play has the highest expected value (EV). These situations are no different. At the same time, I can understand why some people find it hard to follow the math at these times.

If you’re playing max-coin quarters, you’re essentially betting $1.25 per hand. If you’re dealt a flush, you’re going to have $7.50 returned to you. If that flush contains a 4-card royal, you now have a decision to make.

Keep the $7.50, or wager the $7.50 for a chance for the big payout of a royal. Along the way, you might draw another flush, or a straight or a high pair. None of which will increase your original win and many that will actually decrease it.

Depending on your point of view, you may have felt at that point that you ”˜lost’ money. The other problem is that you are in effect wagering $7.50 on the turn of a single card. The average $1.25 player is not ready to move up to that level, even if for one hand. Imagine if a blackjack player who was learning a card counting system, all of a sudden got to a point where the system told him to increase his bet from $5 to $30. He might hesitate a bit.

So, in the end, what should a player do? Basically, I go with the math in almost all cases. The only exception I might consider is a case where the two possibilities are very close and one is much more volatile than the other.

For example, in Double Bonus Poker, if you are dealt a full house with three aces, the full house has an EV of 10. The three aces have an EV of 10.11 (given that you are throwing the pair away). Expert strategy says play the three aces.

However, I won’t scold someone too hard for not doing so. At the point you are dealt the full house, you’re guaranteed to be paid back $10. I can understand if someone decides not to take on the additional risk for the long-term opportunity of making $10.11 instead. Personally, I would go for the quad aces.

The key to this decision is knowing the facts behind the decision. By holding the full house, you will be costing yourself some money in the long run. You will also be reducing the volatility of your results by going with the money that is already won, rather than risking it for a little more in the long run.

There are other situations where the decision is not even close. In the example given earlier, if dealt a flush that contains a 4-card royal, we should always go for the 4-card rRoyal. The EV of the flush is a constant 6, whereas the EV of the 4-card royal is about 18, and will depend slightly on the exact makeup of the hand. Keep in mind that about 15% of your 4-card royals will be flushes, which means by not playing them correctly, you will be reducing the number of foyals you can expect to see. This will greatly lower your chances of winning in the long run.