Ask the Slot Expert: Do slot clubs count your entire bet on Double Down Stud?

Question: I play video poker in Atlantic City. Borgata mostly. I play Double Down Stud where you can double down your first bet if you like the cards you see.

My question is: Does the casino count both the initial 5-credit bet AND the double down credits towards your player card rewards? Or just the initial bet?

Answer: Double Down Stud is the easiest video poker game to play. You don't have to make any complicated decisions about which combination of cards to hold.

The machine deals four cards to you. Then you have to make your yes/no decision. Do you want to double your bet? After you hit the appropriate button, the machine displays your fifth card and pays your winning hand according to the paytable (Yippee!) or displays Game Over (Wah. Wah.)

In addition to being easy to play, it's also easy to analyze. I first published an article about it over 20 years ago.

If you never double down, I calculated that your payback is 72.5%. If you always doubled down, your payback soars(?) to 72.6%. Clearly, strategically doubling down is the way to go. Your payback following the expert strategy is 97.8%. (Paytable is 6s or Better.)

The expert strategy is about as simple as they come:

• all pat hands
• four to a royal flush
• four to a straight flush
• four to a flush
• all outside straights

We can even simplify the strategy down to three lines because four to a flush includes four to a royal flush and four to a straight flush.

Some strategies include another line. They say to double down on unsuited JQKA.

This hand is dealer's choice -- well, player's choice, actually. The Expected Value is the same whether you double down or not.

Let's consider the possible outcomes for unsuited JQKA. There are 4 tens that will give us a straight, and 3 each of aces, kings, queens and jacks that will give us a high pair (a pair of jacks or better).

Using the 6s or Better paytable, a straight pays 6 coins per coin bet, a high pair 2, and a nothing hand nothing.

To recap, there are 4 ways to get a straight, 12 a high pair, and the remaining 32 cards nothing. (Remember that 4 cards have already been dealt, so 4+12+32+4=52. The machine is drawing our fifth card from remaining 48.)

Let's calculate the EV of not doubling down. Payoffs are based on a 5-coin bet.

(4/48)30 + (12/48)10 + (32/48)0 = 5

Now let's calculate the EV for doubling down. The payoff for the straight isn't 10*6, 60. We have to take into account the extra bet we made and subtract it from the payoff. We get paid a net of 55 coins for the straight, 15 for the high pair and lose 5 coins when we get bupkis.

(4/48)55 + (12/48)15 + (32/48)(-5) = 5

Let me do the math in each term so you can see how we end up in the same place regardless of whether we double down.

No double: 2.5 + 2.5 = 5

Double: 4.583 + 3.75 - 3.333 = 8.333 - 3.333 = 5

When we double down, the times we lose wipes out what we gained from the times when we win. The EV for doubling and not doubling are the same. There is 0 house edge on this hand. In the long run, it doesn't matter what we do.

In this column and others I wrote about Double Down Stud, I recommended against doubling on unsuited JQKA because doing so won't improve your long-term results, but will increase your volatility.

Let me finally answer your question and amend that advice.

The casino will give you slot club points based on your entire bet, not just the initial bet. You can verify this by watching your points earned increase -- assuming Borgata's slot club display shows points earned and not just "ACCEPTED", like Atlantic City's slot clubs did decades ago.

The double-down bet is not like the true odds bets in craps, where the house has no edge and therefore doesn't usually use those bets in rating you.

The double-down bet is more like betting full coin in draw poker or an a slot machine. The player actually has the advantage on the last coin played -- the long-term payback is higher when playing full coin -- but the slot club still gives you points for betting it.

My new advice: Double down on unsuited JQKA if you don't mind a little extra volatility. It won't cost you anything in the long run and you'll earn more points.

If you would like to see more non-smoking areas on slot floors in Las Vegas, please sign my petition on change.org.