Doubling up and heaving shingles

Some video poker games, Guy, allow you a double up or double-or-nothing bonus option on a winning hand. Activated by your pressing the "Yes" button after a win, the game then deals one card face up for the dealer and four cards face-down for the player. The player then chooses one of the face-down cards. If this card beats the dealer's, the player wins double the amount previously won, along with the option to try to double op again.

Like the odds bet in craps, the double up wager is one of the few casino bets offered that doesn't have a house edge. You have a fifty-fifty chance of winning any given bet (ties excluded) regardless of the amount wagered or the results of prior bets.

Most machines limit the number of double-ups to five times. How many times you should double up depends on the pay table and your risk tolerance level. Only you, Guy, know how much you are willing to bet on the turn of a card. If your goal is to achieve the highest expected return the machine can offer by lowering the overall house edge with the double-up feature, then you should double up the maximum number of times allowed.

Three caveats though, Guy: Many casinos do not allow you to use your slot club card and chase down cash points on double-up bets. Also, watch your double-up winnings so that you don't go over the $1,200 threshold and end up being handed a W-2G. Finally, because playing video poker is typically a negative expectation game, when saying yes to the double or nothing feature, you increase the total money wagered, but at no cost to that expected loss, thus lowering the overall house edge. But if you are playing a video poker machine that has a 100% plus return pay table, I would recommend against the double-up bet, since it will lower your overall advantage.

Dear Mark,
My brother bet me 10,000 to one for $10 that I would never duplicate what he was dealt naturally on a video poker machine, a natural royal flush in hearts. He believes it would never happen in my lifetime figuring it seldom happens and most players need to draw cards to get royal flush. I figure it's worth $10. What do you think? Charlie G.

With a 52-card deck there are 2,598,960 possible hands, and what you're asking for is that one of them to be dealt straight away, in hearts no less. Those, Charlie, are long, tall odds. And what about all that time and money spent chasing down a natural royal flush in hearts? Well, here's the barnyard math.

Leaving aside the fact that you know damn well that bro's never going to pay you the $100,000 anyway . . . at a buck and a quarter a pop, and a house edge of let's say 4% — I'm guessing you won't play every hand perfectly — you'll end up losing $129,948 to win $100,000. Plus, playing three hands a minute, it could take you over 600 days playing 24/7 before a natural royal flush in hearts appears. But why be extreme? Using ordinary 8-hour days, it would take just under 5 years to play out the bet (no time off for wedding anniversaries, holidays, sick leave, birthdays or any of that foolishness), and even then it's not guaranteed, you know, just because the odds say it's likely. Hmmm. In the same period, the kid that flips burgers, mows lawns and heaves shingles would reel in a cool $147,000. Again, Hmmm.

And yet your brother's proposition isn't even close to being as impenetrable as the one a reader previously wrote in about: a casino offering a poker machine with a payout of $1,000,000 for a sequential royal flush.

For an ascending royal flush in any suit, the odds are 77,968,800. If it is suit specific, such as being in hearts, then the chances are one in 311,875,200.

Sorry, Charlie, I'd pass on both.

Gambling Wisdom of the Week: "The commonest mistake in history is underestimating your opponent; happens at the poker table all the time." --General David Shoup