A shuffle through the gambling mailbag

16 August 2012

By John Grochowski

Question: You say that with a strategy that’s not difficult to learn, I should get a 99% return on 9/6 Jacks or Better quarter machines, at $1.25 per hand. You are saying that for the $110,000.00 I bet last year, I should have got a return of $109,450, a loss of only $550. Last year I lost almost $5,000, a return of 55%.

I guess I played 88,000 hands. Obviously I didn’t hit one royal flush and I’m not very lucky, but I consider myself a very smart card player and very good with numbers and odds. The only way I get close to the 99.5% return is if I hit 4.5 royal flushes.

Answer. Your arithmetic is off. For a return of 55% and losses of 45% on $110,000 worth of wagers, you’d have had to lose $49,500 -- nearly $50,000, not nearly $5,000.

A $5,000 loss is 4.5% of the money you wagered. For you, the return was 95.5%. Part of that is attributable to not having drawn a royal flush. Given expert play in 9/6 Jacks or Better, royals occur an average of once per 40,391 hands. For your amount of play, the average expectation is two royals, but it’s within normal probability to draw one or none, just as it’s within normal probability to draw three, four or even more.

Royals make up about 2% of the overall return on 9/6 Jacks or Better, so in any period without a royal your expectation is about 2% lower than that 99.5% return to experts.

The other 2% of your shortfall could just be random fluctuation, but it also could indicate strategy shortcomings. Even good card players sometimes miss in translating their knowledge to the video game. In video poker, you’re not necessarily looking for the draw that wins most often. You have to balance it against the draw that wins the most money.

Sometimes video poker strategy is counter-intuitive. Dealt ace of clubs, king of hearts, jack of spades and a couple of unsuited low cards, what do you hold? I see many players holding ace-king-jack, but the best play in 9/6 Jacks or Better is to hold just king-jack. We win 38% of the time when we hold all three high cards and only 37.3% when we hold just two, but we get more bigger winners, more three-of-a-kinds and full houses, when we stick to king-jack. The average return per five coins wagered is just over 2.4 coins on king-jack, and just under 2.3 on ace-king-jack.

Do you notice when you have an inside draw with three cards to a straight flush? Dealt 4-7-8 of hearts with a 3 of diamonds and a 10 of spades, holding 4-7-8 will lose 89% of the time. But the potential for a 250-coin payoff on a straight flush raises the average return to 2.23 coins per five wagered, and that beats the 1.80 for tossing all five cards.

Players who think they know cards and odds should not assume they know how that translates to video poker. A good book such as Linda Boyd’s The Video Poker Edge and practice time on software such as Video Poker for Winners, WinPoker or Frugal Video Poker can get you up to speed.