Ask the Slot Expert: Answer to last week's puzzler

Last week I described a decision I had to make while playing video poker. I had very good free play offers at a casino and I was using it playing Triple Illinois Deuces Wild with a separate progressive for a royal on each hand and another progressive for being dealt a royal or drawing to three royals.

Even though drawing to three royals is a long shot, I've seen it happen. I was at Gold Coast with a friend. One of her friends came to her and said that we wouldn't believe what had happened. She was playing Triple Play and held a 4-card royal. She drew the card she needed to complete the royal on all three hands. She had a picture on her phone to prove it. The probability of that happening is (1/47)(1/47)(1/47) or 9.63e-6 or 0.00000963. It's good to remember that unlikely, even extremely unlikely, does not mean impossible.

My plan was to play until my expected loss equaled the free play I had used. It was not a point multiplier day and the cashback from video poker play is minimal at this casino, so I just ignored the cashback.

I was getting close to my loss limit for the day before I had reached my point goal. I was dealt this hand 2 ♣ 5 ♣ 5 ♠ 7 ♠ 9 ♠. Should I hold the three-of-a-kind and be guaranteed at least one more hand? Or should I hold the 4-card double inside straight flush and hope for the best and risk winning nothing?

I said that I decided to make the right play for NSU and held the 4-card straight flush.

I also said that there is an aspect to this situation that makes the whole conundrum moot and challenged you to find it. There was a hint in the prior paragraph.

That aspect is that I followed the strategy for NSU but I wasn't playing NSU. The play with the higher EV for Illinois Deuces is to hold the three-of-a-kind. Illinois Deuces reduces the payout on a straight flush from 10 to 9. The EV for the three-of-a-kind is 1.878816 and the EV for the 4-card double inside straight flush is 1.829787. There was no conundrum had I known the strategy for Illinois Deuces.

Why didn't I learn the differences between the NSU and the Illinois strategies? Three reasons. First, I'm going to play far, far more NSU than Illinois. I didn't want to take a chance that I would accidentally make an Illinois play at NSU. Second, the difference between the EVs of the Illinois strategy and using the NSU strategy on the Illinois paytable is likely very small. Three, a corollary to the first reason, my sample size is going to be so small that luck is going to have a far greater effect on my results than a few strategy mistakes.

There's something else that would have made last week's column very different. I still would have had the choice between a pat hand and the chance at a better hand, but the hands would have been different.

I looked at the column idea notes I take while playing and saw my note about this situation. My actual choice was between a straight and a 4-card outside straight flush (e.g., 2 ♣ 5 ♣ 6 ♠ 7 ♠ 8 ♠).

The play with the highest EV for both paytables is to hold the 4-card outside straight flush.

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

Update: I haven't pursued getting more non-smoking areas in the current Nevada state legislative session for a few reasons. First, there is so much uncertainty about what is going to come out of Washington, Nevada's state legislators are concerned with dealing with that fallout. Second, though it changes day to day, the trend seems to be that it is getting more likely that there will be some sort of economic slowdown ahead. The last thing we need is for casinos to create more non-smoking areas and then have casino revenues fall and then have them blame the non-smoking areas for the downturn. The possibility of economic troubles may also make them reluctant to change regulations at this time. Third, I don't know whether the current governor would support the legislation.

Let's continue collecting signatures for when the Nevada State Legislature meets again in two years, when I hope the climate will be more favorable for getting the measure introduced and passed.

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