What's good about multi-hand poker machines, and what's dangerous

Picture a nothing-wild (jacks-or-better) video poker game, in which you start by receiving a low pair. Assuming you're not so wet behind the ears as to hold some kind of "kicker," you'll keep the pair and draw three new cards. Your chances of improving to a winning hand, and the returns you'll receive at a machine with a typical payoff schedule, are as shown in the accompanying table.

Improvements to a low pair by drawing three cards at jacks-or-better video poker

improved hand	probability	return
two pairs	16.00%	2
three of a kind	11.40%	3
full house	1.02%	8
four of a kind	0.28%	25
any improvement	28.70%	--

You're an underdog when you draw to a low pair, despite its seeming promise. In fact, the expected value per dollar of your bet has dropped from the 95 to 98 cents it was before you hit the "deal" button, depending on payoffs for finishes you can't reach starting with a pair, to 81.36 cents with the returns indicated.

That's an 81.36 percent return rate, or the complementary 18.64 percent house edge. You'd be slightly better off at a "full-pay" machine, where a full house returned nine rather than eight units. Chance of improving would still be 28.70 percent but the return rate would rise a bit to 82.38 percent and the house's edge would slip to 17.62 percent. In contrast, on a full-pay machine, your pre-deal bet had an expected value over 99 cents.

What would happen if you played a game with the same paybacks, on a multiple-hand poker machine? Consider five hands as an example.

Here's how multiple-hand machines work, in case you haven't tried them. The initial deal and your hold decision apply uniformly across all hands. After you make your choice, however, each hand gets dealt new cards independently from its own deck.

The edge doesn't change. As long as you bet the same total amount per round, for instance five coins on a one-hand machine or one coin per line on a five, the casino will average the same commission from your action over an extended period either way.

One thing you'll notice is that your hit rate will go up. Even if some hits return fewer coins than you bet, for instance because one hand finished with two pairs and the other four were duds.

With 28.70 percent chance of improving the low pair to a winner on each hand, the chance of a hit on a five-hand game – whether it's a net win or loss – is 81.57 percent. Higher hit rates increase the fun of gambling sessions, profitable or not. More frequent hits add to the excitement of the casino experience, making most solid citizens happier. And the bosses don't have to give away anything to provide the extra measure of pleasure.

Net losses will occur with no hits (down five units), two pairs on one hand and nothing on the others (down two), and triplets on one hand and nothing on the others (down one). One or another of these conditions will ensue on the average of 53.8 percent of all rounds. The remain¬ing 46.7 percent of all rounds will yield net wins. There will be no pushes where five units in get five back.

The 46.7 percent likelihood of a net winning round with five hands compares well with the 28.7 percent probability of a score on one hand. Of course, the greater win rate in the five-hand game means when a hit does occur it will tend to be lower. And, for the same total bet per round, more frequent but smaller net returns buy you longer sessions for your bankrolls.

Wouldn't life be hunkydory if every silver lining didn't have a cloud? The problem here is that five coins in single-hand machines qualify players for bonus jackpots. But one coin per hand in a five-hand game may not. So the bait to bet the max on a multi-hand machine is, if not compel¬ling, then certainly great. For, as the minstrel of the machines, Sumner A Ingmark, mused:

While many gamblers start with good intentions, too few resist seductive interventions.