Do Video Poker Full House and Flush Payoffs Really Matter?

18 October 2004

By Alan Krigman

Are the gambling gurus right? The ones who are always blathering about the importance of finding the machines and table games with the smallest house advantage. And, boring everyone within earshot about learning and following the statistically optimum rules when there are strategy options. Or, is it purely a question of luck?

Think about jacks-or-better video poker. Many casino aficionados have heard that these games can be ranked by the payoffs for full houses and flushes. Assuming otherwise standard schedules with no bonuses, 9-6 payoffs (9-for-1 on full houses and 6-for-1 on flushes) yield 99.5 percent return, at 8-6 it's 98.3 percent, and 8-5 translates into 97.3 percent. But do these distinctions really matter to solid citizens who take occasional shots with moderate bankrolls during sessions of reasonable duration?

Of course, what really matters to one person is inconsequential to the next. So you'll have to decide for yourself. But you can gain some insights to help do so by considering what a series of computer simulations reveals about the three alternatives.

Each simulation involved 2,500 subjects. Players were dealt identical cards and all followed expert strategy, betting the maximum of five coins per hand on 9-6, 8-6, and 8-5 25-cent machines. Sessions ended if they depleted their bankrolls, hit a jackpot with a royal, or completed specified numbers of rounds corresponding to typical time spans for fast-fingered players. Three different situations were examined: a) $200 bankrolls and 1,800 hands (three hours); b) $200 bankrolls and 2,400 hands (four hours); c) $100 bankrolls and 1,800 hands (three hours).

It doesn't take a Nikolai Ivanovitch Lobatchevskii to deduce that, with other factors being equal for each situation, higher payouts for identical poker results are preferable to the converse. The extra income should keep bettors bumping the buttons longer if worse comes to worst, cost them less when luck is bad but not fatal, snatch wins from the jaws of losses under relatively neutral conditions, earn more during serendipitous sessions, and even lead to jackpots on bets that couldn't have been made were a bankroll exhausted prematurely.

But, are these effects significant enough to warrant ferreting out the looser games -- and, by implication -- learning and following expert strategy? The accompanying tables show the fractions of players who went belly-up prematurely, broke even or earned at least some money, and hit the jackpot in 9-6, 8-6, and 8-5 games under the stated session conditions. Envision these fractions as the probabilities of the various outcomes, and factor the findings into your planning.

Three-Hour Session, $200 Bankroll

	9-6	8-6	8-5
bust	11.60%	16.24%	22.36%
even or win	32.32%	24.12%	18.32%
hit jackpot	4.28%	4.20%	4.16%

Four-Hour Session, $200 Bankroll

	9-6	8-6	8-5
bust	23.24%	32.24%	40.92%
even or win	29.64%	21.20%	14.92%
hit jackpot	5.04%	4.92%	4.80%

Three-Hour Session, $100 Bankroll

	9-6	8-6	8-5
bust	49.88%	59.00%	67.92%
even or win	29.52%	21.20%	15.40%
hit jackpot	3.40%	3.24%	2.88%

Data for busts as well as break evens or wins diverge sharply based solely on full house and flush payoffs. The percentages for jackpots seem, at first glance, not to vary much. However, this is a consequence of the chances of royals being small in any event. A clearer picture is provided by the actual numbers of jackpots in high-return games corresponding to wipe-outs in the others. In the three-hour/$200 simulation, 107 players hit the big time at 9-6; of these, two coincided with folks who took a fall on 8-6 machines and three who bit the dust on 8-5. For the four-hour/$200 and three-hour/$100 cases, the respective numbers were 126 9-6 jackpots with three 8-6 and six 8-5 crashes, and 85 jackpots with four 8-6 and 13 8-5 routs. Results reflected by the remarkable rhetoric of the renown rhymer, Sumner A Ingmark:

It shows good sense that someone strives,
To be there when good luck arrives.