Which is the Better Game?

A gambler friend, Al, and I were on the phone talking about something related to vitamin supplements, and then he said he had a video poker question that he was embarrassed to ask me.

“Go ahead,” I prompted. “If it’s too awkward, I just won’t answer.”

He told me it wasn’t particularly awkward; it was just about a quarter game he found in Mississippi. He normally plays for higher stakes and was embarrassed to let me know that sometimes he went “slumming,” to use his term.

There was a five-coin progressive that was attached to each of several games. The loosest game was pseudo NSU Deuces Wild (which he called Airport Deuces), namely the 15-9-4-4-3 version that returns 98.91% at reset. I’ll refer to this game as pNSU DW. The other game was the 8-5 Bonus Poker game with the 30-for-1 payout on all quads that returns 98.48% at reset. This game I’ll call 8-5-30 BP.

The royal was at $2,250, which is 9,000 coins when you’re playing for quarters. The reason he was asking about it is that the Deuces Wild game has a higher royal cycle, namely 43,432 hands versus 40,169 at reset for the Bonus Poker game.

Since Al was only going to play this game for a couple of hours, to kill time really while he waited for another gambling opportunity to open up in the same casino, he wanted to know if I would ever give up EV to go for the royal with the shorter cycle?

“Okay,” I told him. “It’s not too awkward. Especially if I can get a column out of it too!”

The first thing to consider is that Mississippi has a non-refundable 3% tax on W-2Gs. This tax would amount to $67.50 if he hit the royal right away. It would be larger if the progressive grew before he hit it. I realize I should use 9,000 coins to figure out the strategy and 8,730 coins to determine the return after the non-refundable tax. But for today, I’m just going to use the 9,000 figure. 

The second thing was that the return of the games and royal cycles at 4,000 coins is considerably different than it is at 9,000 coins. Consider the following chart:

4,000-coin Royal 9,000-coin Royal
Return  Cycle  Return Cycle
pNSU DW 98.91% 43,122 101.46% 37,319
8-5-30 BP 98.48% 40,169 101.38% 32,516

There are several things to notice here. First, the returns on the games at the 9,000-coin level are now quite similar. When the royal increases just a little more, the 8-5-30 BP game will actually return more than the pNSU DW game. 

Second, the royal cycle for 8-5-30 BP is decreased by 7,650 as the royal amount goes from 4,000 to 9,000 and the pNSU DW royal cycle over the same change in royal amounts is changed by ‘only’ 5,800. The reason for this difference is that in Deuces Wild variations, you still generally hold on to all dealt deuces, no matter how high the royal gets. (The one exception is four natural cards to the royal along with one deuce.)

So, to answer Al’s question as to which game I would play, my first answer is, “Neither of them.” Depending on how fast you play, these games are only worth $10 to $15 an hour, with significant variance. I would not take the time to learn a brand-new strategy, and the adjustments necessary when the royal went up eventually to 9,500 coins or 10,000 (which it might, but probably not while he was playing if he was only going to play for an hour or two) for that little money. 

Players with small bankrolls who would normally consider a $10-per-hour to $15-per-hour game quite acceptable should realize that a very large percentage of the return is in the royal flush, and if you’re not the one who hits the royal (which is the most likely result in a few hours of play) you’re going to be taking a big loss. Plus, in addition to the 3% state tax, you’re going to be getting a regular W-2G, which has its own consequences.

But those things aside, if I HAD to pick one game or the other, I’d pick the 8-5-30 BP game. It’s simpler to learn well, and while it has a slightly lesser return than pNSU DW now, it’s return will be the best one very shortly.