Discussing going for four-of-a-kind or keeping full house

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Have you ever been tempted to throw away a Full House and go for the Four of a Kind? In a Jacks or Better machine this is essentially a suicidal move. The Full House is obviously worth the full 9 EV. The Trips is worth only 4.3. Further, it is not like the Quads will pay some significant amount of money. Quads paying only 25 doesn’t seem like enough of a payday to even contemplate giving up that Full House.

But, in other version of the game, the spread gets larger. So, does the play get more worthwhile? Well, yes, more worthwhile, but that doesn’t mean worth actually doing. In Bonus Poker, the Full House only pays 8. The Quads pay more so Three of a Kind has a higher EV and depends on the rank of them. But, even Trip Aces has an EV of only 6-plus.

So, at least we’re no longer talking about an EV of half of the Full House, but this is still a very, very bad move. Even the payout of 80 for the Quad Aces is simply not enough to think about doing this. Again, I also don’t think this fits the bill as a significant amount of money to warrant giving up EV in favor of a huge payday.

What happens when we move to Double Bonus Poker where the payouts of Quads doubles from Bonus Poker? Well, the expected value of the Trips goes up considerably. Trip 5-K’s EV goes to over 5, while 2’s-4’s are just under 7. But the Full House pays 10 in a full pay Double Bonus Poker game. So, Full Houses with three 2’s-K’s are not worth scrapping. BUT, if you have Trip Aces, that potential 800 unit payout (for max-coin) is worth discarding our Full House for.

Next, we ramp up to Double Double Bonus Poker. Trip Aces goes all the way to 800 units if you get the right kicker. The Full House pays only 9 so that should help even the score even further. But, not enough to change the strategy any further. A Full House with trip Aces is still worth discarding, but not even 2’s- 4’s are worth doing the same for. The Expected Value of Trip 2’s-4’s is just a bit over 7, which is still a long way from 9.

This of course doesn’t mean certain situations can’t tempt you. I faced this earlier today while playing a Multi-Play Multi-Strke machine. I was dealt a Full House with three 4’s and two 7’s. I had to give it some thought as to how to play it. Now what was the right math play, but the right spur of the moment, what do I want to do.

With five coins in and all five hands still going, I’d have five shots at the Four of a Kind or I could take my five Full Houses. This was on the third level of the game, so all pays are multiplied by 4x. Of course, this doesn’t change the relative expected value of each hand as both are multiplied by 4x. The Full Houses paid 180 units each (4x by 5 coins by 9 payout). My total payout would be 900 units.

My alternative would leave me potentially with five Three of a Kinds, which would give me a total payout of 300 units. Of course, I’ll have five shots for the Quads. If I don’t get my kicker, that Quad will still pay 1,600 by itself. If I can hit the kicker, it will double to 3,200 units. All of a sudden, I have a significant (albeit certainly not life altering) payout happening. But that’s a big IF at the front of the last two sentences.

So, what did I do? I went with the Full House. It is the right play overall and it was also the right play for where I was in my session. This implies there may have been some other point at which I would have gone for it. I can’t say for certain I would have. But, if I had been down a bit and nearing the end of my session, I might have taken the risk. It would have been a pretty big risk.

It’s not like the Expected Values differed by 0.1. They differ by almost 2! But the potential win was large enough to make me give it some thought. Just not enough to make me actually do it!

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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