The Mathematics Of Gambling In Pineapple Open Face

It’s often correct to gamble in Pineapple Open Face Chinese (POFC) Poker; however, we must always assess what we may potentially lose versus what we stand to gain in order to ensure that we are taking intelligent risks. If we gamble and foul, we will get scooped in addition to forfeiting potential royalties that we may have earned. When we hit our hand, the benefits can include big royalties, three bonus points for scooping, and/or a trip to Fantasyland.

So how much is a trip to Fantasyland (FL) worth? In high POFC, some experienced players generally consider the benefit to be worth around eight points, give or take, depending on the level of competition. When considering the potential gain of getting to FL it doesn’t matter if our opponent has a trip currently locked up or appears highly likely to be getting there because we negate his advantage if we also secure a trip.

In addition, our gambling decisions should also ignore any royalties that our opponent looks to be accumulating as we are on the hook to pay them regardless what happens. Our opponent’s hand strength only comes into play when forecasting how many lines he would be expected to win under different scenarios.

If it’s fairly obvious that we are going to get scooped by playing it safe, we have to gamble as we have nothing to lose. When a football team is down by four points with three seconds left to go they don’t kick a field goal. It’s end zone or bust.

For other situations we must estimate the expected value of playing it safe and compare that with the riskier plays would that put us in danger of fouling. We can then solve for the approximate probability where our decision between making the safe play and gambling would be indifferent. A few simple examples will help illustrate this concept.

Example 1 – Opponent Has Clear Advantage

Suppose we are in the late stages of a hand and our opponent has us in bad shape where if we play it safe it’s around 75% likely he will scoop and a 25% chance he will win two out of the three lines. In addition, if playing to avoid fouling we have no chance at any royalties.

Given that we will lose six points when we get scooped and one if we lose two of the three lines, the expectation of playing it safe is as follows:

Expected Value Playing Safe = (75%)(-6) + (25%)(-1) = -4.75 points

However, let’s assume we also have the option of taking a longshot gamble to some very big hands that will hit approximately 5% of the time. If we get lucky we estimate that we will net 16 points plus make it to Fantasyland.

An example where the probability of hitting is low but the upside is quite substantial would be placing a pair of aces up front, and hope to improve both the middle and back hands when a fair amount of our outs are dead.

Based upon our estimated eight-point value for making it to FL, we should consider our potential earn to be 24 total points should we get lucky and hit our hand. Therefore the expected value of taking this risk would be as follows:

Expected Value of Gambling = (95%)(-6) + (5%)(24) = -4.5 points

Under these assumptions, we should gamble even though the probability of it working out is quite low because in the long run we will lose slightly less.

Example 2 – Not In Danger Of Getting Scooped

Now let’s change the assumption slightly to assume that we have one row clinched (but with no royalties), thus if we play it safe we cannot get scooped. However, by playing it safe we are guaranteed to lose two out of the three rows.

Expected Value Playing Safe = -1 point

Assuming we have the same upside potential and probability of hitting our hand as we did in example 1, the expected value of gambling remains the same -4.5 points therefore playing not to foul fares better by 3.5 points.

We can, however, easily calculate the breakeven probability where it would be correct to gamble by solving for X% representing the percentage of time you hit:

-1 = (100-X%)(-6) + (X%)(24)

X = 16.7%

Thus, in this particular situation we must expect to hit our hand approximately 16.7% of the time or greater in order to make the gamble worth it. When compared with the first example, we require a much higher probability as the difference between getting scooped and losing two out of three lines is a substantial five points.

Example 3 – Putting Royalties At Risk

When assessing whether or not to gamble, it is also crucial to reflect any potential royalties we may lose should we foul. Consider a situation similar to example 1 where it’s late in the hand and estimate that if we play it safe we will get scooped 75% of the time and lose two out of three lines the other 25%.

However, in contrast to the first example we have a strong hand (albeit second best) on one of the lines that would give us six bonus points. Without the presence of these bonus points that could be lost, we saw that is was correct to gamble with a small 5% chance of success. How much does the breakeven probability change given that gambling puts these royalties at risk?

When we get scooped we lose six points but pick up six royalty points for a net result of zero. When losing two out of three lines, our net gain is five points thus the expected value of playing not to foul would be as follows:

Expected Value Playing Safe = (75%)(0) + (25%)(5) = 1.25 points

Note: As our opponent will assuredly be getting royalty points of his own this is not the true expected value of the situation. However, as previously discussed, any royalties that we may have to pay out does not factor into our decision making as those will have to be paid regardless if we foul or not.

In order to solve for the breakeven probability of X%, we need to set the following equation equal to the calculated expected value of playing it safe:

Expected Value of Gambling = (100-X%)(-6) + (X%)(24) = 1.25 points

As it turns out our gamble needs to work out at least 24.2% of the time for it to become the more profitable choice. As expected, when compared to the two prior examples, we require a higher likelihood of hitting our hand when six bonus points will be lost should we foul.

Summary Thoughts

These examples were contrived to help illustrate some of the theoretical issues in play when trying to determine whether or not we should gamble. In game it is impossible to be so precise, however, serious students of the game will analyze decisions that they made after the fact using either a solver/trainer or spreadsheet. They will then take what they learned and use it to improve upon their decision making in the future when faced with similar situations.

If you are unsure whether or not to gamble, the following key principles will help guide your play.

If it’s a certainty or near certainty that you will be scooped it is almost assuredly correct to make longshot gambles. Don’t take a knee; throw the Hail Mary into the end zone!

If our opponent is highly likely to foul we should tend towards conservative play.
The higher the potential upside, the more apt you should be to gamble.

The more you have to risk with regards to bonuses and/or a trip to Fantasyland locked up, the less apt you should be to gamble.

An opponent’s holding only makes a difference in your decision making as it relates to his chances of winning various lines; any royalties he may have or the fact that they are going to Fantasyland does not impact our decision making.

Pineapple Open Face is a very intriguing and dynamic game and making optimal decisions in these late game situations is extremely challenging. Don’t be afraid to gamble when the time is right! ♠

Kevin Haney is a former actuary but left the corporate job to focus on his passions for poker and fitness. The certified personal trainer owned a gym in New Jersey, but has since moved to Las Vegas. He started playing the game back in 2003, and particularly enjoys taking new players interested in mixed games under his wing and quickly making them proficient in all variants. Learn more or just say hello with an email to [email protected].