Pineapple Open-Face Chinese Expected Value Calculations

In my last article I advised you to familiarize yourself with some pineapple open-face Chinese (POFC) odds charts, and try your hand at a basic expected value (EV) calculation or risk/reward calculation, in order to familiarize yourself with the logic and mathematical deduction behind this beast of a game. If you haven’t had the time to download my free odds charts at http://www.solvingofc.com/, that’s OK, because I am going to give you an example right now that should help teach you the ropes on basic EV calculations in POFC.

Here is a brief recap of our simple EV calculation equation:

Reward * Chance of Hitting – Risk * (1- Chance of Hitting) > ? Play it Safe Board Value
Where if the left side of the equation is greater than the right, you should gamble, and if it is not, you should play it safe.

Think of, “Reward * Chance of Hitting,” as meaning, “The value of our board if we take the gamble in question.” And think of, “Risk * (1-Chance of Hitting),” as meaning, “How much we lose when we don’t hit our gamble, or when we foul.”

Traditional FantasyLand Gamble

The question is pretty clear here: Should we play K-K up top and gamble for FantasyLand (FL) or play it safe on the bottom to get out of foul territory? Even without doing hard math on the answer, if you know the odds of hitting a jack, deuce, or running pair, you should be able to intuitively decide what to do. Do you know the odds?

The odds of hitting a four outer with one draw left: 39 percent. The odds of hitting a running pair are a bit tougher to calculate and different every time, luckily I created a little calculator for that as well (also available at www.solvingofc.com). Here we have a 17 percent chance of hitting a running pair (that isn’t J-J or 2-2, since we don’t want to double count those), giving us a 39 percent plus 17 percent = 56 percent chance of hitting on our final pull. Given that we get a pretty large reward when we hit, and we make it over half the time, we should already be thinking, “Time to gamble,” but let’s do the math on it anyways to see the value of our gamble:

Reward: 8 Royalties plus 7 FL bonus plus 1 guaranteed to win top (could even be more since we could be getting scooped if we don’t gamble) = 16

Chance of Hitting = 56 percent

Risk = -6 * .61(odds they don’t foul, from below) = -3.66 – this value represents when we and they don’t foul.

Chance of foul = 1-.56 = 44 percent

Current Board Value: To get this we need to figure out the chance our opponent hits their flush vs fouls, as well as the chance they scoop us, and we will ignore any up top royalties for simplicity sake.

Opponent Hits Flush: 61% (7 outs) * (4 royalty points + win bottom + win middle + ~50% win top) = .61 * 7.5 = 4.575

Opponent Misses Flush: 1-.61 = .39 * 6 = 2.34

Our Board Value: The amount we lose when they make it, plus the amount we win when they foul.

-4.575 + 2.34 = -2.235

Put it all together:

16 * .56 -(3.66 *.44) >? -2.235
…
7.35 >? -2.235

If we gamble our EV increases from -2.235 to 7.35, netting us 9.5 points! So anyone not taking this gamble is making a huge mistake. A few reasons our gamble is so plus EV here are:

• We hit over 50 percent of the time
• We make a whopping 16 points when we hit
• We are in a very weak position / we are very likely to get scooped / we have nothing to lose

Let this example be a reminder that, in POFC, playing it safe just to avoid a foul is often not an option. You have to constantly take high variance risks to maximize the overall strength of your board.

Modified FantasyLand Gamble (see chart 2)

Now let’s flip this example on its head and say we have a made full house on the bottom (6 royalty points and guaranteed to win bottom) and 8-8-6 in the middle.Is it worth risking the full house royalties to go to FL?

Reward = 16
Chance of Hitting = 63 percent

Risk = -3.66 – 6 (FH Royalties) = -9.66
Chance of foul = 37 percent

Current Board Value:
-2.68 + 2.34 + 6 (FH Royalty) = 5.66

Put it all together:
16 * .63 -(9.66 *.37) >? 5.66
…
6.5 >? 5.66

We see the EV is a lot closer now. In fact, while it appears to still be a plus EV gamble to risk the full house for the additional royalties and FL, if we had just one 8 or 6 missing, bringing us down to four outs instead of five, it would clearly be a bad gamble. And this is why you really want to know your odds and outs before sitting down to play the game. There is no way to do all of this math on the fly, you need it built into your intuition. So study those boring odds tables, and remember to heed warning signs in close spots. If you are risking a lot of royalties, and a lot of your outs are dead, it’s probably not time to gamble. Likewise, if you have no or low royalties, and/or you are likely to get scooped, and you have a strong number of outs, it’s time to take a risk.

Conclusions

While we were able to get a strong estimate on how to gamble for FL when way behind, using a basic EV formula like this isn’t 100 percent accurate because you aren’t accounting for all of the possibilities. For instance, in the above examples, we neglected to add in the chance our opponent gets royalties up top, which obviously skews our current board value down a little bit. In other situations you may overlook running full houses or trips, or running big pairs up top to hit FL. Just remember that a basic EV calculation is just meant to give you a feel for the underlying values of your board, your opponent’s board, and when to gamble. In order to get a perfectly accurate solution, you either need to account for everything mathematically, which is very tedious and time consuming, or use a POFC simulator. In our next article, we will talk about setting various starting hands, and what the simulator(s) say about the EV estimates of different sets. Until then, practice some late game EV calculations on your own and continue to familiarize yourself with the odds charts. Check out www.solvingofc.com for odds charts, EV calculation templates, and a running pair calculator. ♠

Derric “SixPeppers” Haynie is the author of Quantum Poker and owner of solvingofc.com.  For more articles, OFC solutions, and information on Open-Face Chinese Poker, check out his website: www.solvingofc.com – dedicated to your open-face education.