A quick knowledge dump for Royal Hold'em that you can use to crush your opponents at Oil Storage and Crystal Palace.

## TL;DR

This summary section is for people too lazy to read the rest of the guide:

- Play hands that can make top full-houses. The list is: AA, KK, QQ, AK, AQ, KQ and AJ.
- Fold hands that have trouble making top full-houses before the flop. These are hands with a J or T in them. For example, AT, KJ, KT, QJ, QT, JT, JJ, TT.
- If you flop a straight, you should check. Fold if someone else bets.
- Don't shove all-in on a AKQJT chop-Broadway board. Everyone loses 6% to the house.

## Introduction

This guide is for GOP3 players who have some familiarity with Texas Hold'em poker, but are unfamiliar with Royal Hold'em. In a nutshell, the GOP3 version of Royal Hold'em is just regular no-limit holdem played with only cards ranked Ace through Ten. This means that the deck only contains 20 cards, as opposed to 52. In addition, strong hands such as full houses (boats), four of a kind (quads) and royal flushes are far more common. Properly evaluating the strength of your hand relative to this new scale is important to avoid losing a lot of money with a second-best hand.

The buy-in at the table is fixed at 50 times the big blind (BB). The blinds are 1.5k/3k at Oil Storage, and the buy-in is 150k. The blinds are 50k/100k at Crystal Palace, and the buy-in is 5M.

For this guide, I will be referring to cards using the following symbols:

- A=Ace.
- K=King.
- Q=Queen.
- J=Jack.
- T=Ten.

## Risk vs. Reward: EV

All decisions we make in any game of poker come down to understanding how to risk our chips to win more chips.

Expected Value (EV) is the measure of the profitability of a poker decision, usually, to call or fold vs. an opponent's bet. Our decision will depend on our assumed chances of winning the hand. We'll cover how to evaluate our winning chances in a different section of the guide.

In simple terms, if given a choice between calling and folding against an opponent's bet, we should choose the option that maximizes our profit. Since folding has an EV of 0, we should call if the EV of calling the bet is positive.

The equation for EV is as follows:

- EV = (Probability of Winning)*(Pot size + Bet size) + (Probability of Losing)*(-Bet size)

Note: For probabilities, Probability of losing is always 1-Probability of Winning.

Said another way, when we call an opponent's bet and win, we win the current pot plus our opponent's bet. When we lose, we only lose the additional amount equal to our opponent's bet. When evaluating a decision to call vs. fold, we ignore our previous sunk costs that produced the current pot size.

Here's an example:

The pot is 1000 chips, and our opponent has bet all-in for 500 chips. We think we have a 20% chance to win.

- EV = (.2)*(1000+500) + (1-.2)*(-500) = -100

Hm, even though the pot is fairly large, our winning chances are too poor to justify continuing in the hand. Folding is the best option.

Different example:

The pot is 2000 chips, and our opponent has bet all-in for 500 chips. We think we have a 20% to win.

- EV = (.2)*(2000+500) + (1-.2)*(-500) = +100

Interesting! Even though our opponent's bet size stayed the same and our winning chances stayed the same, the larger pot size justifies staying in. Calling is now the best option.

We now have learned that if the pot has gotten significantly large based on our previous actions, it may become wrong to fold even if we evaluate that our winning chances are weak. We should learn to make better decisions prior in the hand so that we aren't stuck in situations where the pot size has ballooned out of control and we end up "stuck" making marginal calls with weak holdings.

(*) In general, if you have more than a 50% chance to win vs. one opponent, it is incorrect to fold because your EV will always be positive.

(*) See: Appendix: Death and Taxes

## Preflop Hand Selection

In this section, we'll examine the chances of winning with various starting hands, assuming we end up all-in before the flop (preflop) against a single opponent.

The odds of hands winning in Royal Hold'em is vastly different compared to regular holdem. AA, KK and AK are still strong hands in this game, but not to the same extent as in regular 52 card Hold'em.

For example, in regular Hold'em:

- AA vs. KK, AA wins 82%.
- AA vs. AK, AA wins 92%.
- AA vs. a random hand, AA wins 85%.

However, for Royal Hold'em:

- AA vs. KK, AA wins 66%.
- AA vs. AK, AA wins 63%.
- AA vs. random, AA wins 70%.

With fewer cards in the deck, the starting hands run closer to each other in value. This is why when we play Royal Hold'em, it seems like almost any random hand has an equal chance of winning. However, this is not the case, and poor preflop hand selection will make us long term losers at the game.

As a side note, I've ignored suitedness for the following analysis. Suitedness doesn't affect winning chances as much in this game. While royals are far more likely in this game than regular Hold'em, they are still relatively rare. Having a hand like AhQh vs AhQc only raises your winning chances by about 0.3%.

Against a random hand, the following hands have >50% chance to win:

- AA, KK, QQ, AK, AQ, AJ, KQ

Of the above hands, AJ and KQ are barely above 50%. If you take rake into consideration, AQ is questionable as well (see: Death and Taxes).

This means that the remaining hands are below 50% chance to win vs. a random hand:

- JJ, TT, AT, KJ, KT, QJ, QT, JT

The worst hand, JT, has a 44.7% of winning.

Now, you might see this percentage and think, "Hey! 45% is plenty good enough to gamble when team points are on the line!" Let me be the first to warn you that the above percentages only assume that 1 player will call your all-in. In practice, as more players jump into the pot, your chances of winning will decrease faster than the rate that the pot increases.

Also, our winning percentage is calculated as our chance of winning the pot plus half of our chance of tying (and chopping the pot). A large part of "winning" with JT is actually related to our chances of tying (which is somewhat bad in GOP3). A more detailed analysis reveals that we would expect to lose about 20% of our stack if we go all-in with JT vs. another random hand.

## Relative Hand Strength

If you are fortunate enough to play Royal Hold'em at a table where players are not constantly all-in preflop, you'll need to understand how to evaluate your winning chances based on your holdings and the board run-out.

Hold'em is a game of relative hand strengths. That is, the board determines what the absolute best possible hand is at all times.

For example, on a board of:

- Ac Qs Jd Kd Ts

No royal flush is possible, and all players have a straight. No full houses are possible because the board is not paired. In this case, all players have the best possible hand (nuts), and the pot will be split among all players who don't fold.

Example #2:

- Ac As Kc Qd Jh

In this example, AA is the best possible hand for quads. However, if a player holds AK, that player has the best possible hand because there are only 4 aces in the deck and he has one of them. This means that no other player can have quads. In addition, his K kicker matches the 2nd highest card on the board, so he has the top full-house (boat). His opponents can only have the same boat (there is one other possible AK combination) or worse hands.

On a board like the one above, it is important to be careful with a hand like AQ, AJ, QQ or JJ. It's possible that one of your opponents could have AK or AA for the nuts.

Example #3:

- As Ad Ks Kc Th

In the above example, AA and KK are quads and very strong. Again, AK would be a nut hand that blocks our opponents from having stronger hands. Therefore we can bet, confident that no one else could beat us. Even a hand with a lone ace, such as AQ, AJ or AT would give us top boat, where we could only lose to quads.

It is important to note that bottom boat, a hand with a lone K, such as KQ, KJ, KT, is virtually worthless on the above board, and should be folded.

Example #4:

- As Kd Jc Th Ts

In the above example, TT is the rare nut hand. However, AA, KK, JJ and AT also make fairly strong boat hands as well. Many players get in trouble with hands such as KT or JT on low-paired boards like the one above when they fail to realize that there are many other boats stronger than theirs.

## Playing the Flop

After deciding if we'll play our cards preflop, and assuming we're not all-in already, we'll see a 3 card board, also known as the "flop". The flop will significantly change our outlook for the hand, depending on how it fits our holdings. I'll cover some of the more interesting situations, and let you figure out what to do when you flop quads or royals.

**Example #1: Flopping a straight**

Let's say we have a hand like Ah Kh and the board is:

- Qc Jd Th

Our initial response might be, "Horray! We flopped the nuts!" However, once we do the math, we realize the grim news. Against one opponent with a random hand, we have only a 43% chance to win. Against 2 opponents, 20%!

This is because boats are usually the winning hand in Royal Hold'em. Any card that pairs the board makes a boat potentially possible. Any card that doesn't pair the board is likely to give another opponent a straight to split the pot. Our hand can't improve to a boat, although our backdoor royal draw gives us a bit of hope.

It's usually right to just give up on the hand when we flop a straight, unless the pot is already very large relative to our stack.

**Example #2: Flopping a set**

Let's say we have a hand like Qc Qs and the board is:

- Ac Qd Th

We've flopped a set, and are usually in terrific shape. It's only the rare instance when an opponent has AA where we're in trouble, and even then, we'll still win 14% with quads and tie 20% of the time. Against an opponent with AQ or AT, we can expect to win over 60% of the time. Someone with QT is getting smashed, as we'll beat them over 80% of the time. KJ may be the nuts for now, but we'll either pair the board to make a boat, or tie them for the straight, so we can expect to win outright 88% of the time, and tie an additional 11% of the time.

**Example #3: Flopping trips**

Let's say we have AQ and the board is:

- Qh Qs Td

We've flopped top trips with an overcard kicker. Surprisingly, we are in remarkably good shape against boats such as QT and TT. We expect to win over 60% of the time in these situations even though those hands are currently ahead of us. This is because against QT we can win if an ace comes, or chop if the board runs KK, JJ, or Tx. Against TT, we win if an A, Q or the board runs KK or JJ. Because there are so few cards in Royal Hold'em, these outcomes are fairly likely.

This hand further illustrates the dangers of playing the weaker starting hands. You can flop the nuts and still be behind an "inferior" hand.

## Appendix: Death and Taxes

One important topic that we haven't touched upon is the fact that GOP3 implements poker with a rake or tax. This means that the website deducts a percentage from all called bets in a pot, before distributing the winnings. For Royal Hold'em, this amounts to an UNCAPPED tax of 6%

For example:

At Oil Storage, you're playing heads-up vs. 1 opponent. He moves all-in for 150k and you call for 150k. If you've played this situation before, you'll note that you lose 150k if you lose the hand, but that you'll have less than 300k when you win. In fact, you expect to have:

- Win = (150k + 150k) - (150k + 150k)*.06 = 0.94*(300k) = 282k

Also, if you manage to tie your opponent, you should expect to lose 6% from your chip stack.

Tie = 150k => 141k

The cost of rake should be included in all of your EV computations if you're looking to be more precise in your math. The shortcut is to just increase the minimum required probability to win when making an EV call/fold decision.

Pwin_rake = Pwin_norake / 0.94

This means that instead of calling with a 0.5 probability of winning vs. 1 opponent, you now need 0.53.

This also means that when all players shove all-in on a chop-Broadway board (AKQJT no royal), everyone loses 6% of what they bet to the GOP3 devs.