Last Updated: November 16, 2014

# Genie's Hi Lo

## Introduction

Try to concentrate on the cards and not the Genie's lovely big eyes *ahem* in this Playtech game of card prediction. There are actually two different versions of the game with seemingly the same name to make things complicated. For lack of a better idea, I will call them the "classic" and "jackpot" versions, and explain them both separately.

## Classic Version

### Rules

Here are the rules for the classic version of the game.

1. A single 52-card deck is used.
2. Cards are ranked as in poker, with aces LOW only.
3. After making a bet the player will select one of the genie's cards.
4. The player will then make a wager on whether the next card will be higher/lower than the original card and/or on the color of the next card.
5. If the player's prediction is correct, then the player's new balance will be inversely proportional to the probability of winning. To be exact, the formula of the win seems to be wager × 0.97 / (probability of winning). This return is rounded down to the nearest penny.
6. If the player wins, then he may cash out or try to parlay his winnings with the next card.
7. The player may play up to 11 times, or 12 total cards counting the original card.
8. The cards are dealt without replacement. In other words, once a card is played it won't be seen again that game.

### Example

Let's look at an example. The player bets \$1 and the first card is a red 5. Here is what the player would grow his balance to if he wins according to the various bet options. Remember to always round DOWN to the nearest penny.

• Lower: The probability of winning is (16/51) so the balance after a win would be \$1 × 0.97 / (16/51) = \$3.09.
• Higher: The probability of winning is (32/51) so the balance after a win would be \$1 × 0.97 / (36/51) = \$1.54.
• Red: The probability of winning is (25/51) so the balance after a win would be \$1 × 0.97 / (25/51) = \$1.97.
• Black: The probability of winning is (26/51) so the balance after a win would be \$1 × 0.97 / (26/51) = \$1.90.
• Lower and red: The probability of winning is (8/51) so the balance after a win would be \$1 × 0.97 / (8/51) = \$6.18.
• Lower and black: Same as lower and red above.
• Higher and red: The probability of winning is (16/51) so the balance after a win would be \$1 × 0.97 / (16/51) = \$3.09.
• Higher and black: Same as higher and red above.

### Strategy

Much like single-zero roulette, it doesn't make any difference what you bet on as the house edge is always the same. So play it safe or throw a Hail Mary, it is up to you. The only thing that matters a little bit is the rounding. You can save a fraction of a penny with the bets that will get rounded down less if you win. However, if you're the kind of player to worry about a fraction of a penny, like me, then you're probably not playing this game in the first place.

Don't bother trying to count the cards previously played, because the genie does that too and all the wins are based on the true odds according to the remaining cards in the deck at that time.

### Analysis

Not counting the rounding, the house edge is 3% by design. Counting the rounding, it can get as high 3.4%.

## Jackpot Version

### Rules

1. The game is played with a 53-card deck, including one joker.
2. Cards are ranked as in poker, with aces LOW only.
3. After making a bet, the player will select one of the genie's cards.
4. The player must then make one of the following four predictions on the next card's rank and color:
• Higher or equal and red.
• Lower or equal and red.
• Higher or equal and black.
• Lower or equal and black.
5. If the player's prediction is correct, then he will advance a level.
6. If at any time a joker is drawn, it will automatically advance the player a level and a new card will be drawn.
7. Unlike the classic version of the game, the cards are dealt with replacement. In other words, after a card is used, it is immediately returned to the deck. By "used" I mean it is no longer needed. For example, if the first card drawn is the jack of diamonds, then the next card can't be the jack of diamonds because it is still in play. However, once the next card is drawn, then the jack of diamonds is returned to the deck. So, at any given time, there are 52 possible outcomes, the 53 cards in the deck less whatever the last card drawn was.
8. The player will keep playing until he gets a wrong prediction or reaches the 12th level.
9. The player is paid according to the highest level attained, according the following pay table.
10. The minimum bet to win the full jackpot is \$5. If the player reaches level 12 with less than a \$5 bet, then he will win a pro-rata share of the jackpot according to his bet amount. For example, a \$2 bet would win 40% of the jackpot.

Following is the pay table for Genie's Hi Lo Jackpot. Wins shown are on a "for one" basis.

Level Win
12 Jackpot
11 150
10 100
9 50
8 20
7 10
6 6
5 4
4 3
3 2
2 1
1 0

### Strategy

The strategy is pretty simple, as follows:

• With a six or less, for the rank, pick higher.
• With an eight or more, for the rank, pick lower.
• With a seven, you may pick either higher or lower.
• Always pick the opposite color of card you have.

### Analysis

The following return table is based on a \$5 original bet, the amount required to qualify for the full jackpot. The return column is the divided by \$5, to the show the ratio of the expected return to the original wager.

### Return Table

Level Win Probability Return
12 Jackpot 0.000042 ?
11 750 0.000065 0.009678
10 500 0.000160 0.015998
9 250 0.000403 0.020132
8 100 0.001012 0.020249
7 50 0.002549 0.025491
6 30 0.006415 0.038491
5 20 0.016123 0.064491
4 15 0.040501 0.121504
3 10 0.101851 0.203702
2 5 0.254447 0.254447
1 0 0.576433 0.000000
Total 1.000000 0.774183 + ?

As you can see from the return table above, the fixed wins contribute 77.42% to the return. For each \$1,000 in the jackpot, the return goes up by 0.84%. To reach break-even, the jackpot would need to reach \$26,968.06.

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