Bonus Expected Values in Video Poker

Introduction

Since the beginning, bonuses have been the order of the day with Internet casinos. They know most players will eventually lose everything they start with. However, it is a competitive business, and getting a deposit in the first place isn't easy. To entice new players and new deposits, Internet casinos routinely match deposits with bonuses to let the player enjoy the experience longer. The thinking is that the player will likely lose all the money eventually, so why not let it last a little longer.

The good news for players is these promotions can be lucrative if played properly and aggressively. Despite big play through requirements to cash out, they can still be a very good bet if betting big on low house edge games, like video poker.

The purpose of this page is to show some key statistics for playing bonuses in video poker. Specifically:

• Probability of success.
• Average win, including when busting out.
• Average win, conditional on not busting out.

 

It is the goal of this page that the reader not fear playing video poker when given a bonus. Be careful as you select an Internet casino, because some do not allow video poker. Always check the terms and conditions before starting to play to be sure you're compliant with the rules.

The reason I created this page is I played at an Internet casino with an immediate 150% bonus with a play through requirement of 90x. The best game available was 8-5 Aces and Eights, with a return of 99.78%. The most I was able to deposit was 20 units, which was matched with 30 more, for a total of 50 units to start. My tables don't have a column for a 90x play through requirement, so let's take the average of 80x and 100x. The probability of completing the play requirement at 80x is 14.85% and at 100x is 12.58%, for an average of 13.72%. The average bankroll after either busting out or completing the play requirement, whichever happens first, at 80x is 47.05 units and at 100x is 12.58 units, for an average of 46.95 units. Thus, this is a strong bonus, with an average return of 46.95 units for depositing 20, for a player advantage of 134.75%! Of course, it is a volatile play, with a probability of success of only 13.72%. However, assuming you do complete the play requirement, the average bankroll is 46.95/0.1372 = 342.2 units.

It may surprise some readers that the expected return is so close to the starting bankroll, given such a large play requirement. This is because much of the time the player will bust out early, and not have to complete the play requirement. However, sometimes the player will hit an early royal, giving him enough ammunition to complete the play requirement.

All the tables in this page are based on optimal player strategy. I would be remiss in my duties if I didn't mention that the player can get an even greater advantage by playing more aggressively at first. However, the strategy deviations would depend on a host of factors and would be very mathematically complicated to calculate. In the interests of simplicity, my advice is to stick to standard video poker strategy.

9-6 Jacks or Better

The following table shows the probability of surviving a play through requirement in 9-6 Jacks or Better, assuming optimal strategy, according to the initial number of bets in the bankroll (down) by play requirement multiple (across). For example, if the player starts with a bankroll of 50 units, and must play it through 100 times, then the probability of surviving is 12.25%.

 

The next table shows the expected number of units remaining after the player either completes the play through requirement or goes bust trying. For example, if the player starts with a bankroll of 50 bets and must play it through 100 times, or bust trying, then his expected win after either marker is met is 42.75 bets.

 

The next table shows the expected number of units remaining, assuming the player completes the play through requirement. For example, if the player starts with a bankroll of 50 bets and must play it through 100 times, or bust trying, then his expected win, assuming he completes the play requirement, is met at 348.9 bets.

 

8-5 Bonus Poker

The following table shows the probability of surviving a play through requirement in 8-5 Bonus Poker, assuming optimal strategy, according to the initial number of bets in the bankroll (down) by play requirement multiple (across). For example, if the player starts with a bankroll of 50 units, and must play it through 100 times, then the probability of surviving is 10.21%.

 

The next table shows the expected number of units remaining after the player either completes the play through requirement or goes bust trying. For example, if the player starts with a bankroll of 50 bets and must play it through 100 times, or bust trying, then his expected win after either marker is met is 38.31 bets.

 

The next table shows the expected number of units remaining, assuming the player completes the play through requirement. For example, if the player starts with a bankroll of 50 bets and must play it through 100 times, or bust trying, then his expected win, assuming he completes the play requirement, is met at 375.1 bets.

 

9-6 Double Double Bonus

The following table shows the probability of surviving a play through requirement in 9-6 Double Double Bonus, assuming optimal strategy, according to the initial number of bets in the bankroll (down) by play requirement multiple (across). For example, if the player starts with a bankroll of 50 units, and must play it through 100 times, then the probability of surviving is 7.33%.

 

The next table shows the expected number of units remaining after the player either completes the play through requirement or goes bust trying. For example, if the player starts with a bankroll of 50 bets and must play it through 100 times, or bust trying, then his expected win after either marker is met is 40.89 bets.

 

The next table shows the expected number of units remaining, assuming the player completes the play through requirement. For example, if the player starts with a bankroll of 50 bets and must play it through 100 times, or bust trying, then his expected win, assuming he completes the play requirement, is met is 557.6 bets.

 

16-10 Deuces Wild

The following table shows the probability of surviving a play through requirement in 16-10 Deuces Wild (often known as "Not so Ugly Ducks"), assuming optimal strategy, according to the initial number of bets in the bankroll (down) by play requirement multiple (across). For example, if the player starts with a bankroll of 50 units, and must play it through 100 times, then the probability of surviving is 10.85%.

 

The next table shows the expected number of units remaining after the player either completes the play through requirement or goes bust trying. For example, if the player starts with a bankroll of 50 bets and must play it through 100 times, or bust trying, then his expected win after either marker is met at 46.55 bets.

 

The next table shows the expected number of units remaining, assuming the player completes the play through requirement. For example, if the player starts with a bankroll of 50 bets and must play it through 100 times, or bust trying, then his expected win, assuming he completes the play requirement, is met is 429.0 bets.

 

8-5 Aces and Eights

The following table shows the probability of surviving a play through requirement in 8-5 Aces and Eights, assuming optimal strategy, according to the initial number of bets in the bankroll (down) by play requirement multiple (across). For example, if the player starts with a bankroll of 50 units, and must play it through 100 times, then the probability of surviving is 12.58%.

 

The next table shows the expected number of units remaining after the player either completes the play through requirement or goes bust trying. For example, if the player starts with a bankroll of 50 bets and must play it through 100 times, or bust trying, then his expected win after either marker is met is 46.85 bets.

 

The next table shows the expected number of units remaining, assuming the player completes the play through requirement. For example, if the player starts with a bankroll of 50 bets and must play it through 100 times, or bust trying, then his expected win, assuming he completes the play requirement, is met at 372.3 bets.

Written by: Michael Shackleford