Guaranteed Play

Last Update: Sep 24, 2008

There are two versions of Guaranteed Play. In the original version, which this page describes, the player's balance could be negative. In September, 2008, I became aware of a new version in which the player's balance could never go below zero. To pay for this, the player's original wager buys fewer hands. The old games are being gradually replaced. In the future, I may present an analysis of the new rules.

Guaranteed Play is a video poker variant, in which the player prepays for a fixed number of hands of video poker. For example, the player can buy 500 $5 hands of 8/6 Jacks or Better video poker for $200. That is $2,500 worth of action for $200.

The way it works is after the player pays the price for his package of hands, and agrees to the terms, he starts with a balance of $0. Every bet the player makes is deducted from his balance, and any wins are added. For example, if playing with $5 hands and the player got three of a kind (paying $15) on his first hand, his new balance would be $10, $0 less $5 for the bet, plus $15 for the three of a kind, equals $10.

The following two tables show how many hands the player buys for each of the six games available, the package price, and the denomination. These pay tables have been observed at both the Red Rock and Palace Station.

At the end of the package of hands, the player will get back any profit he shows. The player may also quit at any time, keep whatever his balance is, and forfeit any remaining hands.

To get any money back at all, the player will need to show a profit at the end of the series of hands. This is not easy to do, since video poker pay tables available to the player are negative-expectation games. To show a profit the player will need to win more than he paid. For example, if paying $200 for 500 hands the player will need to show a profit of more than $200.

The following table shows the net win after playing 100 hands under both Standard Play and Guaranteed Play, based on the Double Double Bonus game, in which the player pays 20 units for 100 hands. The x axis is bankroll after all hands are played, and the y axis is the amount the player will win.

The table shows that if the player broke even, or had any win, under Standard Play, he would receive 20 units less under Guaranteed Play. For any Standard Play loss the player will lose 20 units under Guranteed Play. If s is the Standard Play win, and g is the Guaranteed Play win, then g=max(-20,s-20). So, a way to think of Guranteed Play, is like an insurance policy, in which the premium amount is subtracted from the net win after the package of hands is played, but the maximum loss is limited to the premium amount.

The first two tables I present show the return of each game in conventional video poker, assuming optimal strategy. The first table is for the 25-cent denomination, and the second for $1. The machines at the Red Rock also allow for the player to play in the conventional way, what was labeled as "Standard Play."

I difficult issue I face in the analysis of this game is how to define the "return." To make a comparison, consider two players playing perfect 9/6 Jacks or Better. The return on said game is 99.54%, or a house edge of 0.46%. Player 1 will play only one hand and quit. Player 2 will play until ruin. Player 1 can expect to lose 0.46% of his initial wager. Player 2 can expect to play on average 219.25 hands, but because it is a negative expected value game, the probability of eventually running out of money is 100%. So, player 1 will get back 99.54% of his initial wager, and player 2 will get back 0% of it. Yet the odds of each hand played is exactly the same. If we base the return on total money bet it is 99.54% for both players. If we base the return on money stuffed into the machine it is 99.54% for player 1 and 0.00% for player 2.

There are two plausible ways to define the return for Guaranteed Play. The first I call the "Premium Return", and is defined as the ratio of the expected loss to the cost of the package of hands. The second I call the "Play Return", and is defined as the ratio of the expected loss to the bets made during the course of the game, not including the cost of the package of hands.

The next two tables are based on optimal strategy for the "Standard Play" game at the $1 denomination. In other words, the table assumes the player is not adapting his strategy for Guaranteed Play rules. The cost is expressed as a number of units. For example, if the fee were $100, and the player received $5 hands, the cost would be 100/5 = 20. The bottom line is that if the player uses conventional video poker strategy, he will probably lose much of the money he actually puts into the machine.

The next two tables show the return following optimal strategy modified for Guaranteed Play, at the $1 denomination. These tables are mostly incomplete, due to the amount of computer time required to analyze a particular pay table. The first table shows the return for packages of hands costing 20 bets, and the second table for 40-bet packages.

The optimal strategy for a single version of Guaranteed Play is so complicated, it would fill something the size of an encyclopedia. My standard video poker program takes about 32 seconds to analyze a standard video poker pay table. However to analyze the 275-hand double double bonus game, for example, my Guaranteed Play program takes just about a month. For the 500-hand Jacks or Better package, my computer would take about eight months. This goes to show just how complicated and vast the strategy for this game is.

The reason the strategy is so complicated is that every combination of remaining hands and bankroll will require a different level of aggressiveness, and corresponding strategy to suit. However, I can give a general comment. Most of the time, you need to be very aggressive. The lower your bankroll, and the fewer hands remain, the more aggressive you will need to be. If it is the last hand, and a dealt straight flush will not get you out of the hole, then toss it.

More Resources

My Guaranteed Play Appendix 1 (520K) indicates the expected value for every state in the 100-hand 9/6 Double Double Bonus game. Between this table and video poker software with a strategy engine, the player could, in theory, develop a strategy for the game. A strategy table is also listed for the first hand only.

Links

There is a very well-done demo at guaranteedplay.com .