Lock and Roll Slot Machine

Introduction

Lock and Roll is a skill-based slot machine found in some jurisdictions, like North Carolina. The game looks like a slot machine but plays more like video poker. Here are the specific rules.

1. After making a bet, the machine spins three reels.
2. The player may hold in place any reels he wishes, including all of them, and re-spin any remaining.
3. The probabilities of each symbol on a given reel are the same in the initial spin and the re-spin. So, the player may get the same symbol he discarded on the re-spin.
4. The player will be paid according to the combination of symbols after the re-spin. If the player chooses to not re-spin any reels, then he is paid based on the initial spin.

The following is the pay table. A single 5X symbol will multiply any win by 5. Two 5X symbols will mutliply any win by 25. An exception is that the wins for only two or three 5X symbols are not subject to the multiplier; in other words, the 5X symbols only multiply pays that do not consists of only 5X symbols.

* The win for three 5X symbols is progressive, starting at 5000 coins.

Deal Return

The next table shows the probabilities and return on the deal (first spin). The lower right cell shows a return of 22.29% after the first spin.

Draw Return

The next table reflects the probabilities and return on the draw (second spin). The lower right cell shows a return of 90.06% after the second spin.

Strategy

The next table indentifies which reels to hold (N=spin, Y=hold) for all possible outcomes of the first spin, assuming a jackpot of exactly 5000.

There are three plays that can be played two different ways, both with the same expected value. They are:

 reel1  reel2  reel3 -----  -----  ----- 2-bar  1-bar  2-bar 2-bar  3-bar  2-bar 2-bar  7-bar  2-bar 

In all three cases, holding all 3 symbols has the same exact expected value as holding only the two double-bars.

As with all progressive video poker games under optimal strategy, changes should be made as the jackpot gets higher. Assuming no changes in strategy, the return will go up by 0.2418% for every 1,000 in the meter above 5,000. To reach a 100% return, the meter would need to be 46,107.57.

Acknowledgement

The question about this game was posted at my companion site Wizard of Vegas. For their contributions toward finding the optimal return, I would like to thank CraigGA, dk, JB, and miplet.