How to Evaluate the Value of Breaking Made Hands in Video Poker
December 26, 2014
In video poker games like Jacks or Better, you often run into the question of if you should break up a made hand like a flush or a straight for a strong draw. We're going to break down the process of figuring out how much value you'll get from a draw here to show you exactly how to evaluate these scenarios. This is a critical skill to have if you end up studying games that don't have widely-published strategies or if you want to develop your own strategies for common games.
The key idea here is that you want to make a list of how many cards will give you a payout and what those payouts are. Then for each possible payout, you multiply the payout size by the chance of getting that payout with your draw, and that's how much value that potential outcome adds to the value of your draw as a whole. Add up all of the possible payouts, and you have the value of your draw, and you can compare this to the value of a made hand to compare which is best in the long run.
Suppose you have JsTs8s7s4s and you want to know if discarding the 4s will give you a better payout rate than the 6x you'll get from just standing pat. There are six ways to get a 1x payout from the three jacks and tens left in the deck. You can also pick up one of the 7 remaining non-straight flush spades for a 6x payout, or three of the non-straight flush nines for a 4x payout. Finally there's the lone 9s which will give you a 50x payout.
So the way you do this is that since there are 47 cards left in the deck, the value from one pair hands is 6/47 * 1 which is 0.128. For the flushes, it's 7/47 * 6 = 0.894, and for the straights, it's 3/47 * 4 = 0.255. Finally for the straight flush, it's 1/47 * 50 = 1.064. You add those values together to get 0.128 + 0.894 + 0.255 + 1.064 for a total of 2.341. As you can see, this is significantly less than the payout for a made flush, so you would be better off keeping your hand pat in this particular situation.