Hitting a straight is great, you generally get paid! But the question that I am going to look at is when should you chase for your straight and when should you fold. Well knowing the math is a must for this situation. Knowing the math informs all of your decisions!
All about Positive Expected Value
Expected value is when the winnings multiplied by the probability of winning is greater than the investment you have to make to have a chance at winning. In other words, if you have positive expected value, then over the long hall you will make money. When looking at a straight draw specifically, to determine if you have positive expected value, you need to know three things:
- The amount of money you can win
- The chances of hitting your straight (assumes you win the pot)
- The amount of money you have to put into the pot to continue to be in the hand
Once you know these things, you can determine if you should call or fold on a mathematical level
Math on hitting your straight
This is going to be the toughest math of the 3 steps. There are going to be 2 scenarios that we are going to look at. A one card straight draw and a two-card straight draw.
The first thing that we have to look at is how many outs we have in each situation. If we are looking at a one card, then there are 4 outs. The 4 outs would be the 4 suits of the same number card you need to complete your straight. In a two card, straight draw there would be 8.
The next thing you need to look at is the number of unknown cards before the turn and the river come. On the turn, it is 47, 52 minus the 3 communal cards and the 2 cards in your hand. On the river, it would be 46 as one more communal card is now exposed.
Now we can figure out the probability of a few things which will dictate how a few different situations play out.
Probability of hitting a 1 card
If the flop has just come out the probability of the next card is one of the 4 that you require is ~8.5% and ~16.5 it is one of the next 2. If the turn has just come, the probability that it comes on the river is ~8.7%. So knowing this you can determine the pot odds you require. If you can guarantee that you will not see another bet on the turn then you can call 6.25:1 pot odds on the flop. If not, you need closer to 12:1 for your expected value to be positive. Same for the river as well.
Probability of hitting a 2 card
It’s essentially double that of the above scenarios except for the probability that it comes on the turn or the river. In this case, it is ~31.5% which makes the pot odds just over 3:1.
Knowing the math is really valuable for determining whether or not you should call, raise or fold with a draw. It is the fundamental behind any poker play.