You're playing blackjack and you're dealt a 16 looking into a Dealer 7. What do you do and why? I've watched a lot of Player with this hand and it is almost fun watching them. Sure, there are some blackjack counters who spend a few seconds thinking about it, thinking about the count and working out what to do in this situation. Then there are the good Player who aren't really counting but trying to figure out what is left in the shoe - big or small cards? Next up are the Players who haven't been paying attention to the shoe but are trying to do some form of math to figure out the probability that they will bust (8 out of 13!) and if they are better off hoping the Dealer will bust. Last, but not least, we have the majority of Players who are simply trying to 'guess' what the next card will be using more ESP than math.
The problem is that this should be solved using math. Trying to 'guess' the next card without math is just, well guessing. Now, if you are that Player who doesn't pay attention to the shoe, you actually have the easiest path. You don't have to do any math on the fly. It would be better if you simply learned the strategy as determined by a variety of experts. How did they arrive at this strategy - well, they did the math for you. While there are a variety of means to determining blackjack strategy, the end results is virtually identical for all situations. And, in the example I presented, the strategy isn't even really all that close. You should HIT. To be certain, this is an ugly hand and not one you want to have often. But playing ugly hands right is as important as playing the good hands right. They all end up to the theoretical payback.
The expected value of Hitting is about 0.59+. The expected value of Sticking is about 0.53. By gambling standards, this isn't much of a decision. Now, if you've been counting, the strategy might be different. But, assuming you're not, you have to assume the deck is neutral. And, a neutral deck will in the long run give us the expected values I just shared. Why? Because the math tells us all this. Through complex formulas or a computer simulation we know that when faced with this situation that the Player will lose less by Hitting vs. Sticking. It's that simple. If you believe you can guess 'right' more often than 'normal', well, quite frankly, you're kidding yourself. If you want to test your powers of ESP, take a penny and flip it a hundred times. But, before you do, mark down if you think it will be heads or tails. How'd you do? Yeah, you might have gotten 51 or even 55 right. Now do this test a hundred times and let me know how you do? You're going to be oh so close to 50%. That's how well you guess - just like everyone else.
Deciding how to play video poker hands is no different. Why do we keep a Low Pair over a 4-Card Straight? The math here is easier than the blackjack math actually. With video poker there is a much more finite set of possible outcomes. With a 4-Card Straight there are 47 possible outcomes as there are 47 possible draws. 8 of these will result in a Straight which pays 4. This is a total return of 32 units out of 47 draws for an expected value of just over 0.67. Now, it is possible that some of these 4-Card Straights might have a High Card or two or three in them which will increase the expected value as for each High Card there are 3 possible draws which will result in a High Pair.
With our Low Pair, there are 16,215 possible outcomes. Most will result in nothing. Some will give us Trips and some will give us Two Pair. When we add up the total payout and divide by 16,215, we get about 0.82 which is higher even a 4-Card Straight with 2 High Cards. So, the proper play is the Low Pair.
A very similar hand is one with a Low Pair that is also a 4-Card Flush. But, a Flush pays 6 instead of 4 and there are NINE cards which complete the Flush. Thus we have a potential payout of 54, which when divided by 47 gives us an expected value of 1.1+ Thus, in this case we play the 4-Card Flush! There is no guessing. There is no staring at the screen trying to figure out which cards will come up next. The simple reality is that the next cards are completely RANDOM. Unlike blackjack, there is ZERO potential for any type of counting. Thus, the Expert Player will use the math to guide him to play the hand the right way.
Now, obviously in any single situation, you may find that you would've been better off playing it the other way. You decide to hit that 16 and you get dealt a 10 and bust. The Dealer turns over his hole card and it is a 6 and he had 13 and he would've busted if you had not hit. This doesn't make what you did wrong. Nothing in our strategy tells us that it will ALWAYS be the better play - just that it will be the better play in the long run.