Easy as one, two, three

28 August 2016

By John Grochowski

QUESTION: I’m mainly a blackjack player, but I’ve been fooling around lately with Ultimate Texas Hold’Em. After you look at you first two cards, you can either check, raise three times your ante or raise four times your ante.

Is there ever a situation where you should raise three times instead of four? It seems to me that if you have an edge, you should make the maximum raise. Raising only three times strikes me as being like doubling down for less than the full amount, something that as a blackjack player I would never do.

ANSWER: Yes, if you’re going to raise after your first two cards, you should make the full 4x bet.

At wizardofodds.com, Michael Shackleford has a strategy chart for the game. To summarize, you should make the 4x bet if you have a pair of 3s or higher; on any hand that includes an ace; on king-high hands where the second card is 5 or higher or on a king with a 2, 3 or 4 of the same suit; on queen-high hands with an 8 or higher or with a suited 6 or 7; and on any jack-10 or suited jack-8 or jack-9.

You have two more opportunities to raise in Ultimate Texas Hold’Em. If you did not make the first raise, you may raise double your ante after you’ve seen your two cards plus the three-card flop. If you don’t raise there, you may raise an amount equal to your ante after you’ve seen the final two community cards.

You can check on the first two raise opportunities, but after all cards are exposed, you must either raise or fold.

For a full strategy that includes when to raise after the flop and after the final two cards, go to https://wizardofodds.com/games/ultimate-texas-hold-em/

If you follow basic strategy, the house edge on Ultimate Texas Hold’Em is 2.2% of your ante, or 0.5% of your total wagers.


QUESTION: I’ve been playing roulette a long time, and I don’t think I ever saw this before. There was a winner on 1, the next number was 2 and the next was 3. After that, it was something in the 20s, and the streak was broken. What are the chances of a 1-2-3 sequence? How big a stretch would it have been to go 1-2-3-4?

ANSWER: On an American double-zero wheel, there are 38 numbers – 1 through 36 plus 0 and 00. To calculate the chances of any specific three-number sequence occurring on consecutive spins, you can cube 38.

So the chances of 1-2-3 coming up on consecutive spins would be 1 in 38 x 38 x 38, or 1 in 54,872.

That’s a big number, but not so big that it doesn’t happen pretty often. There are more than 1,000 casinos in the U.S. Not all have roulette, but even so, a 1-2-3 sequence happens somewhere just about every day.

Make it a 1-2-3-4 sequence, and the chances are more remote at 1 in 2,085,136, though even at that level it happens somewhere in the U.S. several times a year.

There’s another way to look at the problem. What if the 1-2-3 sequence already has occurred, as it did at the casino where you were playing? How likely is it that the next number will be a 4, for a 1-2-3-4 sequence?

At that point, it’s a 1 in 38 chance. The odds of any given number occurring on any spin are 1 in 38. Before the sequence began, 1-2-3-4 was beyond a 1-in-2 million shot, but once the heavy lifting had been done and 1-2-3 was in the books, it was down to 1 in 38.