Poker question

Suppose you get dealt, on a hand of 5 card draw poker, a pair and one other high card. Is it better to ditch all 3 and hope for trips, or to keep the face card also and keep the potential open for two pair? From my experience, I’ve used the second option and gotten a full house several times, but I just can’t figure all the odds involved. What’s the ideal play in that situation?

(BTW, considering recent discussions of the rule against threads concerning illegal subject matter, I’ll mention that there is a legal gaming casino 20 miles from my apartment, and that poker can be played as a game without financial stakes.)

I don’t know the odds either way, but from a bluffing perspective, keeping three cards makes it harder for other players to figure out what you’re holding as oposed to keeping two cards, in which case you’ve (almost) certainly got a pair.

That’s all the advice I can offer - I don’t play five-card draw much. (3-2-1 Roll 'em high/low is my game of choice)

I believe the odds are in favor of making 2 pair, since these are lower rank than 3 of a kind. But I usually go for the 3.

A high card is only useful to you if you are faced with an identical pair. Pitch it. Three chances for an improvement are better than two chances.


“Sic transit gloria mundi. And Tuesday’s usually worse.” ~ Robert A. Heinlein ~

You should keep the pair and ditch the kicker. In addition to the increased chance of drawing to trips, you have a better chance of drawing a second pair by drawing three new cards than by drawing two and keeping one.

Taking bluffing into consideration, then I’d definitely keep the pair and dump the kicker. The other players will assume that you only have a pair. Then start betting big and raising 'em; “Ah,” they’ll think, “he made trips after all.”

Yea but if he keeps 3 cards and then bets big they would think straight, flush, or bigger would they not?

I’m not a 5-card player, but at the highest levels I think it becomes almost game-theoretic in the optimal play. As I recall, one of the problems with holding only two cars is that when you do have trips it becomes impossible to hide. So you have to be willing to hang on to pairs with a kicker as well.

Likewise, I can think of situations where I might hang on to four cards. For instance, if I had a weak hand that I was going to have to call with anyway, and I wanted my oponent to think I was on a flush or straight draw and get him to check to me.

The reason he’ll check to a flush or straight draw if he has something like 2 pair or trips is because either I made my hand, in which case I’ll raise, or I didn’t, in which case I’d fold. So he has absolutely nothing to gain by betting into me. That gets me a free look at his hand on the river with my mediocre one.

Poker being what it is, and me being poor enough that it’s not worth an experts time to take my money, I’ve never played in a game where I had to worry that much about the mathematics of the cards.

What’s it worth to you to see what I’d do with that hand?

Your chances if getting three of a kind are best if you draw three cards. Your chances of getting two pair or a full house are the same whether you draw two or three.

I assume you’re talking about poker with real cards and a table, not the video kind. At the table, you may want to keep the third card just for the bluffing potential as mentioned above, but I think the odds are better if you ditch it.

A local (Reno) column recently answered the question reguarding video poker. On a standard machine, you’re much better off keeping a low pair than a single face card (machines pay for jacks or better).

As a regular video poker player, always keep the pair and draw three.
If you are playing with other people, the bluff might work, but you are still screwing yourself out of the chance of getting four of a kind or full house or even three of a kind.

A more difficult question is what to keep if you have two aces, and four cards of the same suit. Keep the two aces, or keep the four of the same suit…

Thanks for all the advice. Although I do enjoy video poker, I was thinking specifically of the “real” draw poker at a table, the Jacks or better element of the video poker adds an entirely new dimension. I think hearing that taking 3 gives the same chance as getting 2 pair sealed it for me. What I wasn’t realizing is that the firist card I pull of that 3 is like I started with it, no matter what it is I have a certain chance of matching it, so why not pitch it? I wasn’t seeing the stats, but I needed to see the old rule about two coin flips. The chance of matching two coin flips is 1 in 2, because you’re matching to the first result so it doesn’t matter which it is. So if I pitch a card, the card replacing it has just as much chance to end up matching something as the card I threw away. Now that I’ve seen through the odds, I’ve got it.

Thanks, folks.

Showing why drawing three is better would be an enormous task.

I thought I might show the calculation for drawing a full house if you draw only two additional cards.

While more cards have been dealt than five in actual play, we won’t know which cards they were, so for figuring the probability 47 are left in the deck.

For illustration only, I will say the retained cards are two 10’s and an Ace.(It doesn’t matter which however).

The probability of drawing a full house is the additional of two simple cases.

Case #1: The “fourth” card is a 10, then an Ace

2/47 times 3/46

Case #2: The “fourth” card is an Ace, then EITHER a 10 or Ace

3/47 times 4/46

In all the real poker games I have seen, at least a pair of Jacks is required to open. Under those rules, if you have less than a pair of Jacks to start with, you are already beaten. If you insist on throwing your money away, then toss the high card and draw three to your pair. You might trip out, but probably not. You might draw two pair, but two pair are easily beaten. In other words, staying with a small pair against an opening pair of jacks (or better) isn’t worth it. Deal out five hands of five cards each, keep track of what your imaginary foes would do with each hand, and you’ll soon have a much better idea of what and what not to do.

This thread discusses the same question and has some calculations.

My experience in friendly, low-level poker games–the only place I’ve ever seen much five-card draw–is that the winner is usually the guy with the best five cards. The friendlier the game and the lower the limits, the less likely people are to fold, so bluffing them out becomes harder–you’re gonna get called too often to make it worth it.

In that situation, I’d probably sacrifice the bluffing potential of holding the third card for the better chance of improving my pair that I would have by ditching all three.

Dr. J

In my experience most hands are won with a pair.
If you have a decent pair and a good kicker I’d hang on to them and see how the betting goes (lots of raises->may want to get out; just the pot->stay in and try your luck).
Just me 2 cents.

Video poker resembles poker only in the look of the cards!

The machine does not, repeat, DOES NOT deal from a deck of 52.

The card you draw is based upon the pay-out settings not upon any mythical deck of cards.

That is not true. The cards are indeed dealt from a virtual deck of 52 cards, and the actual card distribution is as random as the game designers can make it.

There is no reason for the house to cheat, because they set the payout tables so ensure their profit. It’s a relatively easy matter to calculate the frequency of winning hands dealt from a random deck, and then to set the payout tables such that over the long run the house makes money.

But Video poker and its strategy are significantly different from regular poker, and the strategy varies depending on the payout tables for the particular game you are playing.