Card game math question

Just a quick math question. About how often does a player obtain any pair in the fourth and fifth card positions in a video poker game? I believe this happens quite often but i don't know the percentage. Any help is appreciated.

Quote: RealizeGaming

Just a quick math question. About how often does a player obtain any pair in the fourth and fifth card positions in a video poker game? I believe this happens quite often but i don't know the percentage. Any help is appreciated.

I'll take a stab at it. I don't think the positions matter, the math would be the same. So the number of combinations for the fourth and fifth position would be 52X51/2 = 1326

There are 78 2-card combinations that make a pair:
4X3/2 times 13 ranks = 78

1326/78 = 17

So the frequency of a pair landing in the fourth and fifth positions would be 17.

I know I'm going to get this wrong but here goes....

If you mean fresh off the deal, assuming the 4th card does not match any of the previous 3 I think the chances are 3 out of 48 or about 6% that the 5th card matches the 4th.

This is not correct, but I can see how someone would go down this road.

Ask yourself this - does it matter if the cards in position 1-3 are dealt face up or face down? You should be able to convince yourself that it does not.

If numbers 1-3 are dealt face down and number 4 face up, 3 of the 51 unexposed cards match the one face up in position 4. Thus, 1 in 17.

I totally understand. Thanks.

This would be an ending hand of video poker. The player gets a chance to hold or discard any cards but the ending hand must have a pair in the two last card positions in the hand.

To clear up my question and to show why i was curious about the math, i'm copying the link to my video poker game called slide poker. The demo link is down, but the video explains the game.

http://youtu.be/GbUjqgzRolY

So, about every 17 hands i can expect the slide bonus to happen.

You blew my simple mind!

You guys are amazing in how you figure this stuff out.........thanks!

The numbers that Mickey gave are on the deal. So, the frequency of the bonus will be better than 1 in 17, because it is rare to throw out a pair.

Quote: RealizeGaming

To clear up my question and to show why i was curious about the math, i'm copying the link to my video poker game called slide poker. The demo link is down, but the video explains the game.

http://youtu.be/GbUjqgzRolY

So, about every 17 hands i can expect the slide bonus to happen.

Read with caution, this got long.

Oh. Well, that changes things. It definitely depends on the paytable, and the payoff for getting it is going to factor into the strategy decisions, which will affect the odds. You'll need to hire a mathematician for that. My gut is that this analysis would not be too difficult and an experienced gaming mathematician could do it in a few hours.

With a normal-ish paytable, my (very rough) estimate is that it would be about 1 in 8-12 hands. This is a large range. To get something more precise, you'll need to have some software written to step through a reduced set of all of the possibilities to get a thorough analysis and determine optimal strategy. There is some symmetry in the deck, but there are lots of possibilities to look at. My line of thinking on my admittedly rough estimate is that you're probably almost always keeping a position 4 and 5 pair when it's dealt, which is 1 in 17, and you're going to stumble into others on the draws, which increases the probability.

Please note, a lot of what follows is just my opinion. You're free to take it or leave it. Here is the hurdle that you're going to have to get over. You're giving the player something - in this case, 3 free hands with a held pair sometimes. This is going to add a good amount of expected value to the game. Decent poker paytables already pay back 95% or more, so you can't just give away something that adds much to the player's expected value and still have a game casinos are going to want to offer.

One option is to push down the pays. This causes two problems. First, a lot of players choose games based on paytables. If you push down the pays, a lot of people are going to walk past this game and go find machines with more attractive paytables. Secondly, the more you tinker with the pays, the larger the impact is to the optimal strategy. A lot of people don't want to learn new strategies, especially if they are very different from what they already know and like.

Another option is to leave the paytable alone and charge an extra number of credits. For example, charge a 5 credit maximum bet with an extra 3 credits (or whatever it takes to make the expected value something reasonable) to activate the feature, so the extra amount the player has to bet brings the expected value down by almost all of the extra expected value that is added by the sliding pair feature. There are probably some games that do this and are successful (I honestly don't play much video poker) but I would imagine a lot of players loathe paying extra to play a 5 coin paytable.

You really need to hire someone to work out the math. With his or her help, you will find that this is a concept that can be shaped into a game that is attractive (players will give it a try), fun (players will want to play it instead of something else), and realistically can be offered by a casino (it pays back a sensible percentage). Or you will find that it is a novel concept that will not make a good casino game, and you can move onto something else.

Quote: G71

Read with caution, this got long.


One option is to push down the pays. This causes two problems. First, a lot of players choose games based on paytables. If you push down the pays, a lot of people are going to walk past this game and go find machines with more attractive paytables. Secondly, the more you tinker with the pays, the larger the impact is to the optimal strategy. A lot of people don't want to learn new strategies, especially if they are very different from what they already know and like.

Another option is to leave the paytable alone and charge an extra number of credits. For example, charge a 5 credit maximum bet with an extra 3 credits (or whatever it takes to make the expected value something reasonable) to activate the feature, so the extra amount the player has to bet brings the expected value down by almost all of the extra expected value that is added by the sliding pair feature. There are probably some games that do this and are successful (I honestly don't play much video poker) but I would imagine a lot of players loathe paying extra to play a 5 coin paytable.

You really need to hire someone to work out the math. With his or her help, you will find that this is a concept that can be shaped into a game that is attractive (players will give it a try), fun (players will want to play it instead of something else), and realistically can be offered by a casino (it pays back a sensible percentage). Or you will find that it is a novel concept that will not make a good casino game, and you can move onto something else.

Great information. My current plan is to increase the number of credits needed to play the game. I don't like messing with the pay scale too much since i know most vp players like the familiar payouts. Shortly after the math is completed on the bonus discard poker game, i intend to get the math done on slide poker. Thank you so much for your response.