Paigowpoker without the higher/lower hand rule.

"The player will separate his seven cards into a five-card high hand, and two-card low hand. The high hand must be of higher poker value than the low hand."

Is there any advantage if this rule doesnt exist for the player in paigowpoker? (if the bank does have to follow the standard rule.) And what would be the advantage for the player. I mean the rule that the high hand must be higher of value than the low hand.

How would you set 2234578 if you didn't have to have the hands ordered properly? You're a damn fool if you say anything other than 22 and 34578. So obviously there's an advantage.

Why would anyone spend time figuring out the advantage for you?

The hand with 5 cards will get weaker when moving the best hand to the small one so probably there is no advantage

There would be a huge player advantage, assuming the house had to play the house way. You wouldn't win more often; what you would do is push a lot more of your weak hands, like the example above. If you set that as required, it's going to lose maybe 90% of the time and push the other 10%. But if you were allowed to play the deuces up, you'd push about 50% of the time, maybe more. (dealer having less than a pair up). Not willing to look up exact percentages on any of what I said, but it's that big a difference.

Quote: beachbumbabs

There would be a huge player advantage, assuming the house had to play the house way.

The house way would assuredly be amended to reflect the new rule change. It would probably get very simple too. Always play the best two-card hand possible.

Quote: megaboy

The hand with 5 cards will get weaker when moving the best hand to the small one so probably there is no advantage

Read Sabre's post again.

If you look at his example, what you see is what would normally be a high hand that is extremely likely to lose and a low hand that is extremely likely to lose. What is the result? You're extremely likely to lose your bet. Now, if you don't have the Rule, you can split them to a High Hand that is extremely likely to lose and a low hand that is very likely to win, making the most likely result a Push.

When you lose, you lose money. When you Push, you do not lose money. The conditions under which you have a hand expected to win money do not change. If you win at the same rate and lose at a lesser rate you lose less overall. If you lose less overall that affects the House Edge. If you lose less overall on a game that already has a comparatively low house edge, then the result is probably going to be a player edge.

Will I do the math on it for you? Maybe, my first condition is you tell me where the game is! (I know, not likely)

Perhaps more interesting would be determining the optimal house way for this version where any split is legal. The algorithm in Finding The Edge should still work...

Quote: Mission146

Read Sabre's post again.

If you look at his example, what you see is what would normally be a high hand that is extremely likely to lose and a low hand that is extremely likely to lose. What is the result? You're extremely likely to lose your bet. Now, if you don't have the Rule, you can split them to a High Hand that is extremely likely to lose and a low hand that is very likely to win, making the most likely result a Push.

When you lose, you lose money. When you Push, you do not lose money. The conditions under which you have a hand expected to win money do not change. If you win at the same rate and lose at a lesser rate you lose less overall. If you lose less overall that affects the House Edge. If you lose less overall on a game that already has a comparatively low house edge, then the result is probably going to be a player edge.

Will I do the math on it for you? Maybe, my first condition is you tell me where the game is! (I know, not likely)

Let's do this simply.

Player is dealt: 22-87543.

Standard way 5-card hand must be high: 22-345 wins about 18% of the time, 87 in front wins <1% of time.
Not only does 87 in front win very rarely, but it only wins when the dealer has a straight, or flush or straight flush in the back 50-card hand. So, the player's expectation:
Win 0.00
Push about 0.19
Lose: 0.81
EV = - 0.81.

Player's 2 card hand may be higher than 5 card hand 5 card hand is 87543 which wins against the dealers 5-card hand
0% of the time. The two card hand is 2-2, which wins about 75% of the time. So the player expectation is:
Win: 0.00
Push: 0.75
Lose: 0.25
EV = - 0.25

So, providing the player this freedom made a difference of 0.56 of the bet in the expected value of this one hand.

Quote: gordonm888

So, providing the player this freedom made a difference of 0.56 of the bet in the expected value of this one hand.

Nice work!

Indeed, there are also going to be higher hands that are more border-line type plays that will also offer additional value to the player. I suspect that, in most cases of a player having only One Pair with no straights/flushes or anything like that, that it would benefit the player to play the pair on the Low hand.