My poker club currently has a daily high hand promo where the highest hand of the day gets $250 (must play both cards). If you win the day, you have the option of rolling it to the next day for double or nothing. The club gets 1-3 games of NLHE on a daily basis depending on the week and at least 1 game will go 8 hours.

I made quad 9, ten kicker last night for high hand of day. Sunday is a day they'll get 1 game, maybe a second for 3-4 hours. Should I roll it for double or nothing, or just collect free $250? Also, what's bare minimum hand you'd consider rolling.

FWIW, I rolled AAAAJ earlier this week and held for $500

Sent from my VS996 using Tapatalk

Got me on that one. Maybe the probability forum? Feel free to cross post, and I'll leave it here in case anyone wants to take a crack at the math or just has some "whAt high hands usually hold" observations to share.

Playing 9/10 handed over 8 hours you can expect to see a couple of quads. Straight flushes are still unlikely. So the break even point is going to be good quads but I'm not going to try to calculate it. I would guess quad tens or quad jacks.

It would be effectively impossible to calculate exactly because not every hand gets to the river. So the chances are lower then a simple 7 card calculation suggests. And this effects different hands to different degrees. If you play enough for it to really matter track what the winning hand is over time and work from that.

That's a fun wrinkle on the high hand promo. My room recently changed up the promo, but for a few years it was the high hand in a 4 hour period, minimum hand was AAAJJ. Usually there were 3 or 4 tables going, and it would almost always hit.

In my room the hand didn't have to play to the river. It just had to be a $10 pot to qualify. So if you had 23 and the flop came 222, you wanted to jam, because the turn card will counterfeit your kicker. You just had to show your hand when you dragged it to get the high hand.

Anyway, there's no way to get a perfect ev of whether to roll it over, but there's some good ways to estimate it. You say there are 1 to 3 games a day, with at least 1 going 8 hours? So it sounds like a light traffic room. So lets say the average is 2 games for 8 hours. So 16 hours of play. At 30 hands an hour, that's 240 hands per day. Assuming 9 hands dealt, that's 2160 hands per hour. The odds of making 4 of a kind by the river is 594:1. The odds of there being no 4 of a kinds dealt in a day is (1-1/594)^2160. Which is about 2.6%. So a 97.4% chance it hits that day. Then you can just break it down by combos. You can just change the 594 to reflect the odds of a certain hand or better getting built. So multiply it by 13 to get the odds of quad aces being dealt. You end up with about a 25% chance of quad A's being dealt, so I would definitely roll that over.

Doing some rough calculations, It seems like quad Q's is about the breakeven point. K's or A's and straight flushes I would roll over. J's or worse I'd take the money. This is all based on my very raw assumptions about hands per hour and traffic. It also assumes that all hands that have a chance of qualifying will go to the river, which isn't true. I assume most 4 of a kinds start out as pocket pairs that flop a set, and most PP's will see a flop. But other garbage that could make a qualifying hand, or runner/runner quads might never happen, so you can adjust down a bit if you want and gamble a bit more.

Maybe someone better at math than me can take a crack at it.

Can you only roll it one time?

Yes. Every person gets the option. To role their high hand one day. So if I roll quad 9s, the high hand for that day is worth $500. If it gets beat, then the person can roll that hand into the next day for $750

Sent from my VS996 using Tapatalk

Our casino in Melbourne has a royal flush jackpot that increases about a dollar every couple of minutes. You need to flop it though. Can range between $30k-$40k, has been up in the $80k range a few times..

Slightly unrelated to your question directly, but its funny because some people play any suited broadways for any price. (if you raise and people fold u can roll and request a flop)

Jackpots and promotions do change the way a lot of people play!

Another way to look at it is that there is a 0.245% chance of flopping quads if you have a pocket pair. Since you're only worried about quads better than yours, there's only a 3% chance of someone being dealt TT+. If you flop a set, you have about a 4% chance of getting the quad by the river. Added together, a quad that beats 9999 will happen about once every 6250 times.

Since it an even odds bet, and assuming a 10 person table, you wouldn't want more than 312 hands dealt during that day. About 100 hands will be dealt at the second table, so if the main table runs less than 7 hours, you should roll it over. Since it will run 8 hours, you shouldn't roll it over. You should rollover TTTT or better.

Quad Jack's was hit the next day for those interested. Thanks to all those who contributed and laid out mathematic equations

Sent from my VS996 using Tapatalk