Poker Punch Cards - How to estiamte odds of filling the card
January 25th, 2018 at 11:42:41 AM
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Some buddies in DFW TX have a rotating poker club where we host at various of our houses frequently. Completely non raked, home homes with friends.
We have a player-pool of donation funds that we use to do fun gimmicky games like high hand etc. WE HAVE A NEW IDEA we want to try... but can't figure out how to estimate the risk of depleting the funds too fast (or the hosts going into debt to pay them!). Can you help advise please?
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Idea: Poker Punch Cards (Texas Holdem only)
Premise: Each player will have a card with seven spots representing hands. Once they punch all (or some... see below) of the spots, they get a flat payout of $xx.
The cards will likely have the following SEVEN punch spots:
1. Three of a kind
2. Straight
3. Flush
4. Full House
5. 4 of a Kind
6. Straight Flush
7. Royal Flush
Player will be able to redeem at one of FOUR levels (dollar amounts are examples): $50 after the first 4 punches (up to the full house), OR $100 at the 4 of a Kind, OR $200 at the Str Flush, OR $500 at the Royal.
Knowns:
* We play an average of twice a week.
* Each game plays an average of 12 table hours.
* Average # of players per table is 8.
* Average hands per hour is 25.
* Extrapolated, that means about 2400 hands dealt per game.
* Player pool will be seeded at about $500, and will increase about $135 per game.
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Main Question: Can you advise, or provide a spreadsheet example, on how to even start the whole estimate of how quickly these punch cards will get punched at each level (trips-thru-full house, +4oaK, +Str Flsh, +Royal), using the knowns above? Something that is close to the average pool increase of $135 per game.
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Other Questions:
* What affect: Just showing five cards (whether called or folded) vs requiring Showdown at river?
* Must win hand to get the punch or just be at showdown?
* Must play one, or both hole cards? (if not... when a shared-board has the nuts, a LOT of punches can happen. Example board: AAAAQ)
* I assume we can simply alter two things to 'balance' the risk over time as we gather real-world stats: 1) The hand qualifiers (like A-high flush instead of Flush, and J's full instead of Full House) -- and 2) The amounts paid out for each level.
We have a player-pool of donation funds that we use to do fun gimmicky games like high hand etc. WE HAVE A NEW IDEA we want to try... but can't figure out how to estimate the risk of depleting the funds too fast (or the hosts going into debt to pay them!). Can you help advise please?
--------------------
Idea: Poker Punch Cards (Texas Holdem only)
Premise: Each player will have a card with seven spots representing hands. Once they punch all (or some... see below) of the spots, they get a flat payout of $xx.
The cards will likely have the following SEVEN punch spots:
1. Three of a kind
2. Straight
3. Flush
4. Full House
5. 4 of a Kind
6. Straight Flush
7. Royal Flush
Player will be able to redeem at one of FOUR levels (dollar amounts are examples): $50 after the first 4 punches (up to the full house), OR $100 at the 4 of a Kind, OR $200 at the Str Flush, OR $500 at the Royal.
Knowns:
* We play an average of twice a week.
* Each game plays an average of 12 table hours.
* Average # of players per table is 8.
* Average hands per hour is 25.
* Extrapolated, that means about 2400 hands dealt per game.
* Player pool will be seeded at about $500, and will increase about $135 per game.
-----------------
Main Question: Can you advise, or provide a spreadsheet example, on how to even start the whole estimate of how quickly these punch cards will get punched at each level (trips-thru-full house, +4oaK, +Str Flsh, +Royal), using the knowns above? Something that is close to the average pool increase of $135 per game.
-------
Other Questions:
* What affect: Just showing five cards (whether called or folded) vs requiring Showdown at river?
* Must win hand to get the punch or just be at showdown?
* Must play one, or both hole cards? (if not... when a shared-board has the nuts, a LOT of punches can happen. Example board: AAAAQ)
* I assume we can simply alter two things to 'balance' the risk over time as we gather real-world stats: 1) The hand qualifiers (like A-high flush instead of Flush, and J's full instead of Full House) -- and 2) The amounts paid out for each level.
January 25th, 2018 at 12:44:19 PM
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Do both cards have to play?
What if the hand is on the board?
Fist level for $50 seems too generous.
What if the hand is on the board?
Fist level for $50 seems too generous.
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
January 25th, 2018 at 12:47:00 PM
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Hi TenPercenter, and welcome to the forums.
I like your idea. While I apologize I don't have time to crunch some numbers off the top of my head... I'd say you should be fine to go ahead and start a fund for your Punch Card idea. The odds of any 1 person hitting a royal flush in texas hold 'em is ~1/650,000... the odds of a straight flush are ~1/72,200... just those two alone would take quite some time to achieve. The Trips, Straight, and Flush would be done possible in a session or two, but the upper ones, such as quads and above would take a while longer. Some players, who play live, go years without hitting a royal flush, or even a straight flush.
You should look at the frequencies and the payback though. From what you mentioned I would probably constantly redeem my punch after the first 4, unless I was lucky enough to hit quads or something during the current card. You should give incentive to go for the higher hands and weight the pays more towards the top. I think you're giving too much away for the bottom 4, which aren't too difficult to hit (especially if someone always chases their flush draw because they need that last on their punch card).
I also presume similar to a casino/bad beat jackpot you must finish the hand and have a shown down to get a punch? What if I have a flush, but am certain you have a boat and I fold face up, do I get a punch for the flush? This is a fun idea, but I think your payouts make it too easy to get the bottom one as of now. It depends on you guys and your game, and it's up to you, but I'd be fine if someone "showed their hand" after they win the pot to prove they had the hand. I.E. Must win the pot, and must show your hand to prove the qualifying hand. You'll have to decide if you need both cards to play. I'd assume if the board is the 5 card hand so long as they STAYED IN to chop the pot they would get that as a qualifier (unless your group determines you MUST play 1 card min from your own 2 starting cards). If you wanted to pay the card out less to build the pot more you could make it so they had to have a showdown on the river and win the pot.
Again, I haven't hard crunched the numbers, but just my suggestion. In 2400 hands you'll expect to hit:
1) Trips = ~52
2) Straight = ~9.5
3) Flush = ~5
4) Full House = ~3.5
Of course with poker strategy and folding I'd assume these numbers would go way down for qualifying... as 7-4 off is going to fold the majority of the time and if the flop comes 4-4-Q then they won't get the qualifying trips. Still, it wouldn't be far from it for 1 player to get the majority or all of these in one session.
I like your idea. While I apologize I don't have time to crunch some numbers off the top of my head... I'd say you should be fine to go ahead and start a fund for your Punch Card idea. The odds of any 1 person hitting a royal flush in texas hold 'em is ~1/650,000... the odds of a straight flush are ~1/72,200... just those two alone would take quite some time to achieve. The Trips, Straight, and Flush would be done possible in a session or two, but the upper ones, such as quads and above would take a while longer. Some players, who play live, go years without hitting a royal flush, or even a straight flush.
You should look at the frequencies and the payback though. From what you mentioned I would probably constantly redeem my punch after the first 4, unless I was lucky enough to hit quads or something during the current card. You should give incentive to go for the higher hands and weight the pays more towards the top. I think you're giving too much away for the bottom 4, which aren't too difficult to hit (especially if someone always chases their flush draw because they need that last on their punch card).
I also presume similar to a casino/bad beat jackpot you must finish the hand and have a shown down to get a punch? What if I have a flush, but am certain you have a boat and I fold face up, do I get a punch for the flush? This is a fun idea, but I think your payouts make it too easy to get the bottom one as of now. It depends on you guys and your game, and it's up to you, but I'd be fine if someone "showed their hand" after they win the pot to prove they had the hand. I.E. Must win the pot, and must show your hand to prove the qualifying hand. You'll have to decide if you need both cards to play. I'd assume if the board is the 5 card hand so long as they STAYED IN to chop the pot they would get that as a qualifier (unless your group determines you MUST play 1 card min from your own 2 starting cards). If you wanted to pay the card out less to build the pot more you could make it so they had to have a showdown on the river and win the pot.
Again, I haven't hard crunched the numbers, but just my suggestion. In 2400 hands you'll expect to hit:
1) Trips = ~52
2) Straight = ~9.5
3) Flush = ~5
4) Full House = ~3.5
Of course with poker strategy and folding I'd assume these numbers would go way down for qualifying... as 7-4 off is going to fold the majority of the time and if the flop comes 4-4-Q then they won't get the qualifying trips. Still, it wouldn't be far from it for 1 player to get the majority or all of these in one session.
Playing it correctly means you've already won.
January 26th, 2018 at 12:51:15 PM
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Quote: Romes
Again, I haven't hard crunched the numbers, but just my suggestion. In 2400 hands you'll expect to hit:
1) Trips = ~52
2) Straight = ~9.5
3) Flush = ~5
4) Full House = ~3.5
Thanks so much for the deep and thoughtful response Romes.
Question on the above... can you show me how to get the estimate those, so that we can get it into a spreadsheet and more deeply massage the odds/frequency of them hitting? (such as instead of TRIPS, making the requirement trip 8's or better etc)?
