seabarrister
seabarrister
Joined: Sep 8, 2021
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Mission146
September 8th, 2021 at 9:54:22 PM permalink
ASK THE WIZARD

Caesars seems to have placed a payout cap on its Mississippi Stud Tables of $50,000.

At a $5 or $10 ante this is a non-issue as even if you go against optimum strategy and raise to 3x on all rounds, you've put $100 on the table and the 500:1 Royal payout doesn't cross the $50K threshold.

However, at a $15 ante (and I have seen this as the table minimum) any Royal Flush should be played at Ante-1X-3X-3X or $120 at risk. The $50K cap would then cost the player $10K in payout.

Two questions: 1) (How) Does this affect the optimum strategy? and 2) how much worse does this make the house edge?

If you assume that you play rounds 1 and 2 the same and limit your round 3 bet with a Royal Draw to $25 (the felt does say "1x TO 3x" not "1x or 3x") you've avoided the cap, but you're then missing our on the extra $20 base when you hit a non-royal flush (costing you $120 in winnings), a straight ($80), or a high pair ($20).

Brut forcing that through below yields the following returns when you have 4 to a royal flush draw in any suit (I'll use spades and X is the rank that is missing in the draw):

2h: saved $20
2d: saved $20
2c: saved $20
2s: lost $120
3h: saved $20
3d: saved $20
3c: saved $20
3s: lost $120

This repeats through the 8's rank

9h: saved $20
9d: saved $20
9c: saved $20
9s: lost $2000 the 1 in 5 times the Royal Draw is 10,J,Q,K and $120 the other 4 in 5 times =$2000*.2 + $120*.8 = $496

Xh: Lost $80
Xd: Lost $80
Xc: Lost $80
Xs: zero as this payout is capped at the $20 reduced 3rd Street bet

10h: break even 80% of the time, the other 20% cover by the Xh, above $0
10d: break even 80% of the time, the other 20% cover by the Xd, above $0
10c: break even 80% of the time, the other 20% cover by the Xc, above $0
10s (already in hand 80% of time and cover by the Xs above the other 20%) = $0

Jh: lost $20 80% of the time = $16
Jd: lost $20 80% of the time = $16
Jc: lost $20 80% of the time = $16
Js: (already in hand 80% of time and cover by the Xs above the other 20%) = $0

Repeats for Queens, Kings and Aces ranks.

So over the course of the 48 cards dealt when one has a royal flush draw, reducing your bet on 3rd street to avoid the payout cap yields the following returns:
2-8 ranks (20+20+20-120) x 7 = -$420
9s rank (20+20+20-496) = -$436
10s rank no change -0-
J-A ranks (-16-16-16) x 4 = -$192

= an expected loss of $1048/48 or $21.83 per hand by reducing your bet on third street to avoid the royal payout cap.

Does anyone care to critique my math or method? Also, it seems that this would stay consistent until the straight flush hits the cap which would be a $62.50 ante at optimum strategy (50,000/100 (payout of the SF) /8 (antes at 1x-3x-3x)).

As for the effect on house edge, and assuming that my analysis above is correct and that the cap has no effect on optimum strategy, the return for the royal drops from .006156 to 5/6 of that at $15 (100/120) or .005130 and increases the house edge from 4.9149% to 5.0175% (and this change worsens as the ante increases above $15).

Anyone care to take a stab and the impact of trying to modify the 2nd street bet to avoid the cap instead?
gordonm888
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gordonm888
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September 9th, 2021 at 12:05:56 AM permalink
First of all, welcome to the forum! That's a very impressive post for a newcomer.

I'm not surprised at your major conclusions.

I have a Miss Stud calculation system on Excel. Specifically, I believe I can cap the payout for Royal Flushes and then analyze a starting hand of QJs and examine whether any changes in the 2nd street bet size are warranted. I have a lot of projects in my life right now, but I'll try to find time to take a look at it.

And maybe, one of the other math wizards may weigh in on this before I get to it.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
Mission146
Mission146
Joined: May 15, 2012
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September 9th, 2021 at 8:40:58 AM permalink
Excellent post!

This is a concept that is typically referred to as, "Maximum Aggregate Payout," and is often applied to the base payouts (as opposed to side bets with Progressives) for many Table Games.

Question 1: How Does this impact Optimal Strategy?

Answer: Don't let it. Simply don't bet such that you would go over the Maximum Aggregate Payout. If the Table Minimum is such that the winnings would otherwise be over the Maximum Aggregate Payout, don't play. If the casinos don't want to pay the paytable, then they should not accept the bet.

Question 2: How much worse does this make the House Edge?

Answer: The question is complicated. By necessity, the more you are betting, the worse the House Edge is because that's a greater proportion of the applicable payouts that you are NOT being paid, and thereby, are essentially playing against a reduced paytable. Secondly, if you were absolutely determined to bet such that the MAP could come into play, then there might perhaps be deviations from (otherwise Optimal) strategy which could themselves differ based on how much is being bet.

The easiest way to figure it out without changing strategy is just to look at the applicable wins according to the probabilities on Wizard of Odds, then adjust accordingly for the modified payouts. You'd only have to do this for one bet level as it would also tell you how much you are losing per each dollar bet over what the maximum would otherwise be.

As non Royal Flush payouts get added, then you would have to account for those as well.

Either way, the best thing to do is for everyone to simply NOT bet more than what the casino is willing to pay the paytable on. If they can't afford to pay the paytable, then they shouldn't allow you to bet that much.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
LuckyPhow
LuckyPhow
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September 9th, 2021 at 11:11:18 AM permalink
Quote: seabarrister

ASK THE WIZARD

Caesars seems to have placed a payout cap on its Mississippi Stud Tables of $50,000.
[ ... ]
Does anyone care to critique my math or method?



I just have one note about the $50K max payout cap. Several years ago, I surveyed Biloxi casinos. All casinos that had payout caps told me that the max payout was per hand for the entire table, and not for each individual player's hand.

For example, you could have a Royal Flush where your payout did not exceed $50K. However, If I had the 8-9-10-J-Q straight flush, then neither of us would get a full payout. I wondered whether or not your analysis assumed you were the only gambler playing at the time. My apologies if I'm the one confused.
Wizard
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Wizard
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MrCasinoGames
September 9th, 2021 at 11:16:15 AM permalink
Let me also say, good post.

Forgive me if I don't get into the math. My advice is to never bet more than the maximum payout divided by the maximum odds.

Example:

Let's say the maximum payout is $50,000
A royal flush pays 500 to 1 in Mississippi Stud.
$50,000/500 = $100.
So, $100 should be my maximum FINAL bet.
The final bet can be 7x the initial ante, so I divide $100 by 7, to get a maximum ante of $14.28. However, I'd just round that down to $10.

A decent question is how much expected value is lost with a $15 bet?

If that is too little to make it fun for me, I won't play.
Last edited by: Wizard on Sep 10, 2021
It's not whether you win or lose; it's whether or not you had a good bet.
DRich
DRich
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September 9th, 2021 at 3:06:20 PM permalink
Quote: LuckyPhow

Quote: seabarrister

ASK THE WIZARD

Caesars seems to have placed a payout cap on its Mississippi Stud Tables of $50,000.
[ ... ]
Does anyone care to critique my math or method?



I just have one note about the $50K max payout cap. Several years ago, I surveyed Biloxi casinos. All casinos that had payout caps told me that the max payout was per hand for the entire table, and not for each individual player's hand.

For example, you could have a Royal Flush where your payout did not exceed $50K. However, If I had the 8-9-10-J-Q straight flush, then neither of us would get a full payout. I wondered whether or not your analysis assumed you were the only gambler playing at the time. My apologies if I'm the one confused.
  • link to original post



    Correct, there was a case recently where the pit boss forgot to put the sign on the table for the maximum payout. The Gaming Regulator rightly sided with the player and made the casino pay him the full odds.
    Order from chaos
    seabarrister
    seabarrister
    Joined: Sep 8, 2021
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    Thanks for this post from:
    Mission146
    September 9th, 2021 at 3:27:22 PM permalink
    Thanks for the reply! And please don't take this as a lack of gratitude, but I was really looking forward to the math lesson :)

    Two points/questions:

    First, as the optimum strategy for any non-paired hand on 1st street is Fold or 1x (only JQ suited even comes close to supporting a 3x bet), the final bet for a Royal should never be more than 8x antes, so the math would be $100/8 or $12.50 (though I don't know that they'll let you play the pink chips at the Miss Stud Table)

    As to your (and Mission 146's) point about not betting enough for it to matter, I'm actually beginning to see with more and more frequency a $15 table minimum. The crowd I gamble with love them some Mississippi Stud, so I occasionally buck the 4.915% house edge to be social. I'm just trying to see how much worse this house edge is at the $15 min tables. After all, if we're playing Mississippi Stud over Blackjack, we've accepted a good deal of cost (in terms of house edge) for the video game/slot machine nature of carnival games. If it's an increase of a few tenths of a percentage point, that's one thing.. if it's 1/2 a percent or more, I may have to teach them craps and let them make all the inside bets they want.
    DRich
    DRich
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    September 9th, 2021 at 3:30:15 PM permalink
    Quote: seabarrister

    Thanks for the reply! And please don't take this as a lack of gratitude, but I was really looking forward to the math lesson :)



    That is great to hear. Most new posters want nothing to do with the math because it will disprove their method.

    "That math makes no sense, my friend does it this way and he wins every time".
    Order from chaos
    seabarrister
    seabarrister
    Joined: Sep 8, 2021
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    September 9th, 2021 at 3:30:39 PM permalink
    Quote: gordonm888

    First of all, welcome to the forum! That's a very impressive post for a newcomer.

    I'm not surprised at your major conclusions.

    I have a Miss Stud calculation system on Excel. Specifically, I believe I can cap the payout for Royal Flushes and then analyze a starting hand of QJs and examine whether any changes in the 2nd street bet size are warranted. I have a lot of projects in my life right now, but I'll try to find time to take a look at it.

    And maybe, one of the other math wizards may weigh in on this before I get to it.

  • link to original post



    Thanks for the reply! Any chance you would share your spreadsheet?
    Mission146
    Mission146
    Joined: May 15, 2012
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    September 9th, 2021 at 4:28:47 PM permalink
    Quote: seabarrister

    Thanks for the reply! And please don't take this as a lack of gratitude, but I was really looking forward to the math lesson :)

    Two points/questions:

    First, as the optimum strategy for any non-paired hand on 1st street is Fold or 1x (only JQ suited even comes close to supporting a 3x bet), the final bet for a Royal should never be more than 8x antes, so the math would be $100/8 or $12.50 (though I don't know that they'll let you play the pink chips at the Miss Stud Table)

    As to your (and Mission 146's) point about not betting enough for it to matter, I'm actually beginning to see with more and more frequency a $15 table minimum. The crowd I gamble with love them some Mississippi Stud, so I occasionally buck the 4.915% house edge to be social. I'm just trying to see how much worse this house edge is at the $15 min tables. After all, if we're playing Mississippi Stud over Blackjack, we've accepted a good deal of cost (in terms of house edge) for the video game/slot machine nature of carnival games. If it's an increase of a few tenths of a percentage point, that's one thing.. if it's 1/2 a percent or more, I may have to teach them craps and let them make all the inside bets they want.

  • link to original post



    Lack of gratitude? I take it as a compliment! Iíll knock it out in the morning when Iím back on the computer.
    https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219

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