Mississippi Stud Payout Cap

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?

My strategy for straight flush & Royal Flush would be 8X the ante total bet, because I didn't know I had a hand until the third card but...

WOO strategy is:
How to Play Three Cards

Raise 3x with:

Three of a kind
Pair of sixes or higher
Royal flush draw
Straight flush draw with three connected cards 567 or higher
Straight flush draw with one gap and at least one card jack or higher
Straight flush draw with two gaps and at least two cards jack or higher
Raise 1x with:

Any three-card flush
Pair of 2's through 5's
At least three points
Straight draw of three connected cards 456 or higher
Straight draw with one gap and at least two cards six and higher
All other hands should be folded.
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I'd probably max out at the $50 bet to collect $25K on the 4 of a kind or $50K on the straight flush and not give the Royals much thought. $60 max bet if I play for 8X the ante. Why some table maximums are $1,000 or $2,000 when they won't pay $1M or $5M ($1K bet) or $2M or $10M ($2K bet) is beyond me, because that's what I'd be there for, the million dollar payouts.