A rare edge on Royal Match

**Optimus Prime** · 11-29-2018, 10:14 AM

The other night, the dealer exposed a card - a king - and the guy at first base was told that would be the first card on his next hand. So he decided to bet on the Royal Match, figuring he had one of the 2 cards needed for the big payout. Luckily, he got a suited queen for his next card, winning a 25:1 payout. Whole table erupted, including the dealer.

So of course I had to calculate what his EV was on that bet. I got +35%. Can someone make sure I'm right? This was a 6-deck game, I don't know what the count was at the time, and royal match pays 2.5X your bet if you get any suited pair and 25X if you get suited king and queen.

RS · 11-29-2018, 01:37 PM

I get 30.38% advantage on the side bet only. How did you come up with 35%?

(6*25/311) + (71*2.5/311) - (233/311)

**DSchles** · 11-29-2018, 01:52 PM

Originally Posted by RS

I get 30.38% advantage on the side bet only. How did you come up with 35%?

(6*25/311) + (71*2.5/311) - (233/311)

Your numerators don't add to 311. The last one should be 234. The edge is 30.06%.

Don

**Optimus Prime** · 11-29-2018, 02:08 PM

I'll figure out where my error was. I was doing some rounding, as I mostly wanted to make sure this was a good bet. I've seen enough things like that happen I'm starting to think I should try to sit at FB... I'd have bet as much as they'd let me on both the main bet and the Royal Match if it had been me. Alas.

**DSchles** · 11-29-2018, 02:39 PM

Originally Posted by Optimus Prime

I'll figure out where my error was. I was doing some rounding, as I mostly wanted to make sure this was a good bet. I've seen enough things like that happen I'm starting to think I should try to sit at FB... I'd have bet as much as they'd let me on both the main bet and the Royal Match if it had been me. Alas.

Keep in mind that, for the side bet, the variance is huge. Optimal wager is always tempered by the ratio of a winning payoff to a losing one. I think the average squared result of this is about 14, so the right bet isn't very much more than 2% of your bank.

Don

**Optimus Prime** · 11-29-2018, 02:54 PM

Originally Posted by DSchles

Keep in mind that, for the side bet, the variance is huge. Optimal wager is always tempered by the ratio of a winning payoff to a losing one. I think the average squared result of this is about 14, so the right bet isn't very much more than 2% of your bank.

Don

Yes, I wondered about that. Given the multiple payouts, I figured variance wasn't so bad on this one. So how could I calculate the SD and variance for this bet (assuming I know my first card will be K or Q).