Figuring variance in Let it Ride

I deal at a charity casino and the pit boss was complaining that he was losing money on Let It Ride even though the payouts were pretty brutal. Royal Flush pays 30 to 1 ( instead of 1000:1) and Quads pay 15:1 ( instead of 50:1). I was going to figure out the house edge and variance of the game and of course looked at the wizard of odds site for information.

I looked at his tables and they show all the possible hands and the chance of getting that hand on a particular bet. For the Royal Flush, it shows 0 for Bet1, 0 for Bet 2 and 0.000002 for Bet 3. I get that. Then it shows for the Straight Flush, 0 for Bet 1, 0.000007 for Bet 2 and 3. How do you get a Straight Flush in 4 cards? I thought maybe they are figuring the chances of letting the second bet ride and then hitting but why wouldn't that be the same for the Royal Flush?
The straight through four of a kind also show a value for bet 2.

I'm probably missing something simple. Please help me out if you can.

And what about the straight flush? is that somewhere between 30 to 1 and 15 to 1?

In short though, even if all Straight flushes pay 30 to 1 or even less, this is still a decent paytable for a charity game! This is assuming the paytable pays normally for full houses and lower. (11/8/5/3/2/1 for FH/Flush/Straight/3K/2P/Tens or better)

Note, below ignores any possible strategy changes due to the paytable change, so this won't be exact, but it will be close:

If you look at Pay Table 1 in the Wizard of Odds Let it Ride section and sum the return values for all hands that are Full House and lower: this leads to a 7.815% house edge.

When the quads pay 50 to 1, the return from quads is 0.031582, so if this was lowered to 15 to 1, this reduces the payout to: 15/50*0.031582 = 0.0094746

For any straight flush paying 30 to 1: 30/200*0.006895 + 30/1000*0.004617 =0.00117276

Adding these two adjusted classes into the house edge leads to:

-0.07815 + 0.0094746 + 0.00117276 = -0.06750264 = 6.75% house edge.

The "Bet 2" and "Bet 3" on the page means how many wagers are earned on that particular hand. For example, basic strategy for the 1000 to 1 game says to never pull back a bet when you start off with 3 to a Royal. Therefore if you actually hit a royal, you'll always have 3 bets on it. For straight flush draws, sometimes you pull back the first bet and sometimes you don't. You'll never pull back the 2nd wager since you have 4 to a straight flush. That's why you have probabilities listed for "Bet 2" and "Bet 3"

This charity paytable has a much lower standard deviation than the original casino paytable. It's cut over in half because the payouts on quads or better are significantly reduced. But it is still 2.34 bets per hand where "bet" is a single bet of the 3 bet unit. If we assume a normal distribution (may not be ideal here given the community card nature of the game), over a smaller sample, variance can keep the players temporarily in the black. If 1000 hands are dealt, the house is expected to take 67.5 bets, but the standard deviation is 74 bets over 1000 hands. So after 1000 individual hands, the players are 18% likely to be ahead of the house. After 10,000 hands though, the house is expected to take 675 bets, with an SD of 234, so it's a near 3 SD event (2.88) by the normal distribution for the players to be in the black, and would have a likelihood of 1 in 510.

Edit: If you look at the Missouri Gaming Commission Slot/Table Game detail for July, "Let it Ride Bonus" lost for July at Ameristar St. Charles. My guess is that a couple of Royals hit that month near the payout cap. Royals pay out $50 or $75k max usually.

This link leads to an excel file:
http://www.mgc.dps.mo.gov/2013_fin/FY13_FinReport/detail0712.XLW

Quote: doctorz

I'm probably missing something simple. Please help me out if you can.

How well are the dealers trained? I deal charity and corporate games all the time, going on 4 years. Some dealers are near casino-level, others barely know you use cards for Blackjack.

When one of our clients has a Let-It-Die table, there is only one table and minimal instruction. We have 1-2 people who like dealing that game, but otherwise the dealers get a few minutes instruction from someone who is not very experienced at it themselves.

On BJ I have seen some mistakes that made me wish I could be a player and I would be the chairity for the night! No reason to think LIR is any different.

Remember, too, that charity dealers will not shuffle as well and protect the game as close as the real thing.

AZ definitely makes a good point here. If a dealer is making a significant error consistently, that could easily wipe away the inherent edge of the game.

Quote: tringlomane

AZ definitely makes a good point here. If a dealer is making a significant error consistently, that could easily wipe away the inherent edge of the game.

I imagine a common dealer error on that game for charity would be to allow a player to put back their first two bets if they make a winning hand. I was also going to suggest that the shuffling could make a difference as well, if the dealers are not using proper procedures, it would be very easy to deal out the pairs and three of a kinds.

Despite the significantly lower top payouts, if the above errors were occurring, the charity would be losing money since those payouts are the most frequent. You MIGHT be able to counteract that by taking the bottom payout from 10s or better to Kings or Aces at 1:1. This would eliminate a few more hands that get paid frequently. You could also start at two pair or three of a kind getting the lowest payout, but that would make the house edge so ridiculously high that you would lose nearly all play on the game.

Let It Ride is by nature a high-variance proposition, which is one of the reasons that it has survived so long (gamblers love variance!). Tell your pit boss that he/she should apply for a position at a major casino chain, because he/she already has experience in sweating statistically-insignificant losses and will fit right in!