The Infield Fly Rule and 6:5 Even Money

Sports aficionados take great delight in explaining the esoteric rules of their favorite sport, so much so that those rules are no longer esoteric. Sunday couch potatoes know the difference between “the call stands” and “the call is confirmed.” Olympic hockey fans know why T.J. Oshie became the Russian nemesis. And those who watch regular-season baseball games know about the Infield Fly Rule, probably the most famous “esoteric” rule in sports.

Without getting into the details or the horribly written letter of the law, the idea is this. Let’s say there’s no one out, runners on first and second. The batter hits a short pop-up to the third baseman. Under the IFR, the batter is called out (the umpire will raise his arm even before the ball has dropped from the sky), even if the third baseman drops the ball. Without the IFR, the runners on base would have to wait, assuming the easy fly ball would be caught, but then the third baseman could intentionally let the ball fall to the ground, pick it up, tag third for the force out, throw to second base for the force out (double play), and then the throw to first base could potentially complete the triple play. The IFR prevents the defense from intentionally dropping the ball to turn a double/triple play.

It makes no sense to me why a new rule would be created to protect the offense here. The pitcher succeeded in getting the batter to pop up the ball. To hit into a double/triple play is a bad mistake for the offense—too bad for you! Introducing a rule introduces arguments. People don’t understand the rule. The rule has some conditions that are discretionary for the umpire (whether the ball could have been caught with “ordinary effort”). The wording varies in different leagues (Little League, softball, MLB).

Perhaps the baseball “purists” felt that intentionally dropping the ball would be a crime against nature, and that “bad play” should never be encouraged/allowed. But it isn’t bad play. It’s situational baseball. In football, it would often be correct for the team that is ahead very late in the game to intentionally down the ball on the 1-yard line, instead of scoring the easy touchdown, in order to maintain possession to run out the clock. Or in basketball, a player might intentionally miss a free throw, in the hopes of rebounding the live ball to shoot a 2-pointer or 3-pointer. Fouling the opponent intentionally (which would probably be considered “bad basketball” in some sense) is the norm for the trailing team in the last couple minutes.

These situational plays sometimes add intrigue, and give the smart team another way to separate itself from the donks. Wouldn’t the simple pop-ups in baseball become more exciting if the fielder has to choose whether to let the ball drop, and then attempt to pick it up quickly and go for the double play? If he succeeds, the double or triple play would become a SportsCenter Top 10 play, and sometimes he’ll fail, possibly even throwing the ball away if his teammate isn’t ready for the throw to the base. Sometimes, the fielder would catch the ball, and all the commentators would then chime in about how the smart play would have been to intentionally let the ball drop!

The defense is allowed to intentionally walk the batter, allowing the pitcher to face a weaker batter with a chance for a double play. There is no rule to disallow intentional walks.

For those who live in casinos, their “sport” is gambling, and they, too, take pride in knowing the esoteric rules and procedures pertaining to casino life. Longtime gamblers explain with a hint of pride (!) that you must use only one hand on the cards in handheld blackjack or carny games. On a game like Ultimate Texas Holdem, the grizzled veteran will instantly jump on the newbie to correct the placement of the cards after the Play bet has been made, as if the newbie is an idiot for not knowing the local style (as if there were some standard).

And so it is with taking “even money” in a 6:5 blackjack game. The grizzled “veteran” dealers and pit bosses will triumphantly explain, “You can’t take even money in 6:5 blackjack” as if that’s some deep mathematical truism that only they can understand. They might even say the quiet part out loud: “You can’t take even money in 6:5 blackjack—duh!”

But the real reason you can’t take even money in 6:5 blackjack is because the Table Games Manager is an idiot.

Let’s look into “even money.” In a traditional 3:2 game, if you have a blackjack and the dealer has an Ace up, you can just say “even money” and the dealer will pay you 1:1 on your natural, before she checks whether she has blackjack herself. This “even money” turns out to be equivalent to buying insurance on your blackjack. Let’s see why. Suppose you bet $100, and you get a snapper, and you put up a $50 insurance bet against the dealer’s Ace up. If the dealer has no blackjack, you will win $150 (3:2) on your main bet, minus the losing $50 insurance bet, for a net gain of $100. If the dealer does have blackjack, you will push your main bet, but get paid $100 (2:1 on insurance) on your $50 insurance bet, for a net gain of $100. So regardless of whether the dealer has blackjack, your net gain is $100. To streamline the process, we let the gambler simply say “even money” to collect that $100. [Ken Smith will point out that in a tournament where your $100 bet put you all-in, saying “even money” is effectively allowing you to buy insurance on your natural even though you have no remaining chips to buy insurance. So there is a liquidity difference between saying “even money” and insuring a natural!]

In a 6:5 game, what does insurance look like? If the dealer has no blackjack, you win $120 (6:5) on your main bet, minus the losing $50 insurance bet, for a net gain of $70. If the dealer does have blackjack, you will push your main bet, but get paid $100 on your $50 insurance bet, for a net gain of $100. (An insurance wager of 40% of your main bet would result in a zero-variance net gain of 80% of your original bet, which would be $80 in this example. So, next time you have a natural against an Ace in 6:5, you could ask the dealer for “80% money” and then when she looks at you like you’re crazy, just put out a 40% insurance wager. The confusion might hold up the game for five minutes.)

So we can see that in the 6:5 game, insuring a natural would result in a net payoff of either $70 or $100, and thus is not the same as the sure-thing net profit of $100 that would come from saying “even money”—if they allowed that latter option. In the traditional 3:2 1-deck game, taking even money has an EV of 1, which is lower than the EV of “gambling” on the natural, which is EV = (34/49)x1.5 + (15/49)x0 = 1.0408. Reducing the variance on the hand to zero via “even money” comes at a price of 4.08%, enough for the half-sharps to call even money a “sucker bet”!

In the 6:5 1-deck game, let’s consider four options:

[1] 50% insurance: EV = (34/49)x0.7 + (15/49)x1 = 0.7918

[2] 40% insurance: EV = (34/49)x0.8 + (15/49)x0.8 = 0.8 (no variance, outcome always +0.80)

[3] No insurance: EV = (34/49)x1.2 + (15/49)x0 = 0.8327

[4] “Even money” (if allowed): EV = 1

In the eyes of an idiot Table Games Manager, those EVs create a problem, because it would be correct for the player to take “even money” if it were available, raising the EV from 0.8327 to 1, when holding a natural against a dealer’s Ace up.

When asked to explain why even money isn’t offered, an “astute” boss will state the “logic” that it would be correct to take even money if offered. Yes, that’s true, but how is that a problem? It’s situational blackjack.

Changes to rules and payoffs can change the basic strategy in the game. So what? In a 6-deck shoe, you would not double down on hard 9 v. 2 up. But in a 1-deck game, that hand becomes advantageous to double down. So what? In a 6-deck shoe game, doubling 11 v Ace becomes the correct basic-strategy play once we introduce H17. Does the Table Games Manager suddenly say that players aren’t allowed to double down on 11? Or not against an Ace up? I wonder if they had a meeting where the Table Games Manager lamented that players are now going to be correctly doubling on 11 v Ace. It’s not like the good ol’ days when Benny Binion stood on soft 17 with an iron fist!

Perhaps the No-Even-Money rule is based not on stupidity, but on greed. Maybe casinos feel that offering even money would be giving up too much, but do they even know the numbers on this? Paying 6:5 instead of 3:2 gives the casino a massive boost of 1.3948% in a single-deck game. What would it cost for the casino to “give back” even money when the scenario arises? The scenario occurs with probability 2 x (4/52) x (16/51) x (3/50) = 0.0028959 (1 in 345 hands), because you would have to hold a natural against a dealer’s Ace up. When it occurs, the player would get 1 unit instead of the 0.8327 units we computed above from sitting on the natural without insuring, for an improvement of 0.167347 units. So offering even money when the player holds a natural against a dealer’s Ace up would cost the casino only 0.0485%, after they just scammed the player out of 1.3948% by short-paying 6:5 instead of the traditional 3:2.

By allowing even money, the casino would make things simpler for their own dealers, who probably switch from 6:5 to 3:2 tables during the day. Also, there would be no arguments with the players. The fact of the matter is that players feel ripped off when they can’t take even money. Incredibly, many of these players consider the scam of 6:5 the fact that even money has been taken away from them, not the massive shortening of the payoff itself. You tell them blackjack pays 6:5, and they don’t care much, because they believe that single deck is juicy for the player; but then you tell them they can’t take even money, and NOW they feel ripped off!

Tossing the players a really tiny 0.0485% bone has an additional benefit to the casino: By creating a version of blackjack where it is now correct to take even money, the casinos could spread the bogus narrative that a “smart” player takes even money. This notion would then be cemented as THE basic strategy, even in 3:2 games where taking even money costs the player 4%.