Recently I was having a conversation via email with a player about offers. The specifics of that conversation aren’t really relevant for a post here, except for a conversation about free bets vs. match plays. He asked me if match plays had a different expected value than free bets. I replied:
The expected value (EV) is nearly the same (technically a bit less due to the requirement of -EV wagers in the process of using the match play) but if you happen to trend a bit ahead of the expected outcome your ending total is amplified because you also wagered actual cash. Conversely if you trend badly you could end up behind because of the loss of actual wagers. So it is a more volatile trip for roughly the same EV.
He replied:
See I would’ve thought that it would be better, because you’re getting paid 2 to 1 on every wager that should be an even money payoff. so how is every wager not +EV?
So let’s do some basic math. Let’s assume you’re playing a game where you’ll have 100 outcomes. Let’s presume that over time, you’re expected to win 49 outcomes, and lose 51 outcomes, out of every 100. Let’s presume this works out perfectly to start the conversation.
For free bets it’s easy – you get nothing for the 51 losing outcomes, and you win 49 wagers (we’ll consider each wager 1 unit) so you win 49 units.
For match play, you also have to bet 1 unit, and this is the additional risk that reduces the EV. Each win gets you 2 units and each loss costs you one unit. So for 49 wagers you’ll win 2 units, or 98 total units. But on the other 51 wagers you lose 1 unit, or 51 total. 98-51=47 units. In that 100 outcome session, the free bets will garner you two more units than the match play.
What Match Play does and Free Bet does not is amplify the variance and volatility that comes with playing a casino game. You win more, but you can lose more, depending on how you run in a short term string where variance can come into play.
Let’s assume you won one more wager – 50 wins, 50 losses. With the free bets you’d win 50; with the match play you’d also win 50 because you’d win 100 on the 50 winning outcomes and lose 50 on the losses – 100-50=50.
In 100 outcomes you could run hot or cold – that’s just the natural underlying variance in casino games. So here’s a small chart showing various possible outcomes on 100 wagers, and how each would fare:
| Wins out of 100 | 30% | 40% | 45% | 49% | 50% | 60% | 70% |
| Free Bets | +30 | +40 | +45 | +49 | +50 | +60 | +70 |
| Match Play | -10 | +20 | +35 | +47 | +50 | +80 | +110 |
As you can see the swings on Match Play are much more volatile. I suspect casinos are much more fond of Match Play for a few reasons:
- You’ve got skin in the game. With free bets they are literally giving you free money without any sort of upside potential for them; you could theoretically walk. While you likely won’t see that offer return if you do, most casinos prefer match plays, since you have to have some money on the line, exposed to the house edge, to have a chance at converting that money.
- The swings suck players in. Humans are emotional and many get caught up in the emotions when they’re winning, and when they’re losing. Players go on tilt and think they can win back their losses; conversely others think they can keep winning if they just keep betting. Both are mindsets that work in the house’s favor, as the longer you play, the more wagers you’re exposing to the house advantage.
So technically, if you have a choice between Match Play and Free Bets, free bets have a slightly higher Expected Value, but they’re also much less volatile outcomes because you don’t have to put your own money on the line on top of it.
Of course many of us are gamblers, and the upside potential if you even get a bit ahead of the expected outcome is greater, so many like that concept of getting two chips back for each winning one.
The good news is both should generally deliver some value, although match plays can get harder to do so if you hit a tough spell. The more outcomes you can accomplish, the better the chances you can ride out a tough spell, but if you’re only going to get a handful of tries at most, Free Bets will certainly be the less risky scenario.
I’ll close by noting this is very high level, very light math. People much smarter than myself, on forums much more specialized than my site, get into the weeds with statistics and math that can calculate such things on a more precise level. But this hopefully helps, at a very basic level, explain how the two differ.
